To Whom it May Concern

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Bergstrand M, Söderlind E, Weitschies W, Karlsson MO.

Mechanistic modeling of a magnetic marker monitoring study linking gastrointestinal tablet transit, in vivo drug release. and pharmacokinetics. Clin Pharmacol Ther. 2009 Jul;86(1):77-83.

II Bergstrand M, Karlsson MO. Handling Data Below the Limit of Quantification in Mixed Effect Models. AAPS J. 2009 Jun;11(2):371-80.

III Bergstrand M, Hooker AC, Wallin JE, Karlsson MO, Prediction Corrected Visual Predictive Checks for diagnosing nonlinear mixed-effects models. AAPS J. 2011. [Epub ahead of print]

IV Bergstrand M, Söderlind E, Eriksson UG, Weitschies W, Karls-son MO. A semi-mechanistic model to link in vitro and in vivo drug release for modified release formulations. Submitted.

V Bergstrand M, Söderlind E, Eriksson UG, Weitschies W, Karls-son MO. A semi-mechanistic model for characterization of re-gional absorption properties and prospective prediction of plasma concentrations following administration of new mod-ified release formulations. Submitted.

VI Bergstrand M, Visser SA, Sjödin L, Al-Saffar A, Karlsson MO. Semi-mechanistic PK/PD modeling of Paracetamol and Sulfa-pyridine to characterize pharmacological effects on gastric emp-tying and small intestinal transit. In manuscript.

Reprints were made with permission from the respective publishers.

Contents

Introduction ................................................................................................... 11 Pharmacometrics ...................................................................................... 12 Nonlinear mixed-effects models .............................................................. 14

Model parameter estimation ................................................................ 15 Mechanistic models ............................................................................. 16 Handling of censored and missing observations .................................. 17 Model diagnostics ................................................................................ 19

Oral drug absorption ................................................................................. 22 Gastro intestinal transit ........................................................................ 24 Modified release formulations ............................................................. 25 Absorption models ............................................................................... 26 In vitro - in vivo correlation for oral dosage forms .............................. 28 In vivo methods to study GI transit and regional absorption ............... 31

Aims .............................................................................................................. 34

Material and Methods ................................................................................... 35 Software ................................................................................................... 35 Mixed-effect modeling methodology ....................................................... 36

Handling of censored observations ...................................................... 36 Simulation based diagnostics ............................................................... 37

Model development .................................................................................. 40 Drug release ......................................................................................... 40 Regional absorption ............................................................................. 43 Tablet GI transit ................................................................................... 45 Paracetamol and sulfapyridine double marker method ........................ 46

Results ........................................................................................................... 49 Mixed-effects modeling methodology ..................................................... 49

Handling of censored observations ...................................................... 49 pcVPC and pvcVPC ............................................................................ 51

Tablet GI transit ....................................................................................... 53 Oral absorption from felodipine ER formulation ..................................... 54

Drug release ......................................................................................... 54 Absorption and GI distribution ............................................................ 54

Oral absorption from AZD0837 ER formulations .................................... 55 Drug release ......................................................................................... 55

Absorption and GI distribution ............................................................ 58 In vitro to in vivo predictions ............................................................... 60

Paracetamol and sulfapyridine double marker ......................................... 61

Discussion ..................................................................................................... 65 Mixed-effect modeling methodology ....................................................... 65 Mechanistic modeling of oral absorption ................................................. 66

Conclusions ................................................................................................... 70

Populärvetenskaplig sammanfattning ........................................................... 72

Acknowledgments......................................................................................... 73

References ..................................................................................................... 76

Abbreviations

ACAT Advanced compartmental absorption and transit ADAM Advanced dissolution, absorption and metabolism AUC Area under the curve (plasma concentration vs. time) BOV Between occasion variability

(also known as inter-individual occasion IOV) BQL Below the quantification limit BSV Between subject variability

(also known as inter-individual variability IIV) CAT Compartmental absorption and transit CI Confidence interval Cmax Maximum concentration CV Coefficient of variation DR Delayed release DV Dependent variable ER Extended release FDA Food and Drug Administration (US) FO First-order method FOCE First-order conditional method GE Gastric emptying GI Gastro intestinal HPMC Hydroxypropyl methylcellulose IDV Independent variable IPRED Individual model prediction IR Immediate release i.v. Intravenous IVIVC in vitro - in vivo correlation LLOQ Lower limit of quantification LOQ Limit of quantification MAR Missing at Random MCAR Missing Completely at Random MMC Migrating Motor Complex MMM Magnetic Marker Monitoring MNAR Missing Not at Random MR Modified release MTT Mean transit time NDA Dew drug application OFV Objective function value

ΔOFV Difference in OFV; likelihood ratio PCM Paracetamol pcVPC Prediction corrected VPC PD Pharmacodynamic PI Prediction interval PK Pharmacokinetic PPC Posterior predictive check PRED Population typical model prediction PsN Perl-speaks-NONMEM pvcVPC Prediction and variability corrected VPC RSE Relative standard error RUV Residual unexplained variability SITT Small intestinal transit time SP Sulfapyridine USP United States Pharmacopeia VPC Visual Predictive Check

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Introduction

The oral route is and will for, a foreseeable future, be the by far most com-mon way of administering pharmacological substances. This is natural given the convenience that it offers and the fact that the gastro intestinal (GI) tract is a natural site for absorption. Oral administration is, however, far from uncomplicated. Absorption from the GI tract is highly variable for different compounds and formulations both with respect to rate and extent of absorp-tion. Absorption properties do not only vary between substances and formu-lations but also from subject to subject and from time to time. A contributing factor to why absorption differs between different formulations and between and within subjects is that factors involved in absorption vary along the GI tract. Examples of factors that can vary along the GI tract are pH, permeabil-ity and intestinal metabolism. These factors can be especially important for modified release (MR) formulations [1].

Several sophisticated techniques to study in vivo GI transit and regional absorption of pharmaceuticals are available and increasingly used. Examples of such methods are imaging techniques such as, gamma scintigraphy or Magnetic Marker Monitoring (MMM), and local drug administration with remote operated capsules like the Bioperm® capsule. Another approach is the paracetamol and sulfapyridine double marker method which utilizes ob-served plasma concentrations of the two substances as markers for GI transit. Common for all of these methods is that they generate multiple types of ob-servations e.g. tablet GI position, drug release and plasma concentrations of one or more substances. This thesis is based on the hypothesis that applica-tion of mechanistic computer models could facilitate a better understanding of the interrelationship between such variables.

Pharmacometrics is a young scientific discipline focusing on developing and applying mathematical and statistical computer models to characterize, understand and predict a drug’s pharmacokinetics (PK) and pharmacody-namics (PD). The analysis of data from absorption studies has emphasized the need for methodological development which is also of general interest to pharmacometric research. One general problem in model based evaluation of PK and PD is censoring of data. Non random censoring, such as observa-tions below the quantification limit (BQL), can bias estimation of model parameters and can also hamper the assessment of a model’s predictive per-formance. This issue and a more general issue of diagnosing model perfor-mance have been addressed as part of the thesis.

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Pharmacometrics In the book Pharmacometrics: The Science of Quantitative Pharmacology, edited by Ene I. Ette and Paul J. Williams, pharmacometrics is defined as “the science of developing and applying mathematical and statistical models to characterize, understand and predict a drug’s pharmacokinetics, pharma-codynamics and biomarker-outcome behavior” [2]. Pharmacometrics origi-nates from the field of pharmacokinetic research. PK is often referred to as “what the body does to the drug” in contrast to PD that is “what the drug does to the body” [3]. Methods to characterize the link between drug expo-sure that is governed by PK and pharmacological response (PD) were an essential key to the emergence of the new scientific discipline. In order to accurately understand and characterize PK and PD relationships over time it can be vital to first describe the baseline response in a healthy or diseased biological system. For this reason also modeling of disease progression (DP) and normal physiological functions like the nature of gastro intestinal transit can be important parts of pharmacometric research. Pharmacometrics hence includes a large variety of applications and is foremost defined by a common goal of facilitating more efficient development and usage of pharmaceuticals by application of mathematical and statistical models. Most pharmacometric research is based on mixed-effects models, which are especially useful in application to heterogeneous biological data by its ability to characterize many sources and levels of variability.

A pharmacometric approach to analyzing data from clinical trials of new investigational drugs has become increasingly more common over the last 10 years. It has been shown to influence the approval of new drug applications (NDAs) to FDA (Food and Drug Administration, US) in more than 70% of the cases when it has been applied and to almost always affect a final labe-ling [4]. FDA and other important stakeholders have highlighted the poten-tial of pharmacometric model-based drug development to help turn around the negative trend of less successful NDAs despite increasing investments in pharmacological research [5-7]. The obstacles for a broader application of pharmacometric principles to drug development are currently under discus-sion and it is likely that we are at the start of a paradigm shift from tradition-al biostatistical to pharmacometric model based evaluation as a standard [4, 8, 9]. Five key benefits with a model based approach is (1) better opportuni-ties to utilize longitudinal data over time and multiple response variables in making statistical inference [10, 11] (2) increased possibility to incorporate prior knowledge and pool data across studies [12, 13] (3) possibility to inter-polate between investigated doses, dosage regiments etc., and potentially extrapolate to longer treatment times and/or other target populations [14, 15] (4) facilitation of improved study design by optimal design theory and clini-cal trial simulations [16, 17] and (5) a framework for developing individua-

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lized treatments [18, 19]. How these advantages fit in the circular process of scientific learning is illustrated in Figure 1.

Figure 1. Pharmacometric model based scientific learning. Learning in science is a circular process: A study/experiment is initialized to address one or several missing pieces of information. The design of the study is based on previous knowledge and the observations made according to that design constitute the study data. Interpretation of study data by statistical summarization and comparison generate new information out of the raw data. By integrating different sources of information from the study with previous information new knowledge is generated. Based on the extended knowledge new studies can be designed to address other pieces of missing information. Advantages with a model based approach to scientific learning are pointed out with “+” in the figure.

The circular knowledge generation and propagation presented in Figure 1 fits well with the learn and confirm paradigm for drug development that was introduced by Lewis Shiner in 1997 [20]. A first cycle can represent a learn-ing phase (hypothesis generating) and a second consecutive cycle the con-firming step.

Information Knowledge

StudyDataExecution

Interpretation

Integration

Study design+ Identify what to study+ Design optimization + Trial simulation

+ Facilitate integration of different sources of information+ Inter-/extrapolation

+ Facilitate mechanistic interpretation+ Higher power for statistical inference

Model

+ Individualized dosing+ Adaptive design

Observation

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Nonlinear mixed-effects models Mathematical models are based on a set of mathematical equations aimed at describing a system of interest. These models can then be used to explore the structure and behavior of the system. One or more dependent variables (DVs) are described as a function of one or more independent variables (IDVs) and a set of model parameters. Most biological processes are best described with models featuring nonlinear functions. Models featuring such functions are referred to as nonlinear models and are commonly used in pharmacometric research.

Mixed-effects models are models featuring a mixture of fixed and random effects. The fixed effects build up the structural model that describes the population typical response (e.g. a typical plasma concentration vs. time curve). The fixed effects therefore describe the variability in the DVs that can be explained by the available information about the IDVs. The remain-ing unexplained variability is described by random effects, which are divided into several different levels; between subject variability (BSV) with regards to model parameters, residual unexplained variability (RUV) i.e. the residual difference between the model prediction and the observations. There is also within subject variability with respect to model parameters, which often is characterized in the form of between occasion variability (BOV). The ran-dom effects are typically estimated in the form of variances around the popu-lation typical parameter (fixed effect) assuming a normal distribution or some transformation of a normal distribution (e.g. log-normal or logit-transform).

The general structure of a mixed-effects model is expressed as follows: , , ~ 0, (1)

where yijk is the jth observed dependent variable at occasion k in individual i. yijk is described by a function of a vector of individual parameters Pik and a vector of independent variables Xijk. Typical influential independent va-riables in most pharmacometric models are dose and time but the vector Xijk can contain also many other important predictors often referred to as cova-riates. A relatively unusual covariate that is explored within this thesis is tablet gastrointestinal position. The εijk describes the difference between the individual prediction and the observation and is referred to as RUV or resi-dual error. In equation 1 the RUV is expressed as a simple additive term, normally distributed with a mean 0 and variance σ2. However, residual error models can take many different shapes although the most common once are additive, proportional or a combination of the two.

Assuming a log-normal distribution the individual parameter Pik for the ith individual at the kth occasion can be described by the following expression: · , ~ 0, and ~ 0, (2)

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In which θ is the typical value (fixed effect) of the parameter P in the studied population, and ηi anb κi are the random effects that describe the differences between the typical value and the individual parameter with respect to the individual and the occasion, respectively. The exponential implementation of the normally distributed random effects results in a log-normal distribution for the individual parameters Pik. Other parameterizations of the random effects can be used to apply other shapes of distributions [21].

A key advantage with mixed-effects models is that they can be applied to sparse data and/or combinations of sparse and rich data and still characterize several levels of variability [22, 23]. This is a distinct advantage of the mixed-effects modeling approach over other methods such as naïve pooling and standard two-stage approaches. For this reason nonlinear mixed-effects modeling has become the predominant method of choice for population PKPD modeling.

Equation 1 describes the general structure of mixed-effects models ap-plied to continuous data, however mixed-effects models can also be applied to categorical observations or a combination of continuous and categorical observations. An example of combined continuous and categorical observa-tions that is dealt with throughout this thesis (primarily Paper II) is a dataset with plasma concentrations (continuous) and certain observations reported to be below the quantification limit (BQL, i.e. categorical).

Model parameter estimation The nonlinear mixed-effects modeling software NONMEM (Icon develop-ment Solutions, Ellicot City, MD, USA) [24] was used in all projects in-cluded in this thesis. NONMEM has been an important tool in the develop-ment of pharmacometrics as a scientific discipline and remains the most widely used software in pharmacometric research. Parameter estimation in NONMEM is based on maximum likelihood. The model parameters are estimated by maximizing the likelihood of the data given the model. This is performed by minimization of the extended least squared objective function. The objective function value (OFV) is approximately proportional to -2 times the logarithm of the likelihood of the data. The difference in the OFV (ΔOFV) between two nested models is approximately χ2-distributed under the assumption that the model is correct and that the errors are normally distributed. The likelihood ratio test can be used to compare nested models (e.g. the inclusion of a covariate effect) where a difference in OFV of 3.84 corresponds to a significance level of p<0.05. The nominal significance level can however be compromised by the approximations within the applied es-timation method and the number of observations [25-27].

Due to the nonlinearity of the model with respect to the random effects the likelihood function can generally not be calculated exactly. An approxi-mation of the likelihood function is therefore obtained by different types of

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linearization. Traditional linearization options available in NONMEM are the first-order method (FO), the first-order conditional estimation method (FOCE) and the Laplacian second-order approximation method. More re-cently a wider range of estimation methods has become available in NON-MEM, however they have not been applied in the projects described in this thesis. These includes maximum likelihood methods that do not rely on li-nearization such as the stochastic approximation expectation maximization method (SAEM) [28, 29] and a full Bayesian estimation method [30].

Mechanistic models Mechanistic models or “mechanism-based models” attempt to represent phy-siological and pharmacological processes as accurately as possible [31-33]. One purpose of mechanistic models is to better understand the structure of a physiological system and the interplay between biological processes. The mechanistic models are never completely mechanistic but contain different elements of empirical simplifications, and therefore sometimes identified as semi-mechanistic or semi-physiological models [34, 35].

Mechanistic models typically contain a high level of complexity and it is often not possible to estimate all parameters based on observations of one dependent variable from a single experiment. Instead, information about sub-structures and parameter values are obtained from several independent expe-riments or from the literature [32, 36]. Mechanism-based models may allow for hypothesis testing of suggested mechanisms and for learning about sys-tem processes which are not easy to test experimentally. Furthermore, they typically allow for more credible interpolation between, and extrapolation outside, of situations which were the basis for the model [33, 37]. As extra-polations depend on assumptions incorporated into the model, the validity of the assumptions needs to be scrutinized carefully. Sensitivity analysis should be made with regards to less obvious assumptions and limitations to the pre-dictions must always be considered.

Just as there is a gradual scale between completely empirical to highly mechanistic models, there can also be said to be a gradual scale between a ‘bottom-up’ and a ‘top-down’ approach [38, 39]. With a pure ‘top-down’ approach the model is only informed by (trained on) the type of data that it aims to predict, e.g. for PK models typically plasma concentrations. A pure ‘bottom-up’ approach instead takes its basis in information about the system (i.e. human body) and the drug separately. The information about the drug is primarily based on in vitro experiments and physicochemical characteristics. More and more however, a combination of a ‘bottom-up’ and ‘top-down’ approach is used. The development towards such a combined approach comes from two directions. Research groups and software packages that traditionally applied a pure ‘bottom-up’ approach are implementing solu-tions to let their models be informed also by clinical data (e.g. Simcyp Ltd,

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Sheffield, UK, http:www.simcyp.com) [40, 41]. Whereas research groups that previously applied mostly quite empirical models and primarily used a ‘top-down’ approach today apply more and more mechanistic models and hence also include more and more ‘bottom-up’ information [42-44]. This development is made possible by increased availability of computer power and more efficient algorithms for parameter estimation as well as increased awareness of a systems pharmacology approach [45, 46]. Regarding oral absorption the full range of empirical to highly mechanistic models and ‘top-down’ to ‘bottom-up’ approaches are available, which is dwelt upon in a specific section (Oral Drug Absorption, Absorption models).

Handling of censored and missing observations Censored observations are characterized by the fact the value of the observa-tion is partially missing. This differentiates censored observations from ‘missing observations’, where the value is completely missing. A model based approach is typically less sensitive to censored and missing observa-tions than traditional descriptive statistics and statistical tests [47]. However, censored and missing observations can still be a complicating factor in the analysis of repeated-measures longitudinal study that is typically the case in pharmacometric research. Both in the case of censored and missing observa-tions it is important to understand the mechanism of the missing information. A specific terminology has been adopted to characterize censored and miss-ing data. Censored observations are characterized as left censored, interval censored or right censored (with regards to time-to-event analysis there is further classifications of censoring but that is not relevant for this thesis). Processes generating the missing data are typically classified into 3 catego-ries: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) [48].

A left censored observation is known to be below a certain value but it is unknown by how much. This could for instance be the bioanalytical estimate of a plasma concentration reported to be below the limit of quantification (LOQ). However if logical reasoning allows us to assume that the plasma concentration could not be below 0 we instead have an interval censored observation that has both a lower and upper boundary. Following the same logic a right censored observation is an observation that is larger than a cer-tain known limit. Interval censored observations between 0 and a specific LOQ are the most frequently occurring censoring in the pharmacometric setting. This situation can be transformed into the situation of left censoring by log-transforming the dependent variable before applying the model. Since the natural log of a value that goes towards 0 goes towards minus infinity. Traditional approaches for handling concentration measurements reported as being below the quantification limit (BQL), such as omitting the information or substitution with the LOQ divided by two, have been shown to introduce

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bias in parameter estimates [49, 50]. More informative methods to include the information about censored observations in a maximum likelihood framework were outlined already in 1957 [51]. In 2001, Stuart Beal pub-lished an overview of how this could be applied to a nonlinear mixed-effects model [52] and compared it to the traditional substitution and censoring ap-proaches. The method referred to as M2 in the publication applies condition-al likelihood estimation to the observations above LOQ and the likelihood for the data being above LOQ are maximized with respect to the model pa-rameters. This approach can be implemented in NONMEM by utilization of the YLO functionality [24]. The methods M3 and M4 also suggested by Beal are based on simultaneous modeling of continuous and categorical data where the BQL observations are treated as categorical data. The likelihood for the BQL observations are maximized with respect to the model parame-ters and the likelihood for an observation was taken to be the likelihood that it was indeed below LOQ. The M3 and the M4 methods differ in that the M3 method assumes left censored observations and the M4 method assumes interval censored observations between 0 and LOQ. The likelihood expres-sions for observations above and below LOQ based as implemented with the M2 respectively the M3 method is presented together with a principal illu-stration in Figure 2. A comparison of the different methods to handle BQL observations occurring in three distinctly different patterns and application of an approach to deal with censored observations in simulation based model diagnostics is presented in Paper II.

Figure 2. Likelihood for observations above and below LOQ depending on observed dependent variable y(t), model prediction f(t), residual error variance g(t) and LOQ. Method M3 maximizes the likelihood for BQL observations being indeed BQL (3) simultaneous to maximizing the likelihood for observations above LOQ (2). M2 maximizes the likelihood for observations above BQL conditioned on that they are part of a truncated distribution.

Dep

ende

nt V

aria

ble

Time

M2 for observa�on > LOQ

LOQ

M3 for observa�on > LOQ21 1 ( ( ) ( ))(2) ( ) exp(

2 ( )2 ( )y t f tl tg tg tπ

⎛ ⎞−= − ⎜ ⎟

⎝ ⎠

( ( ))(3) ( )( )

LOQ f tl tg t

⎛ ⎞−= Φ⎜ ⎟

⎝ ⎠

M3 for obs < LOQ

21 1 ( ( ) ( )) ( ( ))(1) ( ) exp( / 12 ( )2 ( ) ( )

y t f t LOQ f tl tg tg t g tπ

⎛ ⎞⎛ ⎞ ⎛ ⎞⎛ ⎞− −= − −Φ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠⎝ ⎠

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Data are missing completely at random if the reason for the missingness is unrelated to the observed and missing response values. An example of this is if samples from a clinical study accidentally are lost, or study drop-out that is unrelated to the investigated dependent variable. This kind of mis-singness does of course, like all missingness and censoring, reduce the over-all information content of the collected data but does not call for any specific measures to avoid biased parameter estimation and assure accurate model diagnostics. Data are MAR if the missingness depends on the response val-ues only through observed components of the response. An example of when MAR can occur in a clinical study is if subjects are automatically taken out of the study if the response variable of interest reaches a certain level. Ob-servations at the following visits are then MAR. This kind of pattern of miss-ing information typically does not bias parameter estimates, given that you are applying a mixed-effects modeling approach, but is important to consider for model diagnostics and clinical trial simulation. Data are MNAR if the missingness depends on both the observed and missing data; that is, the probability that an observation is missing depends on the value of the miss-ing observation itself. Observations MNAR could occur if for example sub-jects are less likely to show up at study visits in the case of poor clinical performance. Observations that are MNAR generally cause more problems and do require careful attention. The MNAR pattern of missingness can se-verely bias parameter estimates and statistical inference between for instance different treatment groups. The way to at least reduce the bias that this pat-tern imposes is to perform joint modeling of the probability of the observa-tion being missing (e.g. subject dropped-out of the study) and the response variable of interest [47, 48, 53].

Model diagnostics The model building process is often difficult and involves testing, evaluat-ing, and diagnosing a range of plausible models with a major aim to make an adequate inference from the observed data. Establishment and verification of an appropriate model is crucial in order to put confidence in the inferences made based on the model. Graphical diagnostics are extensively used during the model building process and are considered an essential tool for data vi-sualization, inspection of model adequacy, and assumption testing [54, 55]. Graphical diagnostics are considered powerful and are often more or less intuitive to interpret. There is a large range of available graphical approaches to evaluate different aspects of model adequateness. Model diagnostics sel-dom provide a modeler with definitive answers. Thus it is important that a pharmacometrician can interpret the information obtained correctly. To do so the pharmacometrician needs to be aware of each diagnostic’s assump-tions, strengths and weaknesses [56].

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Plots of population typical model predictions (PRED) and individual model predictions (IPRED) versus observations are routinely used as a diag-nostic throughout the model building when dealing with continuous observa-tions. Intuitively an interpreter of these plots looks for how well the observa-tions are centered along the line of identity. The assumption that plots of PRED versus observations should fall uniformly distributed around the line of identity is however flawed. Only the fact that the unexplained parameter variability enter nonlinearly into the model will produce individual predic-tions that are expected to have a mean different from the typical individual prediction (see Equation 2). In addition, factors like censoring and adaptive designs (e.g. therapeutic dose adjustments) can cause an even more skewed distribution [56]. The solution to this problem lies either in relying more heavily on other types of diagnostics or to create reference plots (mirror plots) based on simulations with the model to be diagnosed. If the pattern in the mirror plot for the observed data and the simulated data are similar, no model misspecification is evident from this diagnostic. For plots of IPRED versus observations on the other hand, a seemingly perfect alignment along the line of unity is not necessarily a strong support for model appropriate-ness. A so called “perfect fit phenomenon” occurs especially in the case of studies with sparse sampling. ε-shrinkage is a measure of the over fit that causes the perfect fit phenomenon and should generally be assessed to in-form about the level of appropriateness for diagnostics based on IPRED. An ε-shrinkage greater than 20% has been described to render IPRED versus observations plots essentially uninformative [56, 57].

Residual based diagnostics are commonly used and have the advantage of being useful in diagnosing several aspects of a models performance. Resi-duals can be plotted versus time or some other independent variable to iden-tify possible model misspecifications with regards to the relationship to in-dependent variables. The general interpretation of residual plots is that they should, in the case of adequate model fit, be normally distributed with a mean of 0 across any independent variable. However, the same limitations that have been discussed for PRED and IPRED vs. observations plots do of course apply also to residual based diagnostics that take their basis in the very same quantities (e.g. RES = Observations – PRED, IWRES = (Observa-tions – IPRED)/σ) [56]. Especially IWRES can still be very informative given that these limitations are considered (i.e. ε-shrinkage is verified to be low). Weighted residuals such as WRES and CWRES do not suffer from the same shortcomings as RES and IWRES. However, WRES are weighted based on the FO approximation and hence suffer from the same draw backs that are associated with the crude first-order linearization. It has been dem-onstrated that conditional weighted residuals (CWRES), which are instead based on the FOCE linearization, have better properties [58]. Also CWRES plots have been demonstrated to falsely indicate model misspecifications, in the case of highly non-linear models [56, 59]. Another “residual like” type of

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diagnostic that has been demonstrated to have good, even though not ideal properties, is the Normalized Prediction Distribution Errors (NPDE) [59-62]. The NPDEs are not true residuals but based on the rank order of the observa-tions in relation to multiple model simulations of the original dataset. The interpretation and use of NPDE plots are however very similar to traditional residual plots. Global Uniform Distance (GUD) is a recently suggested diag-nostic tool described to have ideal statistical properties [59]. Further testing is however needed to verify this claim and demonstrate the practical useful-ness.

Simulations based on the model and the underlying design of the ob-served data is increasingly used for model evaluation. The NPDE plots are a special case of a type of diagnostic tools called predictive checks [63]. With this approach multiple simulated replicates of the original dataset are used to create a reference distribution that can be compared to the observations. Some predictive checks focus on secondary statistics (e.g., area under the curve, time above a minimum inhibitory concentration, or the number of responders) that can be derived from both the raw data and the simulated data. This type of diagnostic is useful if such statistics can be accurately calculated and if they pinpoint the primary purpose of the model. Posterior predictive check (PPC) is a predictive check that is based on simulations from the posterior distribution (uncertainty distribution) of the model para-meters rather than only the point estimates [64]. This approach appears to be especially geared towards external validation. The most common form of predictive check is the so called visual predictive check (VPC) [65]. The principle of the VPC is to graphically assess whether simulations from a model of interest are able to reproduce both the central trend (median) and variability in the observed data, when plotted versus an independent variable (typically time). The variably component is typically assessed by comparing observations to simulations for a particular prediction interval (inter-percentile range). The widespread use of VPCs can be attributed to two main advantages of the approach; (1) the principle behind the diagnostic is simple and easily communicated to both modelers and other modeling stakeholders and (2) by the retention of the original y-axis scale the nature and clinical importance of an indicated model misspecification can be easily appreciated. This makes the VPC powerful both as a tool for communication and for guiding model development. As a part of this thesis it is demonstrated how the VPC can be adapted to censored observations and categorical data in general. Ideally a VPC will diagnose both the fixed and random effects of a mixed-effects model. In many cases this can be done by comparing different percentiles of the observed data to percentiles of simulated data. It has been described though that whenever the predictions within a bin differ largely due to different values of other independent variables (e.g. dose, covariates) the diagnosis may be hampered or misleading [66]. Furthermore VPCs have been described to be non-applicable to data following adaptive dosing (e.g.

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therapeutic drug monitoring (TDM)) due to the inherent correlation between the realized design and individual parameters within such studies [56, 67]. As a reaction to these shortcomings of the VPC the principle of prediction corrected VPC (pcVPC) and prediction and variability corrected VPC (pvcVPC) were outlined and tested in Paper III of this thesis. The pcVPC and pvcVPC plots were further applied in Paper IV, V and VI.

Oral drug absorption Absorption of drugs from the GI tract is complex and often not well unders-tood [68]. The absorption process is influenced by a large number of factors that not only vary between drugs but also between different GI regions [69]. For many of the involved physiological factors there is also a substantial amount of between and within subject variability. The primary physico-chemical factors affecting absorption proprieties of a drug are: pKa, solubili-ty, stability, diffusivity, lipophilicity, and salt form. Physiological factors that influence the rate and extent with which orally administered drugs reach the systemic circulation include: pH, ionic strength, influx and efflux trans-porters and gut wall metabolism. All these factors more or less differ along the GI tract. For this reason the GI motility in the form of gastric emptying, small intestinal transit time etc are also very important. One important factor that limits the extent of oral absorption that does not depend on the absorp-tion site along the GI tract is the first pass extraction in the liver. Indepen-dent of the absorption site in the GI tract the substance passes via the portal vein through the liver once before reaching the systemic circulation. There are important interactions between the physiochemical properties of the ac-tive ingredient and the physiological factors such as the fact that solubility often is pH dependent. In the same way there are interactions between for-mulation characterizing factors and physiological factors. Paper I and Pa-per IV of this thesis investigate how drug release from different extended release (ER) formulations varies along the GI tract as a consequence of dif-ferences in physiological factors.

Figure 3 features a schematic representation of important processes in-volved in oral absorption along the GI tract. The structure of that picture is also the mechanistic basis for the models applied in Paper I and Paper V. The picture illustrates how a single piece solid dosage form transits between the different GI regions with discrete movements (e.g. it is only in one place at one time). The movements between the different GI regions can be de-scribed by movement probabilities (MP1-4). The picture have been simpli-fied by assuming small intestine and colon as single characteristic positions but this could typically be divided into several regions.

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Figure 3. Principal figure of processes involved in oral absorption from solid dosage forms. The picture have been simplified by assuming small intestine and colon as single characteristic positions but this could typically divided into several regions.

Figure 4. Summary of some primary determinants for the processes involved in oral absorption from solid dosage forms and available measurements of amount of drug substance throughout the cascade.

Due to differences in physiological conditions in the different GI regions (pH, mechanic stress etc.) the rate of drug release (R1-4) can differ between the GI regions. Released drug substance need to go into solution to be able to be absorbed through the gut wall. The rate of dissolution (S1-4) and precipi-tation (P1-4) can differ along the GI tract for the similar reasons that drug

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release can e.g. pH, intestinal water content, ionic strength. The rate in which dissolved drug is absorbed from the gut lumen is dependent on passive diffu-sion as well as influx and efflux transporters (KA/Kef). Efflux transporters are potentially also of importance for gut wall metabolism since efflux transpor-ters can increase the exposure to metabolizing enzymes in the gut wall [70, 71]. This is best described for efflux protein P-glycoprotein and CYP3A4 that share substrate specificity and act synergistically in preventing drug from passing through the gut wall [72]. Expression of CYP3A4 and other drug metabolizing enzymes in the enterocytes (cells in the gut wall) has been described to differ between the different segments of the GI tract [73, 74]. Solubility, active membrane transport and metabolism in the gut wall and liver are all processes that can be subject to saturation. Such non-linear processes in combination with large within and between subject variability, in many of the involved processes, have often made it difficult to accurately predict oral absorption based on preclinical data and mechanistic models but also difficult to characterize the absorption based on clinical observations [75, 76].

Gastro intestinal transit As described above the gastro intestinal transit of both solid dosage forms and liquid forms (in solution or suspension) can be of great importance for the absorption of drugs. The gastro intestinal transit is governed largely by GI motility. Studies of GI motility are also important from a pathophysiolog-ical perspective since it is associated with abnormal syndromes like gastro-paresis, constipation and diarrhea [77, 78].

Under fasting conditions the gastro intestinal transit throughout the upper gastro intestinal tract (stomach and small intestine) are primarily governed by the Migrating Motor Complex (MMC). The MMC is a distinct cyclic pattern of electromechanical activity in the mouth muscle that triggers peris-taltic waves that originate from the stomach and propagates through the small intestine. The MMC cycle consists of 4 distinct phases that recurs every 1.5 to 2 hours in the fasting state [79, 80]. Postprandially, MMCs dis-appear to be replaced by a digestive motor activity characterized by regular mixing and propelling movements that optimize nutrient absorption [81].

The GI motility is important in governing the transit of solid oral dosage forms. Larger solid objects such as capsules or single unit tablets have been demonstrated to have significantly different GI transit patterns compared to solutions or small solid units like pellets, especially with respect to gastric emptying and colon transit time [82-84]. With regards to gastric emptying the size effect is most obvious when the dose is administered together with food. In that case smaller units and dissolved drug is emptied significantly faster than larger units. This is in line with the stomachs functionality of grinding the solids down to a manageable size before emptying into the duo-

25

denum. For heavy meals in combination with large non-disintegrating cap-sules gastric emptying have been reported as late as 10 h post dosing [84]. When administered in the fasting state gastric emptying is generally fast and any reasonably sized particles are typically emptied within a few minutes [85].

Small intestinal transit is less dependent on the size of the formulation and concomitant food intake. If anything, solid particles appear to transit slightly faster than liquid content [84]. GI fluid is not continuously available throughout the GI tract but is found in clusters. GI transit for a solid dosage form is a heterogonous process, sometimes moving quickly, sometimes slowly, sometimes passing through fluid of varying composition, and being subject to varying peristaltic pressure. A typical small intestinal transit time in healthy subjects is reported to be between 2 and 4 h for solid dosage forms. However, there is a considerable between and within subject variabil-ity, with reports of between 0.5 and 9.5 h. It should be recognized that a considerable part of the small intestinal residence time is spent in rest and not in continuous movement [86].

Before entering the colon solid dosage forms typically stagnate in cecum for a variable period of time. Food intake stimulates emptying of cecum into the colon, a mechanism that is known as the gastro-ileocecal reflex [87, 88]. Further transit of dosage forms through the colon is highly variable and ap-pears to occur during periods of relatively fast movement followed by long periods of rest. The movement periods are stimulated by food intake but can also occur without food stimulation [86]. Small solid pellet particles have been reported to have a slower movement through the colon compared to larger single-unit formulations. For the single-unit formulation the mean (SD) total colon transit time was 15.2 (8.7) h whereas it was 28.4 (14.5) h for the multi-unit formulation [82].

The between and within subject variability is large with respect to GI transit in general, even for a homogenous healthy populations studied under highly controlled conditions. Taking into account the fact that disease and pharmacological treatments can alter the GI transit [83] and the fact that feeding habits generally vary more in natural life the true expected popula-tion variability is likely to be substantially larger.

Modified release formulations There is a large variety of available oral formulations, oral solutions and suspensions that are utilized to a certain degree but solid dosage forms (i.e. tablets and capsules) are far more frequently used. The solid formulations are primarily divided into immediate release (IR) and modified release (MR) formulations. The MR formulations are further divided into extended release (ER) and delayed release (DR) formulations. Other notations such as “con-trolled release” (synonymous with MR), “prolonged release” and “sustained

26

release” (synonymous with ER) have historically been used but these are now gradually disappearing since the IR/MR/ER/DR terminology has been endorsed by FDA and International Conference of Harmonization (ICH) [89-91].

Oral MR formulations are designed with the aim of achieving specific pharmacokinetic profiles, delivering to specific gut localities or reducing the number of drug administrations. MR dosage forms can be formulated either as single-unit or as multiple-units, the latter where the formulation consists of many, often small-sized, units (pellets, beads or granules) which are either filled in a capsule, a sachet or are compressed as tablets which disintegrate to release the individual units [92]. There is a range of different mechanisms that have been used to modify the release for both single and multiple unit formulations. Most mechanisms are aimed at achieving an ER that will sup-port once daily dosing and which result in minimal fluctuations in plasma concentrations [92].

Hydroxypropyl methylcellulose (HPMC), a semi-synthetic cellulose de-rivative, is widely used as a matrix former in single-unit ER formulations [93] and of particular interest to this thesis. The fact that HPMC is “general-ly recognized as safe” (GRAS) by the FDA and also safe from an environ-mental perspective is one of the reasons for its popularity. Furthermore, it is compatible with numerous drugs and can accommodate high levels of drug loading [94]. In contact with water, HPMC swells to form a gel, which serves as a barrier to drug diffusion. Drug release from the HPMC-drug ma-trix involves solvent penetration into the dry matrix, gelatinisation of the polymer, dissolution of the drug and diffusion of the solubilised drug through the gel layer. Concomitantly, the outer layers of the tablet become fully hydrated and dissolve, a process generally referred to as erosion. Fac-tors such as the HPMC concentration in the tablet, the viscosity grades of HPMC and the solubility of the active ingredient is important factors mod-ifying the drug release rate from HPMC matrix tablets. The release mechan-ism from HPMC matrix tablets can either be controlled by diffusion, diffu-sion and erosion or only erosion depending on the choice of viscosity grade and/or addition of additional polymers [95].

A wide range of mathematical models have been applied to describe drug release from HPMC-based pharmaceutical devices [96]. These range from empirical models to characterize in vitro drug release profiles [97, 98] to highly mechanistic models to prospectively predict diffusion, swelling and dissolution (erosion) properties [99].

Absorption models Models to describe oral absorption exist in many shapes and forms. They range from simplistic and highly empirical models to more complicated and mechanistic models. Typically PK analysis based on sampled plasma con-

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centration has used first or zero-order rate constants with or without lag-time to describe oral absorption [100]. In some cases combinations of two or more first or zero-order process have been applied, either in parallel [101] or sequentially in time [102, 103]. There are also examples of models with mixed zero-order and first-order absorption [104, 105]. These models can be defined as primarily empirical even if a mechanistic interpretation can some-times be made. A range of more complex but still primarily empirical ab-sorption models have also been described and applied to so called ‘atypical absorption profiles’ [100]. Examples of such models are; the Weibull func-tion [106, 107], the inverse Gaussian density input function [108, 109], tran-sit compartment models [110, 111] and other kinds of time dependent func-tions with or without nonlinear elements [112, 113]. These models are gen-erally more flexible in nature and hence often result in a closer fit to ob-served plasma concentrations. This group of absorption models is sometimes referred to as semi-mechanistic since they are thought to more closely re-semble GI distribution etc. However the simulation properties and extrapola-tion possibilities with these models has generally not been sufficiently ex-plored.

More mechanistic models for oral absorption have existed in parallel with the more empirical one for many years but in contrast have primarily been used for ‘bottom up’ prediction purposes [114, 115]. The basis for these models are physiological information regarding factors such as pH, tissue surface area along the GI tract and available physicochemical information (e.g. permeability, solubility) regarding the substance based either on chemi-cal structure input and/or in vitro experiments.

Most mechanistic absorption models are based on a compartmental struc-ture describing the distribution of drug substance throughout the GI tract. A distinction is typically made between; stomach, duodenum, upper and lower jejunum, one or several ileum compartments (including cecum) and a colon compartment. Early mechanistic models such as the compartmental absorp-tion and transit (CAT) model [68] and the Grass model [116] initially only described the GI distribution of disintegrated drug substance (i.e. in liquid form), dissolution and passive absorption (diffusion). The CAT model was later further developed to also include elements of active transport through the gut wall, intestinal degradation and a simplistic handling of drug release from modified release formulations [117, 118]. The advanced compartmen-tal absorption and transit (ACAT) model was based on the CAT model but included several significant improvements [119]. The model distinguished between six states of drug component; unreleased, undissolved, dissolved, degraded, metabolized, and absorbed substance (similar to Figure 3). First pass metabolism in both gut wall (enterocytes) and the liver are incorporated in the ACAT model.

The ACAT model is the basis for the commercially available software GastroPlusTM (Simulations Plus, Inc. Lancaster, CA, USA,

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http://www.simulations-plus.com) and within that framework the ACAT model has been gradually upgraded to improve the predictions. The compet-ing software solution Simcyp® (Simcyp Ltd, Sheffield, UK, http://www.simcyp.com) was initially a software primarily designed for the predictions of metabolism but has grown to be a widely applicable database and physiology based simulator of pharmacokinetics, including absorption. Since the release of Simcyp® version 7 it has also included an advanced dis-solution, absorption and metabolism (ADAM) model [120]. The ADAM model is structurally very similar to the ACAT model but does, for instance, include a more sophisticated dissolution model [121]. In contrast to GastroP-lusTM the Simcyp® solution has naturally incorporated courses of between subject variability to facilitate predictions of population variability in differ-ent demographic groups. PK-Sim® (Bayer Technology Services www.pk-sim.com) is a third software solution for predictions of oral absorption [122]. In PK-Sim® the GI tract is described with a dispersion model [123] that can be seen as a continuous tube with spatially varying properties (pH, surface area etc.) rather than a series of transit compartments.

In vitro - in vivo correlation for oral dosage forms An in vitro - in vivo correlation (IVIVC) has been defined by the FDA as “a predictive mathematical model describing the relationship between an in vitro property of a dosage form and an in vivo response” [124]. Generally, the in vitro property is the rate or extent of drug dissolution or release while the in vivo response is the plasma drug concentration or amount of drug ab-sorbed. IVIVC plays an important role in product development in that it: (1) can serve as a surrogate for in vivo studies, (2) supports and/or validates the use of dissolution methods and specifications, (3) defines the quality control requirements and (4) guides the selection of appropriate formulations [125].

The Biopharmaceutics Classification System (BCS) suggested by L.A. Amidon, H. Lennernäs et. al. [126] has been used to predict whether in vitro in vivo correlation (IVIVC) can be expected based solely on in vitro dissolu-tion experiments for IR formulations. The BCS classifies drugs into 4 classes based on estimates of solubility and permeability (Table 1).

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Table 1. Biopharmaceutics Classification System (BCS) and associated expectation of IVIVC for IR formulations

Class Solubility Permeability IVIVC based on dissolution rate

I High High IVIVC expected if dissolution rate is slower than gas-tric emptying rate, otherwise limited* or no correlation.

II Low High IVIVC expected if in vitro dissolution rate is similar to in vivo dissolution rate, unless dose is very high.

III High Low Absorption (permeability) is rate determining and limited or no IVIVC expected.

IV Low Low Limited or no IVIVC expected. * A limited correlation means that the dissolution rate while not rate controlling may be similar to the absorption rate and the extent of correlation will depend on the relative rates.

The FDA has adopted the BCS as an approach to grant waiver of in vivo bioavailability and bioequivalence testing (biowaiver) of IR solid dosage forms for Class I high solubility, high permeability drugs when such drug products also exhibit rapid dissolution [127]. A drug substance is considered ‘highly soluble’ when the highest dose strength is soluble in 250 ml or less of aqueous media over a pH range of 1–7.5 at 37○C. A drug substance is considered to be ‘highly permeable’ when the extent of absorption (parent drug + metabolites) in humans is determined to be ≥90% of an administered dose, based on a mass balance determination or in comparison to an intra-venous reference dose. This can be established in clinical studies or by stu-dies of intestinal permeability in in vitro/in situ permeability studies. The BCS approach to grant biowaivers has received criticism for using extent of absorption (a thermodynamic measure) and intestinal permeability (a kinetic measure) interchangeably [128, 129].

Table 2. FDA categories of IVIVCs for ER formulations

Level Description

A A functional relationship between in vitro dissolution and the in vivo input rate, correlation of profiles, linear or non-linear relationship

B A correlation based on statistical moment analysis (in vitro dissolution time is correlated with mean residence time)

C A single point relationship between one dissolution parameter, (e.g. T50%, % dis-solved in 4h) and one pharmacokinetic parameter (e.g. AUC, Cmax)

D A multiple Level C correlation relating one or several pharmacokinetic parameters of interest to the amount of drug dissolved at several time points.

For ER formulations five correlation levels have been defined in the FDA IVIVC guidance (Table 2) [124]. Even though the IVIVC level terminology was introduced for ER products the same principles appears to also be fre-quently used also for IR formulations of BCS class II and IV. The concept of correlation level is based upon the ability of the applied model to reflect the complete plasma concentration versus time profile based on in vitro dissolu-tion data. The highest correlations level (A) represent a direct relationship

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between in vitro dissolution rate and in vivo input rate. This type of correla-tion can have all the previously mentioned benefits of established IVIVC including granting of a biowaiver. The lower levels of IVIVC have limited usefulness since they do not guarantee temporally correct relationship be-tween in vitro and in vivo drug release/dissolution.

The FDA guidance states that in order to develop an IVIVC model, at least three drug formulations with a range of release rates, differing from one another by at least 10%, be studied. Assessment of the models predictability can be carried out with internal validation or by external validation based on a fourth or subsequent formulation that was not used in the model develop-ment stage. In conflict with the definition of a level A IVIVC the assessment of the predictability is typically made with respect to the Cmax and AUC. The conflict lies in that the guidance document states that “the model should predict the entire in vivo time course from the in vitro data” while the as-sessment of Cmax and AUC cannot guarantee that the entire time course is well described.

There are a number of modeling approaches for establishing IVIVC, in-cluding those based on convolution, compartmental models and most fre-quently used, deconvolution [130, 131]. There are many methods of decon-volution which all rely on similar principles and assume linearity and time invariance of the system being studied [132]. The deconvolution is typically based on observed plasma concentrations following administration of the oral formulations (which depends on dissolution, absorption, distribution, metabolism and excretion of the drug) and observed in vivo reference data i.e. plasma concentration following i.v. dosing or administration of oral solu-tion. The idea of the deconvolution is to isolate the information of interest, that is, the rate at which the dosage unit dissolves in vivo. The exact same sampling time points are needed for the correlation of in vitro and in vivo drug release since no continuous model is used to describe the drug release. The deconvolution should preferably be done on an individual level but fre-quently it is done based on average data. The use of average data is proble-matic from two perspectives; (1) it prohibits identification of inter-subject or inter-dosage unit differences and (2) averaging over several experi-ments/individuals cause bias since average profiles does not reflect a typical profile [133]. The largest problem with the deconvolution approach is how-ever the assumptions of a constant rate and extent of absorption over time (i.e. no differences along the GI tract or saturable processes). However, the deconvolution methods have several other well documented weaknesses, such as the clearly flawed assumption that observations from a single expe-riment or individual are independent [132].

Some of the weaknesses with the deconvolution methods are resolved with a nonlinear mixed-effects modeling approach that incorporates a convo-lution step [131, 134]. This technique models in vitro and in vivo data simul-taneously and allows the prediction of plasma concentration–time profiles on

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an individual subject level using in vitro dissolution data. The assumption of a constant rate and extent of absorption over time is however the same for both convolution and deconvolution based approaches. This does limit the types of formulations and active ingredients for which the approaches can be successfully applied. Differential equation based compartmental models have also in rare cases been applied for establishing IVIVC [130, 135, 136]. Such models can be adapted to take into account nonlinear rate and/or extent of absorption [136] and theoretically also differences along the GI tract.

Conceptual attempts have also been made to demonstrate IVIVC by pros-pective simulations based on ‘bottom up’ mechanistic absorption models [120, 137-139]. With this approach the idea is to make prospective predic-tion of plasma concentrations following different oral formulations without any fitting to the clinical observations. The predictions are based on in vitro dissolution profiles, a mechanistic absorption model and a model for the disposition of the active substance (possibly based on reference plasma con-centrations following i.v. dosing or administration of oral solution).

In vivo methods to study GI transit and regional absorption A variety of methods have been used to study GI transit of pharmaceuticals and/or site specific rate and extent of absorption. Perhaps most common, different kinds of intubation techniques that differ in terms of convenience, tolerability and capabilities have been used [140-144]. As an alternative to these methods non-invasive remote operated capsules have been developed [145-148]. After swallowing the capsules are monitored while moving along the GI tract (X-ray, gamma scitigraphy or magnetic labeling) and drug can be released as a solution or powder when activated by an external signal.

A methodology that has introduced the potential of characterizing in vivo behavior of solid dosage forms with respect to GI transit, drug release and regional absorption is gamma scintigraphy [149]. A major advantage of this methodology is the broad availability of the imaging technique [150, 151]. The required imaging equipment as well as the data evaluation methods are essential tools in nuclear medicine and therefore easily accessible. Further-more, gamma scintigraphy can be applied to solid, liquid and semi-solid dosage forms as it is based on the addition of trace amounts of the C-emitting radioisotopes. The temporal and spatial resolution with gamma scintigraphy is limited to approximately a few centimeters and about one minute respectively. However, the major drawback is the ethical problem that healthy subjects become exposed to radiation without having any impor-tant personal benefit, which principally goes against the principals outlined in the declaration of Helsinki [152].

Magnetic Marker Monitoring (MMM) is a non-invasive tool for high res-olution investigation of the gastrointestinal transit of ingested dosage forms without the need to apply radiation [86] that has become an attractive alter-

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native to gamma scinitraphy [153]. MMM is described in larger detail be-low. Similarly, the methodology of intubation with Bioperm® capsules and the paracetamol and sulfapyridine double marker method, for a simpler cha-racterization of gastric emptying and small intestinal transit, is outlined un-der separate headings.

Magnetic Marker Monitoring MMM is based on the labeling of solid dosage forms as a magnetic dipole and determination of the location, orientation and strength of the dipole after oral administration using biomagnetic instruments [86]. The magnetic dipole is generated by incorporation of ferromagnetic material in the formulation and subsequently magnetized using a static magnetic field. Black iron oxide (E172), a color pigment that is commonly used as a colorant for food and orally applied dosage forms, can be used as the magnetic material and fol-lowing magnetization results in a dipole moment of about 30-60 μAm2. This weak magnetic field can be detected with an extremely sensitive biomagnet-ic measuring device (multichannel SQUID sensor) resulting in three dimen-sional localization and orientation as well as determination of the strength of the magnetic source over time. The obtained three dimensional localization of the labeled formulation is transferred to a coordinate system that refers to the anatomy of the investigated subject (Figure 5). In this way the position in relation to the different religions of the GI tract can be obtained [154].

Figure 5.MMM assessment of GI transit for felodipine ER tablet following fasting administration. The locations of the ER tablets are shown in frontal (left) side (right) view. Each circle represents the mean location of the tablet during a 1 second interval [155]. Reprinted with permission of the copyright owner.

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For dosage forms where the drug release rate is determined by the erosion of the dosage form, the decrease in magnetic moment can be linked to the drug release. In these cases, a relationship between the decrease in magnetic sig-nal and drug release characterized in in vitro experiments can be used to obtain actual in vivo drug release profiles [156].

Bioperm® capsule intubation Bioperm® capsule intubation was recently reported to have been successfully applied in 13 phase 1 studies to study regional absorption properties throughout the GI tract [144]. The method features a thin tube introduced through the nose, retrieved from the pharynx, attached to a 30 mm long cap-sule, and swallowed. Peristalsis moves the capsule to the desired location in the gut (monitored by X-ray) where it is anchored before administration via the tube takes place. Substances can be administered in the form of solution or as pellets.

The double marker method The paracetamol and sulfapyridine double marker technique is based on combined gastric administration of paracetamol and sulfasalazine followed by plasma concentration measurements of paracetamol and sulfapyridine. Paracetamol is poorly absorbed from the stomach but rapidly absorbed from the duodenum. Measurements of paracetamol in plasma can hence be used as a marker gastric emptying (GE) [157]. Sulfasalazine is poorly absorbed in the stomach and small intestine but is rapidly metabolized by the bacterial flora in the large intestine to the metabolite sulfapyridine, which is absorbed. Appearance of sulfapyridine in plasma can therefore be used as a marker to determine the small intestinal transit time (SITT) [158, 159]. The double marker method has mostly been used to study GE and SITT in dog or mon-key [160-162]. However there are also examples of when the methods have been applied to clinical studies [163, 164].

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Aims

The primary aim of the thesis was to improve mechanistic understanding and prospective predictions of oral absorption by establishing nonlinear mixed-effects modeling approaches to analyze observations from advanced in vivo studies of oral absorption. A secondary aim was to advance nonlinear mixed-effects modeling methodology with respect to handling of censored observa-tions and model diagnostics to facilitate the primary aim and pharmacome-tric research in general.

The specific aims were to:

• Outline a suitable integrative approach for quantifying gastro in-testinal tablet transit, in vivo drug release, absorption and disposi-tion based on MMM study observations.

• Characterize the relationship between in vitro and in vivo drug re-lease along the GI tract for hydrophilic matrix ER tablets, by the estimation of the relative mechanic stress in different GI regions.

• Develop a model characterizing absorption properties along the GI tract for the investigational drug AZD0837 and demonstrate how that model in combination with models for drug release and tablet GI transit can be utilized to make prospective predictions of absorption from new ER formulations.

• Demonstrate how semi-mechanistic modeling of GI transit based on paracetamol and sulfapyridine data can facilitate characteriza-tion of pharmacologically induced changes in gastrointestinal transit.

• Evaluate methods for handling censored observations in mixed-effect models to prevent bias in parameter estimates and for diag-nosing model fit using visual predictive checks (VPCs).

• Introduce the concepts of prediction and variability correction in VPCs and highlight situations where this could add significant di-agnostic value.

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Material and Methods

The thesis is based on six papers. Paper I involves the development of a mechanistic model describing the interrelationship between tablet GI transit and in vivo drug release and plasma concentrations of felodipine. The obser-vations of tablet GI transit and in vivo drug release for the felodipine ex-tended release (ER) formulation were made possible by Magnetic Marker Monitoring (MMM). This project can be seen as a pilot study to evaluate the feasibility of applying a mixed-effects modeling approach to data from MMM studies. The successful outcome of that pilot study lead to the initiali-zation of a project described in Paper IV and V. In these two papers an ex-tended version of the methodology outlined in Paper I has been applied to studies of the investigational drug AZD0837, aiming to perform prospective predictions of PK profiles for newly developed ER formulations. Important model building features from these three projects are described in the Model building section. Paper VI features a semi-mechanistic model that characte-rizes pharmacological effects on gastric emptying and small intestinal transit time based on paracetamol and sulfapyridine double marker studies. Impor-tant methodological aspects of that project are described under the subhead-ing Double Marker Model in the Model building section.

Paper II and III deal with extensions to pharmacometric methodology concerning censored observations and model diagnostics. These methodo-logical advances were later applied in Paper IV, V and VI. The general me-thodology aspects of these papers are presented in the Mixed-effect modeling methodology section.

Software Data analysis in all projects included in this thesis were performed with a nonlinear mixed-effects approach as implemented in the NONMEM soft-ware (version 6.1.0 to 7.1.2) [24]. The PsN toolkit [165, 166] was used in conjunction with NONMEM for atomization and post processing purposes (e.g. log-likelihood profiling, VPC). The Xpose 4.3.0 [167, 168] package in R [169] was used for graphical diagnostics. Methodological developments with respect to VPCs presented in Paper II and III have been implemented in PsN and Xpose in line with how it is presented in the papers.

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Mixed-effect modeling methodology Handling of censored observations In Paper II the influence of different methods for handling censored BQL samples was investigated with a simulation and re-estimation approach. Three distinctly different models were used for simulation. Model A was a one compartment model with oral dosing and absorption transit compart-ments [110, 111]. For model A BQL observations were located with absolute predominance in the absorption phase. Model B was a two-compartment model with intravenous dosing. Model C was a PKPD, indirect response, model where Kout increased linearly with drug concentration [170]. The ef-fect driving drug concentration followed a fixed one-compartment model with oral absorption (not estimated). For model C the BQL samples occurred during the drug induced dip in the response variable. Log-transformation of the dependent variable was applied for all models to avoid negative predic-tions. The residual unexplained variability (RUV) was simulated using an error model designed to mimic combined proportional/additive error within the relevant prediction range. The assumed LOQ levels were chosen so that the CV of RUV was equal to 20% at this typical prediction. The limit of 20% CV corresponds to the FDA Guidance for Industry Bioanalytical Me-thod Validation definition of LOQ [171] under the assumption that mea-surement error is the only source contributing to the RUV. Three different residual error magnitudes and hence also three different LOQ limits was investigated. LOQ limits and proportion of censored observations are pre-sented in Table 3. For each model and LOQ level 100 datasets were simu-lated.

Table 3. Three models were investigated based on three different assumed LOQ limits, resulting in different fractions of overall BQL samples and fraction of BQL samples at critical sampling points.

Model LOQ limit

I II III

A LOQ: 0.2 BQL: 12% of all, 28% of samples 1-3

LOQ: 0.4 BQL:15% of all, 35% of samples 1-3

LOQ: 0.8 BQL:19% of all, 44% of samples 1-3

B LOQ: 1.25 BQL: 10% of all, 40% of last sample

LOQ: 1.75 BQL: 20% of all, 70% of last sample

LOQ: 2.5 BQL: 30% of all, 90% of last sample

C LOQ: 1.6 BQL: 10% of all, 17% of samples 2-4

LOQ: 2 BQL: 18% of all, 30% of last samples 2-4

LOQ: 2.5 BQL: 28% of all, 46% of last samples 2-4

Estimation of the simulated data sets was performed with four different ap-proaches for handling BQL observations. As a reference, estimation was also performed with the entire datasets without any assumed BQL samples [a].

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The investigated traditional approaches to deal with BQL was to either simp-ly omit all BQL samples [b] or to substitute them with LOQ divided by two (LOQ/2) [c]. For model B and C the first in the time series of BQL mea-surements was substituted with LOQ/2 and later BQL samples were omitted. In the absorption case (model A) all BQL observations was substituted with LOQ/2. The estimation alternatives a, b and c were performed both with the first-order conditional estimation method with interaction (FOCE INTER) and with addition of the LAPLACIAN option. The LAPLACIAN option was necessary for the execution of the likelihood based methods M2 [d] and M3 [e]. By the fact that the observations were log-transformed the predictions had no lower theoretical boundary and hence the M3, and not the M4, me-thod was applicable. The M2 method was implemented by setting the YLO parameter to the LOQ value. The M3 method was implemented with the built in NONMEM VI functionality F_FLAG. The general coding and expli-cit likelihood expressions for the M2 and M3 method were implemented according to Ahn et al [172].

The bias and precision of the different methods was assessed as a percent mean prediction error (mpe) and root mean squared prediction error (rmse), respectively. Judgment of significant bias was based on 99% confidence intervals for mpe excluding zero. The ratios of parameter estimates divided by the true parameter (pr) value are depicted in box-plots for graphical com-parison of the different methods.

Simulation based diagnostics VPCs have become a frequently used standard diagnostic tool in PKPD modeling. However, for certain types it has been reported that the interpreta-tion of VPCs can be hampered. In the presence of censored observations or observations missing not at random VPCs can be misleading if this is not accurately taken into account [173]. This issue was addressed in Paper I and has also been further addressed in a separate conference poster [174].

The VPC methodology has also been demonstrated to be unable to cope with large variability in independent variables and adaptive dosing. In Pa-per III further development of the VPC methodology in the form of predic-tion corrected VPC (pcVPC) and prediction and variability corrected VPC (pvcVPC) was outlined and investigated as a solution to this problem.

Basic VPC methodology VPCs were based on 500 or 1000 datasets simulated with the obtained final parameter estimates and the same data structure as the original dataset. In the case of BQL samples these were retained in the dataset and the dependent variable was set to value less than LOQ. Binning on the independent variable was, in cases of a fixed sampling design carried out, such that there was a single bin for each protocol time point or protocol sampling window. In cas-

38

es of data with less structured sampling times, binning was performed to maintain approximately the same amount of observations in each bin. Statis-tics were calculated in the same manner for the observed and all simulated datasets. For each dataset and in each bin the median dependent variable (DV) value was calculated. Out of the median values for each bin originating from the model simulations a non parametric 95% confidence interval was calculated (the 2.5th and 97.5th percentile). Similarly to the median, other percentiles of the data were presented with an observed value and a 95% confidence interval based on the simulated datasets. The percentile chosen to be depicted graphically was dependent on the size of the original dataset. Typically the 2.5th and 97.5th percentiles of the datasets were depicted, cor-responding to a 95% prediction interval, but in examples with fewer obser-vations a 90% inter-percentile-range (5th and 95th percentiles) was instead utilized. In the case of binning across more than a single unique value for the independent variable (x-variable) the size of each bin was illustrated by the width of the square formed confidence intervals.

VPC in the presence of censored observations A two panel type of VPC was chosen to evaluate the model with respect to both data above and below LOQ. The top panel consisted of a VPC for the continuous observations (>LOQ) following the principle presented above. Percentiles for observed data could only be adequately calculated and pre-sented for the percentiles where BQL data constituted a smaller fraction than the percentile in question. The bottom panel compares a simulation based 95% non-parametric confidence interval for the fraction of BQL samples with the corresponding observed fraction. Binning across the independent variable was performed similar to the basic VPCs and identically for the upper and lower panel. The same approach that is used for BQL samples can also be applied for categorical data in general [174].

For application to datasets featuring observations MNAR a slightly mod-ified approach is needed. A requirement for accurate estimation of model parameters in the presence of observations MNAR is that the model can predict the missingness pattern [53]. Accurate prediction of the MNAR pat-tern is also essential for VPC diagnostics and needs to be monitored as a prerequisite for unbiased assessment of any other dependent variables. The accuracy of MNAR predictions can be monitored in a VPC by comparing the predicted and observed fraction of missing observations across time (or some other independent variable) similar to how censored observations are diagnosed. The important difference is the fact that nothing is known about the observations that are MNAR in contrast to censored data that is known to be above/below a limit or within a certain interval. Due to that fact observed and predicted MNAR data needs to be censored before percentiles are calcu-lated for the dependent variable of interest.

39

pcVPC and pvcVPC pcVPCs differ from traditional VPCs in that the dependent variable has been subjected to prediction correction before the statistics are calculated. Predic-tion correction aims to correct for the differences within a bin coming from independent variables (time, dose and other covariate values) in the model and hence more clearly diagnose model misspecifications both in fixed and random effects. The normalization is done with respect to the median predic-tion for each bin across the independent variable (Equation 3). If the typical model prediction (PRED) has a lower boundary that is different from 0 (e.g. relative change from baseline has -100% as a lower boundary) the correction can adjust for this ( ). It is important to note that the lower bound is for the typical model prediction and not the dependent variable which could be lower than the lower boundary for the typical model prediction (e.g. due to random effects). By normalizing the dependent variable to the median popu-lation prediction as well as to the typical variability (Equation 4) of each bin a pvcVPC may be constructed. Many factors will cause the expected relative variability to differ between observations even after prediction correction. Predictions rely in different extents on the parameters in a model, hence are affected to a different extent by the between subject/occasion variability in these parameters. Another reason for non-constant relative variability is if a residual error model other than a strictly proportional model is used.

In Paper III five different examples were investigated in order to high-light situations when pcVPCs can add significant diagnostic value. The ex-amples used were simulated hypothetical examples as well as applications to real data. In application to the in vivo drug release model presented in Pa-

Prediction correction for dependent variable, , with lower bound, .

(eq. 3)

Variability correction for prediction corrected dependent variable, , with standard deviation,

(eq. 4)

= observation or prediction for the ith individual and jth time point, = Prediction corrected observation or prediction, = Typical population prediction for the ith individual and jth time point, = Median of typical population predictions for the specific bin of independent variables. = Prediction and variability corrected observation or prediction for the ith individu-al and jth time point, = Standard deviation of simulated ,

= median for the specific bin of independent variables.

40

per IV a situation when a pvcVPC offered and important advantage was demonstrated and the power to detect misspecified random effects was in-vestigated.

Model development In Papers I, IV, V and VI models were developed to characterize different aspects of oral absorption. Data from MMM studies were a key component in Papers I, IV and V. The methodology applied in these projects share as-pects with respect to model building and is presented below under the head-ings Drug release, Regional absorption and Tablet GI transit. Paper VI is based on studies of paracetamol and sulfapyridine as markers for GI transit. The model developed in application to these data is presented under a sepa-rate heading. The disposition of the investigated substances (felodipine, AZD0837, paracetamol and sulfapyridine) was in all cases modeled with standard compartmental models. Detailed aspects of the disposition models are presented in each paper but not elaborated on further here.

Drug release In Paper I the drug release from felodipine ER tablet was described solely based on in vivo observations of drug release based on MMM. In application to the investigational drug AZD0837 (Paper IV) the approach to describe drug release was refined by utilizing information from in vitro drug release experiments and prior information about pH and Ionic strength along the GI tract.

In vitro drug release In vitro drug release for 6 different investigational HPMC ER formulations was assessed under different experimental conditions (pH, Ionic strength and rotations speed) with USP apparatus 2 equipped with a stationary basket [175]. One of the investigated formulations (Z) was also investigated in a modified ERWEKA (m-ERWEKA) dissolution tester [156] and studied in vivo with MMM. For eroding hydrophilic matrix ER tablets, the dissolu-tion tests measure the composite of drug release and drug dissolution. Under the investigated conditions the dissolution of released AZD0837 was very fast in comparison to the drug release. Hence, the measurements could be considered to describe only drug release.

A model attempting to describe drug release as a function of the dynami-cally changing surface area was constructed. The weight of the tablet raised to the power of ⅔ (γ in equation 1) was used as an approximation of the sur-face area of the tablet. This follows the logic that the surface area is propor-tional to the volume raised to the power of ⅔ and the weight is proportional

41

to the volume. This approximation assumes that the substance is evenly dis-tributed in the formulations and that the tablet erodes in a symmetrical fa-shion (i.e. maintains its original shape during the disintegration). Equation 5 features the differential equation that describes how the amount of non-released substance in the tablet (A1) decreases with time (initialized to Dose), dependent on a release rate constant (R), the initial tablet weight (mg), the nominal amount (mg) of AZD0837 in the tablet (Dose) and the power factor (γ).

· · · (eq. 5)

The effect of experimental conditions was investigated as covariate rela-tionships on the typical release rate Rtypical (formulation X, rotation speed = 50 rpm, ionic strength = 0.1 mol/L, pH 6.8). The relative differences in re-lease rate for formulations other than the reference formulation (X) were also estimated (CovForm) and the between tablet variability (BTV) in release rate was described with an exponential random effect (ηR) (see Equation 6). · · · · 1 · (eq. 6)

The effect of rotation speed and ionic strength on the release rate (R) was well characterized with simple linear functions whereas the relationship to pH was more complicated. The relationship to pH was described with the estimation of a linear slope parameter (EpH) and a breakpoint at the pH where no further effect could be seen (BreakPointpH) according to Equation 7.

1 · . · · (eq. 7)

Prior information indicated that the effect of pH on drug release was dri-ven by pH dependent solubility of the active ingredient AZD0837 since the disintegration of the HPMC hydrophilic matrix previously was shown to be relatively insensitive to pH [176]. An interaction term between fraction of active ingredient in the formulation (API) and pH was therefore considered in the model. A linear effect of API (normalized to the API of formulation X, 0.55) on the pH covariate relationship was estimated (EAPI).

In vivo drug release For the felodipine ER tablet, drug release was based solely on MMM derived in vivo drug release. This was modeled with zero-order drug release rate constants. The effect of concomitant food intake and tablet GI position on drug release rate was investigated.

For AZD0837 the model developed based on the in vitro dissolution ex-periments was applied to the in vivo drug release data derived with MMM.

42

The drug release data was complemented with literature information on pH and ionic strength in the different GI regions (Figure 6).

Figure 6. Literature information on pH throughout the GI tract under fed and fasting conditions [177, 178]. Fed (dashed line) and fasting (solid line) conditions differ for pH in the proximal and distal stomach. The lines and error bars represent the mean and standard deviation respectively.

Figure 7. The in vivo mechanical stress are characterized in units equivalent to the rotation speed (rpm) in an USP 2 apparatus based on in vivo drug release observations, an in vitro drug release model and literature information about pH and ionic strength along the GI tract.

Assuming that pH and Ionic strength were according to literature and the observed GI position, meant that mechanic stress (i.e. rotational speed) in the

43

different GI regions was the only unknown factor in comparison to the in vitro experiments. The mechanic stress in the different GI regions was hence estimated with the final in vitro model. All fixed effects of the in vitro model were fixed at the final estimates. Random effects were estimated for R and the relative dose amount. The mechanic stress was estimated (RPM) based on the covariate relationship for rotation speed in the in vitro experi-ment and the estimates were hence of a unit equivalent to rpm in the USP 2 apparatus.

Regional absorption The assessment of regional absorption in Paper I and V is primarily based on MMM study data. The structure of the models applied in these two projects was based on the conceptual model structure presented in Figure 3. This model structure was simplified in such a way that the model parameters could be estimated based primarily on clinical data (Figure 8). One such simplification was to exclude the dissolution step and let the first-order ab-sorption rate constants (KA) represent the rate limiting process of either solu-bility or permeability. This simplification was possible due to the docu-mented relatively high solubility and rapid dissolution for both felodipine and AZD0837 under physiological conditions. Another simplification was to omit the gut wall compartment and replace it with parameters governing the bioavailability over the different gut-wall regions (FA). The fast dissolution and absorption of substance released in the small intestine also made it im-possible to quantify any mass transfer of released drug substance between different small intestine regions and further into colon.

The previously described drug release models in combination with the observed tablet GI position governed the amount of substance available for absorption in the respective GI regions over time. In both models there was assumed to be no significant absorption from the stomach. Transfer of re-leased drug substance from the stomach into the small intestine was go-verned by first-order rate constants.

As a complement to the MMM study the AZD0837 model (Paper V) was also informed by observations following local colon dosing with a Bioperm® capsule. Furthermore, the disposition part of the model for both felodipine and AZD0837 model was informed by the inclusion of plasma concentra-tions from studies with intravenous administration.

44

Figure 8. Compartmental model structure applied to drug release, absorption and disposition of AZD0837 (Paper V). Compartment 1 represented the amount of drug present in the remaining tablet, A1, Equation 5. The substance released from the tablet was directed into GI compartments 2-8 depending on the observed tablet position. Gastric emptying from the stomach compartments (comp. 2 and 3) were governed by first-order rate constants (K2T3, K3T4), and from the duodenum drug was absorbed through the gut wall via first-order absorption rate constant (KA4). The extent of absorption was limited by the fraction absorbed through the gut wall (FA4). Since the absorption rate was found to be rapid from both the duodenum and lower parts of the small intestine no significant downstream mass transfer could be estimated for these compartments. Potential differences in rate and extent of absorption along the GI tract were assessed by investigating the benefits of assuming separate KA (KA4-KA8) and FA (FA4-FA8) for the different GI compartments. Compartment 9 was a semi-physiological representation of the liver with a fixed volume (VH = 0.0143 L/kg). Hepatic elimination is governed by allometrically scaled liver blood flow (QH), the blood plasma concentration ratio (Cb/Cp) and the estimated hepatic extraction ratio (EH). A relatively small renal CL (CLR) was assumed to be 0.78 L/hr for all subjects. The systemic distribution of AZD0837 was described by a central observation compartment (comp. 10) and two peripheral compartments (comp. 11 and 12).

ProximalStomach

DistalStomach

Duodenum

SmallIntestine

AscendingColon

TransverseColon

DescendingColon

Tablet Liver Central

Shallow

Deep

R

× ×

45

Tablet GI transit The GI positions were characterized slightly differently in the primary as-sessment of the MMM data for felodipine (Paper I) and AZD0837 (Pa-per II). For felodipine, a distinction was made between proximal and distal small intestine that was not made in the AZD0837 study. For the felodipine formulation there was very limited observations of the formulation in colon compared to the AZD0837 tablet, due to a generally faster drug release (LOQ = 15% of nominal dose).

The tablet transit pattern throughout the gastrointestinal tract was de-scribed with Markov chain type models. This means that the probability of observing the tablet in a specific GI position is dependent on where it was last observed and the time since the last observation. Due to the irregular observation periods of GI position (approximately 10 min continuous obser-vation periods separated with 20 min breaks) a traditional Markov chain model approach could not be used [179]. Instead a compartmental model where amount adds up to one and represents probability was used. Each of the distinct GI positions were represented by one or more compartments (Figure 9). First-order rate constants were then used to govern how probabil-ity shifted within the compartmental system between observations. At each observation, the system was reset and the probability was set to one for the observed compartment.

Figure 9. Schematic picture of the final compartmental Markov model used to characterize tablet GI transit in Paper IV (the model in Paper I is slightly different but based on the same principle). Compartment amounts represented probability of tablet position and the shift in probability over time were governed by first-order rate constants (Kij). Compartment amounts were reinitialized following each observation to represent the obtained information. The tablet could move backward and forward between the proximal and distal parts of the stomach but only downstream post transition into small intestine.

StomachF = proximal stomachA = distal stomach

ColonAC = AscendingcolonTC = TransversecolonDC = Descendingcolon

KFA

Sigmoid Colon / Rectum

FAKAF

SI:1 SI:3 SI:4SI:2

ACTCDC

SCR

Small Intestine

KAS

KSIKSI KSI

KSI

KACKTC

KDC

46

The physiology limited minimum retention time the in small intestine was handled with a number of transit compartments. A sufficient number of tran-sit compartments were found by increasing the number of transit compart-ments in a stepwise fashion until there was no further improvement in the NONMEM OFV value. The reinitialization of the transit compartments after an observation of the tablet in one of the small intestine positions was done in relation to the probability of each of the transit compartments immediately prior to the observation. The reinitialized probability of compartment i ( ) was given by the expression in Equation 8, where represents the probabil-ity of transit compartment i just previous to observation and ∑ the sum of probabilities for all transit compartments just previous to the observation.

∑ (eq. 8)

The Markov models were parameterized with mean transit times (MTT). MTT between positions i and j (MTTij) relates to the first-order transit rate constants (Kij) and the number of transit compartments (Ni) according to Equation 9.

(eq. 9)

Potential effects of concomitant food intake were evaluated for all MTT parameters in the model.

Paracetamol and sulfapyridine double marker method Paper VI aimed at developing a model to characterize the effect of erythro-mycin and atropine on GE and SITT based on observations of paracetamol and sulfapyridine plasma concentrations (Figure 10). Stomach and colon are represented by single compartments and connected by a series of transit compartments (SI:1-N) representing the small intestine. The transit com-partments are linked by first-order transit rate constants (Ktr). Ktr are mathe-matically derived as the number of transit compartments (N) divided by the mean transit time (i.e. SITT). In line with the idea behind the double marker method, paracetamol was rapidly absorbed from the small intestine (Ka,si) whereas sulfapyridine was formed and absorbed according to the first-order rate constant Ka,col. Disposition for paracetamol and sulfapyridine was de-scribed with a 2 compartment model and a 1 compartment model, respec-tively.

47

Figure 10. Schematic picture of the final model applied in Paper VI.

Observations from three studies in male beagle dogs were included in the analysis. Two 3 way cross-over studies investigated the effect of atropine and erythromycin under fed and fasting conditions (study 1 and 2). The two studies were both carried out in beagle dogs but different animals were used. Apart from the different feeding patterns the protocol in the two studies was largely the same. Observations from a small cross-over study featuring intra-venous and intra gastric administration of PCM in two dogs were also in-cluded to better support disposition of PCM (study 3).

A slow rate of gastric emptying was found to be associated with a lower bioavailability for paracetamol. This was explained by including saturable first pass metabolism, implemented as a typical Michaelis-Menten elimina-tion directly from the small intestine compartment (see Figure 10).

The effect of concomitant food on GE and SITT was investigated using time dependent functions. Several approaches to account for the hypothe-sized time dependent effect on KG and SITT were investigated. The function used to describe the stimulating food effect on KG is described in Equa-tion 10 and was based on the estimated parameters AmpGE,stim, λGE,stim and the time since last food intake. A parameter reflecting the inhibitory effect, FoodGE,inh, was also estimated and implemented together with the stimulation function as presented in Equation 14. The effect of food intake on SITT was also found to be of a time dependent nature. The effect was described with a surge function dependent on the time since last food intake as described in Equation 11.

, 1 , , (eq. 10) 1 / (eq. 11)

In the absence of observed plasma concentrations for atropine and eryt-hromycin a hidden concentration effect relationship for the effect on GE and

Stomach Colon

FoodDrug

SI:1 SI:2 SI:N...

Compartmental models for paracetamol and sulfapyridine disoposition

SITT

48

SITT was estimated. This was based on literature information about the typi-cal half-life for atropine and erythromycin and the assumption of 1 com-partment pharmacokinetics. For erythromycin the half-life was assumed to be 1.35 h based on a recent study in beagle dogs [180]. No data on atropine pharmacokinetics in beagle dogs was found in the literature but based on a study in mongrel dogs (mixed bread) of approximately the same size the half-life was assumed to be 2.1 h [181]. The drug effect was characterized with a sigmoidal Emax function (Equation 13) and the approximated drug concentration (X) (Equation 12). The parameters EX50 were estimated in units of percentage of maximum concentration of the effector drug.

½ · (eq. 12) 1 ·

(eq. 13)

The gastric emptying was described as the sum of two independent first-order processes (KG,Active and KG,Pasive). KG,Active was affected by drug treatment and the stimulating food effect (FoodGE,stim). The inhibitory effect (dilution effect) of food intake (AmpGE,inh) was assumed to act on both KG,Active and KG,Passive (Equation 14). The hypothesis behind this implementa-tion is further elaborated on in the discussion section.

, · · · , ,, (eq. 14)

· · · (eq. 15)

49

Results

Mixed-effects modeling methodology Handling of censored observations Three typical ways in which BQL observations can occur in a model were investigated and four methods for handling the censored observations were compared to the reference situation with no censored observations. A com-parison of the performance of the four methods with respect to the absorp-tion parameters in example A is presented in Figure 11. Omitting the BQL observations (bL) resulted in substantial bias in parameter estimates for all investigated examples. For the absorption parameters, in example A, substi-tution with LOQ/2 (cL) induces an even larger bias than omitting the BQL data. For example B, where the BQL observations occurred in the terminal elimination phase of a traditional bi-exponential PK profile the substitution method resulted in less pronounced bias compared to omission. In the PKPD example (C), where BQL observations occurred in a transient dip in the re-sponse variable, substitution with LOQ/2 resulted in positive bias for typical value and between subject variability for the PKPD interaction parameter (SLOPE). This is the opposite of omission that resulted in negative bias. The M2 method (d) generally demonstrated a similar but less pronounced pattern of bias compared to omitting the BQL observations. The M3 method (e) did result in generally unbiased parameter estimates but did, as expected, result in an inflated root mean squared prediction error compared to the reference estimation with no BQL observations (aL).

Handling of censored observations in VPC diagnostic plots was evaluated based on the same examples. A double panel type of VPC that focused on both the continuous observations (>LOQ) and the fraction of censored ob-servations was introduced. These VPCs was demonstrated to identify bias introduced by suboptimal handling of BQL observations. The same approach has later been applied in Papers IV, V and VI and an example can be seen in Figure 15.

50

Figure 11. Box-plots depicting parameter estimates (n=100 per box) divided by the true parameter values for a selection of parameters from model A. Absorption rate constant (KA), mean transit time (MTT), number of transit compartments (NTC) and corresponding between subject variability (BSV). Results are presented for method a, b, c (Laplacian), d and e and for LOQ level I, II and III.

IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII

IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII

IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII IIIIII

51

pcVPC and pvcVPC pcVPC and pvcVPC plots were evaluated against standard VPC plots for 5 different examples in Paper III. The principal benefit with pcVPC plots in application to data from studies with adaptive dosing is illustrated in Figure 12. The observations in the VPC demonstrated a decreasing variabili-ty with time as a result of the dose adaptations. In contrast, the model-predicted inter-percentile-range increased since the simulations based on the realized design do not maintain any correlation between dose-alterations and the previous observed concentration. The pcVPC corrects for the dose ad-justments and correctly indicates no discrepancy between the observations and the model prediction.

It has been put forward as an alternative to prediction correction to instead simulate the dose adaptations and that way generate comparable model pre-dictions. In a comparison it was illustrated how a pcVPC could be more po-werful in detecting model misspecifications and highlighting the underlying nature of a model misspecification.

For the examples investigated in Paper II no added diagnostic value was seen with variability correction in addition to the prediction correction (pvcVPC). Such an advantage was however seen in application to the exam-ples in Papers IV, V and VI where pvcVPC was utilized. In application to in vivo drug release model (Paper IV), pcVPC and pvcVPC were used for diagnosing primarily the random effects of the model with all observations from all three treatment cohorts pooled (fasting, before and after food in-take). In this example, the relative expected variability differed substantially between the different profiles since the expected variability in drug release rate was dependent on the time spent in the different GI regions. The drug release rate was proportional to pH in the range below 3.5 and stomach pH has a relatively high between subject variability especially in the fasting state (CV = 33%). The variability in initial drug release rate was hence expected to be higher for subjects with a late gastric emptying of the tablet. In this situation it was an important advantage to use a pvcVPC over a pcVPC, for assessing the overall variability rather than only the variability for the sub-jects with the highest expected variability (see Figure 15 and Figure 17).

52

Figure 12. A posteriori dose adaptation (TDM) based on observed trough plasma concentration (U/L) monitoring over time. Traditional VPC (top) and pcVPC (bottom) for the true model applied to a simulated dataset. The solid black line represents the median observed plasma concentration (ng/L) (prediction corrected plasma concentration in the pcVPC) and the dark gray field represents a simulation based 95% confidence interval for the median. The observed 2.5% and 97.5% percentiles are presented with dashed lines and the 95% confidence intervals for the corresponding model predicted percentiles are shown as light gray fields. The observed plasma concentrations (prediction corrected in the pcVPC) are represented by open circles.

VPC

pcVPC

53

Tablet GI transit Parameter estimates for the tablet GI transit model were estimated based on MMM observations for the felodipine and AZD0837 ER formulations in separate analyses (parameter estimates presented in Table 4). Food was iden-tified in both analyses to prolong the tablet residence time in the proximal and distal stomach. The tablets could also move backwards from distal to proximal stomach but no significant food effect was found for the MTT from distal to proximal stomach. The parameter estimates correspond to a fasting average stomach residence time of 57 min and 34 min for felodipine and AZD0837, respectively. The corresponding fed values are 6.6 h for felodi-pine and 7.2 h for AZD0837. Parameter estimates for the stomach move-ments were uncertain especially for felodipine and not found to be signifi-cantly different between the two products.

In the felodipine, but not the AZD0837 study, a distinction was made be-tween proximal and distal small intestine. The typical total small intestinal transit time was 3.4 h for felodipine and 4.8 h for AZD0837. The colon tran-sit could not be characterized for felodipine since complete tablet disintegra-tion (i.e. >85%) was achieved in small intestine or initial parts of colon. For AZD0837 formulation the drug release/disintegration was slower and hence the transit times between colon regions could be estimated. Estimates regard-ing the lower parts of the colon (descending/sigmoidal colon and rectum) were however based on a sparse number of observations.

Table 4. Parameter estimates for GI transit of felodipine and AZD0837 ER tablet

Mean transit times (min) Estimates

Felodipine* AZD0837§

Prox. Stomach -> Distal Stomach (fasting) 24 (14-46) 12 (22)

Prox. Stomach -> Distal Stomach (fed) 63 (38-115) 81 (23)

Distal Stomach -> Proximal Stomach 165 (85-385) 265 (44)

Distal Stomach -> Small intestine (fasting) 22 (11-47) 16 (44)

Distal Stomach -> Small intestine (fed) 222 (107-576) 245 (18)

Prox. small intestine -> Distal small intestine 130 (98-178) -

Distal small intestine -> Ascending colon 73 (51-109) -

Small intestine -> Ascending colon 203# 291 (25)

Ascending colon -> Transverse colon - 327 (28)

Transverse colon -> Descending colon - 185 (64)

Descending colon -> Sigmoidal colon and rectum - 240 (17) * 90% confidence interval within brackets § RSE (%) within brackets # Sum of the two above parameters

54

Oral absorption from felodipine ER formulation Drug release The in vivo drug release was best described with three different zero-order rate constants depending on the position of the remaining extended release tablet. A relatively slow release rate of 0.68 mg/h was estimated for fundus (proximal stomach). Whereas a significantly faster drug release of 1.91 mg/h was estimated for antrum (distal stomach) and proximal small intestine. An intermediate drug release rate of 1.16 mg/h was established for the distal small intestine and colon. The between subject variability for the three zero-order rate constants was highly correlated and sufficiently described with only one variability term affecting all rate constants. The magnitude of the between subject variability was small, with a value of 9%. No significant effect of concomitant food intake on drug release could be detected when the effect of gastro intestinal position was taken into account in the model.

Absorption and GI distribution The drug release model governed the amount of substance that was available for absorption in the different GI compartments. First-order rate constants were found to best describe the distribution of released drug substance from fundus (i.e. proximal stomach) to antrum (i.e. distal stomach) (K2T3) and from antrum to proximal small intestine (K3T4). An apparent increase in these rates was seen in association with the tablet movement. It was hypothesized that this was due to a higher concentration of released drug substance in the local proximity of the tablet, which would move simultaneously with the tablet. This was mimicked with adding an accelerating factor to the rate con-stants K2T3 at the time point of tablet movement from fundus to antrum and similarly to K3T4 at the time of transit from antrum to small intestine. K3T4 was further found to be four times faster when the tablet was administered in the fasting state compared to the fed state.

The rate of absorption for felodipine was similar in the proximal and dis-tal part of the small intestine, 2.87 h-1. A significantly slower rate of absorp-tion was established for the colon, 1.15 h-1. No significant distinction could be made between the extent of absorption from the small intestine and colon, i.e. fraction absorbed through the gut wall was sufficiently characterized with one single parameter (FA). FA was found to be significantly higher when the tablet was administered together with food compared to when it was administered to fasting subjects (0.23 vs. 0.39).

55

Oral absorption from AZD0837 ER formulations Drug release The final in vitro model provided a good description of all experiments, across the six formulations and different experimental conditions. In Figure 13 the model fit is illustrated for formulation X with a random sam-ple of 1 experiment (out of several replicates) for each unique investigated experimental set-up. An acceptable, but slightly worse than average, fit was seen for experiments performed with high ionic strength (0.3 mol/L). This was judged to be of low clinical interest since the anticipated physiological ionic strength was in the range between (0.1 - 0.14 mol/L) and hence not investigated further.

Figure 13. Individual goodness-of-fit plots for formulation X, 1 randomly sampled in vitro dissolution experiment for each investigated combination of experimental conditions. The observed amount of released substance (mg) are depicted with open circles, the individual model prediction with a solid black line and the population typical prediction with a dotted black line. The pH, rotation speed (rpm) and ionic strength (M=mol/L) of each experiment is presented in the header of each plot.

The final established covariate relationships for pH, rotational speed and ionic strength are illustrated in Figure 14. The best fit to the data was achieved with the power factor (γ) estimated to 0.56 (RSE 2.1). Compared to

Time (h)

Obs

erva

tions

/ Pr

edic

tions

(mg) 0

50

100

150

0 5 10 15 20 25 30

0 5 10 15 20 25 30

0

50

100

150

0

50

100

150

0 5 10 15 20 25 30

0 5 10 15 20 25 30

DV IPRED PRED

pH 6.8, 10 rpm, 0.1M pH 6.8, 50 rpm, 0.1 M pH 6.8, 100 rpm, 0.1 M pH 1, 50 rpm, 0.1 M

pH 2, 50 rpm, 0.1 M pH 3, 50 rpm, 0.1 M pH 5, 50 rpm, 0.1 M pH 6, 50 rpm, 0.1 M

pH 1, 100 rpm, 0.1 M pH 3, 100 rpm, 0.1 M pH 6.8, 50 rpm, 0.2 M pH 6.8, 50 rpm, 0.3 M

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the originally assumed theoretical value of ⅔ (assuming symmetrical erosion and drug release proportional to the surface area) the estimate of 0.56 cor-responds to a slightly more constant (zero-order) drug release. The estimated relative drug content was very close to the nominal dose (99%) and the va-riability in drug content between tablets was estimated to 4.4%.

Figure 14. Covariate relationships for typical release rate (R). Left: Relationship between pH and R, for three API fractions. Right: R as a function of ionic strength (dashed line, upper x-axis) and rotational speed (rpm) in the USP 2 apparatus (solid line, lower x-axis).

The modeling of the in vivo drug release data was based on the in vitro drug release model and prior information on pH and ionic strength along the GI tract (see Figure 6). The mechanic stress representative of the different GI regions was estimated in a unit equivalent to rotational speed in the USP 2 in vitro apparatus. Parameter estimates are presented in Table 5.

Table 5. Parameter estimates for in vivo drug release. Typical estimates, between tablet variability (BTV) and associated relative standard errors (RSE)

Parameter (Unit) Estimate (RSE, %) % BTV (RSE, %)

Typical release rate, R (h-1) 1.03 (7.0)* 18 (28)

Relative drug content, (% of nominal dose) 103 (1.0) 4.0 (34)

RPMProximal Stomach (rpm) 94 (9.6)

RPMDistal Stomach (rpm) 134 (4.8)

RPMSmall intestine (rpm) 93 (6.8)

RPMColon (rpm) 38 (17)

RUV (mg) 6.3 (8.5) * Parameter estimate and RSE from fit to in vitro data

No significant effect of concomitant food intake was detected apart from that explained by differences in lower pH and longer residence time in the sto-

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mach. Satisfactory predictability was demonstrated both for the typical (me-dian) drug release profile under the different investigated conditions (VPCs in Figure 15) and for the overall predicted variability in drug release (pvcVPCs in Figure 15).

Figure 15. Model diagnostics for in vivo drug release. VPCs: observed median for remaining drug substance in tablet (black line) and corresponding model predicted median (gray line) and 95% CI (gray field). pvcVPC: 90% prediction interval for all subjects independent of fed or fasting administration (observations and predictions <40 mg censored). The 5th and the 95th observed percentile (dashed black line) and corresponding model based 95% CI (light gray field). Lower panels: Observed fraction of observations indicating less than 40 mg remaining in tablet (black line) and model predicted 95% CI (gray field).

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Absorption and GI distribution Rate and extent of absorption for AZD0837 was found to be significantly higher for substance released in the stomach and absorbed in duodenum compared to substance released in the main part of the small intestine. The fraction absorbed through the gut wall in the duodenum was 70% compared to 25% in the rest of the small intestine. The typical rate of absorption in the duodenum was also significantly faster than the 3.3 h-1 estimated for the small intestine. In the ascending colon the extent of absorption was similar to that in duodenum but the rate of absorption was considerably slower, 0.2 h-1. Rate of absorption was even slower and less complete in the lower parts of colon. Neither rate nor extent of absorption was found to be significantly different between the transverse and descending colon.

Figure 16. Individual plots of plasma concentration and tablet GI position versus time for 3 out of 6 subjects in the MMM study. Individual plasma concentrations are depicted with open circles, population typical prediction with a dotted line and individual model prediction with a solid line. The gastro intestinal tablet position is indicated by a gray line represented on a secondary y axis.

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The AZD0837 estimate on distribution rate of released drug substance from proximal to distal stomach (K2T3) and gastric emptying (K3T4) was somewhat higher (20–50%) compared to what was previously established for the felodipine ER formulation. However, concomitant food intake was found to similarly decrease the rate of gastric emptying in both studies. The rapid absorption from the small intestine made distribution of released drug sub-stance between the duodenum, small intestine and ascending the colon neg-ligible and hence not possible to characterize. However, the slow rate of absorption in colon made it possible to characterize the rate of distribution between the ascending and transverse colon (K6T7 = 0.23 h-1).

Individual model fit to plasma concentration observations in the MMM study are exemplified in Figure 16 together with the observed tablet GI posi-tion. The internal validation utilizing VPC and pvcVPC demonstrated a good predictive performance across all the investigated routes of administration (i.e. ER tablet, i.v. infusion, oral solution and infusion/bolus dose in colon). The VPCs and a pvcVCP for the ER formulation are presented in Figure 17.

Figure 17. VPCs: observed plasma concentrations (open circles), observed median (solid black line), predicted non-parametric 95% CI for the median (gray field) and 90% prediction interval (dashed gray lines). pvcVPC: prediction and variance corrected plasma concentrations (open circles), observed 90% inter percentile range (dashed lines) and corresponding 95% CI (light gray fields).

pvcVPC: All tabletVPC: Fed tablet adm.

VPC: Tablet adm. followed by food

VPC: Fasting tablet adm.

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In vitro to in vivo predictions The final models for the AZD0837 tablet GI transit, drug release, absorption and disposition was used together to simulate an external validation dataset. The external dataset included administration of three different formulations for which no clinical data had previously been obtained (formulation A, B and C). The model describing tablet GI transit was initially used to simulate tablet GI transit profiles. The GI transit profiles were subsequently used as a covariate for simulations using the drug release and the absorption models.

A comparison of observations and model predictions for the validation dataset demonstrated a good agreement for formulation A and overall ac-ceptable predictions also for formulation B (fed and fasting) and C (Figure 18). For formulation B and C there was a possible deviation indi-cated around 5-8 h after dose intake. Approximately 2-3 subjects indicated an increase in plasma concentration during this interval that was not pre-dicted by the model.

Figure 18. Predictions of external validation dataset, study 4. Observed plasma concentrations (open black circles) connected with dotted black lines, observed median (solid black line), predicted non-parametric 95% confidence interval for the median (gray field) and 90% prediction interval (dashed gray lines).

Formulation A, fasting

Formulation B, fasting Formulation B, fed

Formulation C, fasting

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Paracetamol and sulfapyridine double marker The final model featured a compartment representing the stomach linked to a colon compartment via a series of four transit compartments representing the small intestine. Rate of GE (KG = KG,Active + KG,Passive) was for the fasting reference situation estimated to be 3.6 h-1, which corresponded to a GE half-life of 12 min. Food intake was found to have an initial stimulating ef-fect on GE that transited into an inhibitory effect (Figure 19). For the vehicle treated dogs this corresponded to a typical time of 8 min for 50% GE.

The estimated typical value for SITT, 6.8 h, was an extrapolation to a hy-pothetical longer fasting period than the 6 h before food intake that was the case in this study. Food intake was found to stimulate the rate of small intes-tinal transit in a time dependent fashion (Figure 19) that resulted in a median SITT of 2.7 h and 6.5 h for the fed and fasting administration respectively.

Figure 19. Food and drug effects on GE (KG = KG,Active + KG,Passive) and SITT (Ktr) illustrated for the fasting (upper row) and fed (bottom row) drug administration studies. Feeding of the dogs in the study with fasting condition was carried out at 6 h post dose.

The effects of atropine and erythromycin on SITT and GE were characte-rized using prior literature data on the half-life of the respective drugs and an Emax function (Equation 12 and 13). The final estimates of the drug effects under fed and fasting conditions are presented graphically in Figure 19.

fasting condition

Rate of gastric emptying (K ) G Rate of small intestinal transit (K )tr

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The saturable first pass metabolism implemented for paracetamol did explain the observed lower exposure that was associated with a lower rate of gastric emptying. The most rapid gastric emptying was seen in erythromycin treated fasting dogs, which was associated with a model predicted bioavailability of 90%. The corresponding bioavailability for vehicle and atropine treated dogs was 67% and 50% respectively. The slowest gastric emptying and therefore lowest bioavailability of paracetamol (44%) was seen for fed atropine treated dogs.

Figure 20. VPCs for sulfapyridine (SP) plasma concentration. Observed plasma concentrations (open circles), observed median (solid black line), predicted non-parametric 95% confidence interval for the median (grey field) and 90% prediction interval (dashed grey lines).

The predictive performance of the final model was evaluated with VPCs stratified for the different treatment cohorts and marker substances (Figure 20 and Figure 21). These VPCs focused on the median prediction due to the sparse sample size (6 dogs). To also diagnose the random effects of the model, pvcVCPs were applied to both the sulfapyridine plasma con-

Vehicle, fed

Vehicle, fasting Erythromycin, fasting

Erythromycin, fed Atropine, fed

Atropine, fasting

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centrations and to the paracetamol plasma concentrations pooled across the different the treatments (Figure 22). These plots revealed no obvious model misspecification either for the central trend (VPCs) or with respect to be-tween and within subject variability (pvcVPC).

Figure 21. VPCs for paracetamol (PCA) plasma concentration. Observed plasma concentrations (open circles), observed median (solid black line), predicted non-parametric 95% confidence interval for the median (grey field) and 90% prediction interval (dashed grey lines).

Vehicle, fed

Vehicle, fasting Erythromycin, fasting

Erythromycin, fed Atropine, fed

Atropine, fasting

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Figure 22. pvcVPCs for paracetamol (PCM) and sulfapyridine (SP) plasma concentration, across all treatment cohorts. Prediction and variance corrected plasma concentrations (open circles), observed median (solid black line), predicted non-parametric 95% confidence interval for the median (dark grey field), observed 90% inter percentile range (dashed lines) and corresponding 95% confidence interval (light grey fields).

pvcVPC: All PCMpvcVPC: All SP

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Discussion

Mixed-effect modeling methodology All investigated methods for handling censored observations (i.e. BQL) in mixed-effect models, with the exception of the M3 method, was associated with bias in parameter estimates. The bias ranged from minor to substantial enough to for example alter the judgment of clinical efficacy. Longer run-times and a lower rate of successful terminations is a major obstacle when applying the M3 methods, especially for more complex models (e.g. the GI transit model in Paper VI). In this situation it is essential that there are tools available that can diagnose the models predictive performance in the pres-ence of censored observations. VPCs performed without acknowledging the presence of a detection limit can be misleading. The approach with a double panel VPC that was outlined in this thesis has been demonstrated to be use-ful in identifying model misspecification. The bootstrap VPC introduced by Post, T.M., et al. is a slightly different extension to the VPC methodology that also handles censored observations [173]. With this method a 95% boot-strap confidence interval for the observed median is compared to the model predicted median. In theory, the same approach could also be applied, for example, to the 5th and 95th percentile to diagnose the variability as well as the central trend. However, if the dataset is not very large the more extreme percentiles will be dependent on observations from very few subjects. This is a weakness with that approach compared to the approach that we suggest that compares a model predicted 95% confidence interval to the observed percentiles.

The traditional VPC may fail to adequately evaluate a model’s predictive performance when the expected value or expected variability in observations within a bin differs due to variations in predictors such as time, dose or cova-riate values. The pcVPC and pvcVPC was designed to address such short-comings of the traditional VPC and hence act as a valuable addition to the PK/PD modeler’s diagnostic toolbox. One of the advantages lies in improved possibilities to diagnose the random effects of a mixed-effect model. An illustrative example of this are the models for in vivo drug release and plas-ma concentrations of AZD0837 (Figure 15 and Figure 17) where each study cohort was too small to adequately way diagnose whether the predicted be-tween and within subject variability was appropriate or not. With a tradition-al VPC pooled across the different treatment cohorts the majority of the ob-

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served variability could have been attributed to relationships to covariates such as tablet GI-position, and concomitant food intake. The VPC would therefore not to any large degree diagnose the random effects of the model. For these models not only did the population typical prediction vary between different observations within a bin but also the relative magnitude variability also differed quite substantially. Only doing a prediction correction (pcVPC) will in that case primarily diagnose the random effects with respect to the observations with the highest expected variability. By applying variability correction on top of the prediction correction all observations can be com-pared on the same scale. The examples investigated in Paper III did not highlight this advantage with pvcVPCs since the expected variability was similar across all observations. In these cases the pvcVPC and pcVPC will look largely identical.

Applying traditional VPCs to data following dose adjustments correlated to the dependent variable can be deceiving. This was demonstrated both for a simulated example (Figure 12) and a real life example of data following TDM dose adjustments. The issue arises from the fact that TDM dose ad-justments and the observed dependent variable are inherently correlated. Such correlations can sometimes be due to indirect effects and can be less obvious. Dose adjustment may be done based on the adverse events that occur in a dose/concentration dependent manner. This is not only a pheno-menon that occurs in studies including TDM, but in all clinical studies with possibilities for dose-adjustments based on an individual response. For these types of situations pcVPCs were demonstrated to be an especially useful diagnostic.

Mechanistic modeling of oral absorption The felodipine project (Paper I) outlined an approach to model tablet GI-transit, drug release and absorption properties along the GI tract based on MMM study data. This approach was further refined especially with regards to drug release when applied to the investigational drug AZD0837 (Paper IV and V). In the AZD0837 project the MMM data was complemented with data from local colon intubation studies adding robust information about the rate and extent of absorption from the colon. The model structure applied in these projects was based on the fact that the released substance for the inves-tigated compounds was highly soluble and rapidly dissolved throughout the GI tract. In application to drugs with poor solubility and/or low dissolution rate the models applied in Paper I and V would have to be modified to in-clude compartments differentiating the released and dissolved substance, as it is presented in Figure 3. Furthermore, such substances would likely neces-sitate the use of a series of transit compartments to describe the small intes-tine, similar to in Paper VI and in the ACAT [119] and ADAM [120] model.

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Further complexity such as saturable first pass metabolism etc. might also have to be added on a case by case basis.

The modeling of in vitro and in vivo drug release presented in Paper IV was novel in some aspects. The multivariate relationship between drug re-lease and experimental conditions in vitro are rarely described with conti-nuous functions. The advantage with this is that it can be used together with information about between subject variability with regards to pH and GI transit to predict population variability for in vivo drug release. In vivo ero-sion controlled drug release from HPMC formulations has been studied be-fore, primarily with gamma scintigraphy, and compared to in vitro dissolu-tion studies [182-184]. However, it has never previously been described as a function of the tablet GI position and the associated physiological conditions with a model structure based on in vitro experiments. The estimates of me-chanical stress along the GI tract correspond to rotational speed higher than what is typically recommended for in vitro predictions [124]. The actual investigated rotation speeds is however not of any great importance given that a linear relationship can be established between release rate (R) and rpm in the USP 2 apparatus. The estimates of equivalent rotation speed in the different GI regions are possibly dependent on the type of formulation that was used since the type of mechanical stress along the GI tract is quite dif-ferent from the one in a USP 2 apparatus. These estimates are therefore pri-marily thought to be representative for HPMC hydrophilic matrix formula-tions with erosion controlled drug release. Further investigations based on in vitro and in vivo drug release data from other types of modified release formulations are necessary in order to assess to what extent these estimates are formulation dependent.

The physiological prior information that was applied in linking in vitro to in vivo drug release could be improved in many aspects. The prior on pH along the GI tract could be improved by acknowledging the fact that the pH change dynamically after food intake. Dressman et al. has demonstrated that pH is at its highest just after food intake and after that falls back to the nor-mal fasting conditions in a mono-exponential fashion [185]. Furthermore, there could be advantages with investigating if there are any important corre-lations between pH in different GI regions.

The model describing tablet GI transit could also most likely be im-proved. Concomitant food intake has for both felodipine and AZD0837 been identified to prolong the tablet stomach residence time by decreasing the probability of moving from the proximal stomach to the distal stomach and from the distal stomach further into the small intestine. It has been hypothe-sized that there is a time dependent element to this interaction but due to the relative sparseness of observations this could not be characterized. Another effect of food intake that has been described in the literature, which could not be identified based on the available data, is the so called gastro-ileocecal reflex [87, 88]. A limitation with the GI transit models presented in this the-

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sis is that they do not predict any terminal excretion of non-disintegrated tablets with feces. This was a natural consequence of the fact that complete tablet disintegration was achieved prior to excretion in all investigated cases. However, this may limit the usefulness of the model in applications to for-mulations with significantly slower drug release where there is an important risk of incomplete drug release. A meta-analysis across several MMM and/or gamma scintigraphy studies with a variety of formulations would have an increased power to characterize the GI transit and in particular the food inte-raction.

Improvement with respect to the prior information on pH etc. along the GI tract and the model for tablet GI transit should contribute to more accu-rate predictions of plasma concentration profiles for newly developed MR formulations such as the ones presented in Figure 18. There are several stu-dies described in the literature that have studied the physico-chemical condi-tions in the GI tract and the GI transit of different kinds of solid, semi solid and liquid formulations [69, 84, 86]. However, to be able to use as a basis for a model that takes into account within subject correlations etc. the raw data from these studies should preferably be used.

A famous quote by George Edward Pelham Box (1987) [186] reads: “Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful”. The traditional deconvolution method for establishing IVIVC assumes that the rate and extent of absorption is con-stant. For many compounds and formulations this assumption makes the model so wrong that it is no longer useful for the main purpose of establish-ing IVIVC. A mechanistic approach such as the one described in this thesis, that can account for nonlinear absorption processes and regional differences in absorption, could be far more widely applicable.

The application of a semi-mechanistic modeling approach to data from the double marker studies under fed and fasting conditions revealed that accurate description of the drug and food effects on GE and SITT was not trivial. The complexity was driven by characteristics in the data that could not be easily perceived without application of simultaneous modeling of both paracetamol and sulfapyridine following both fed and fasting condi-tions. One of these complexities was the saturable first pass metabolism which has been described previously [187], also in the form of an association between rate of gastric emptying and bioavailability [188], but never has been considered when using paracetamol as a marker for gastric emptying. The general advantages with the semi-mechanistic approach compared to more empirical approaches to evaluate double marker studies are: (1) the characterization of saturable first pass elimination, (2) assessment of SITT independent of GE, (3) dynamic food intake on GE and SITT and (4) ac-knowledgment of changing effector drug concentration over time. These all together improve the characterization of drug-induced effects on GE and SITT based on the paracetamol and sulfapyridine double marker studies.

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The confidence in quantitative measures based on the semi-mechanistic approach could be improved further if the rate of conversion of sulfasalazine into sulfapyridine as well as the absorption rate of sulfapyridine was studied in vivo. Other experiments that would generate useful information is intra-venous administration of sulfapyridine to better support the disposition mod-el, and administration of PCM in a wide dose-range to better characterizing the saturable first pass metabolism. Using estimates from such studies as priors [12] in the analysis of future double marker studies would improve reliability in quantitative measures of SITT and GE. The use of mechanistic prior information could also allow for the simplification of the double mark-er study protocol.

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Conclusions

The complex interrelationship between tablet GI position, drug release, and absorption studied with the MMM technique is difficult to comprehend without the application of computer models. The application of a mixed-effect modeling approach to MMM study information has made it possible to quantitatively characterize the transit of solid dosage forms as well as re-leased drug substance, the in vivo drug release and the rate and extent of absorption throughout the GI tract. A model established for an AZD0837 ER formulation has been demonstrated to be useful in prospective in vitro to in vivo predictions of modified ER formulations. Mechanistic approaches similar to this have the possibility to establish IVIVC for substances and formulations where traditional methods are predestined to fail.

The modeling approaches applied in this thesis have a physiology based structure that makes it possible to discriminate between different mechanistic hypotheses e.g. differentiation between a direct or an indirect effect of food on drug release and absorption processes. A novel model to describe erosion controlled drug release was developed and used to characterize the effects of experimental conditions i.e. pH, ionic strength and rotation speed on the rate of drug release. The in vitro drug release model was combined with physio-logical prior knowledge about pH and ionic strength along the GI tract. When applying this to MMM observations of tablet GI transit and in vivo drug release a link between in vitro and in vivo drug release could be esti-mated in the form of in vitro experiment rotation speed equivalent to the mechanical stress in different GI regions. It is reasonable to believe that these results are generally applicable for in vivo extrapolations with regards to HPMC hydrophilic matrix formulations with erosion controlled drug re-lease.

A semi-mechanistic model applicable to paracetamol and sulfapyridine double marker observations was developed and applied to quantify pharma-cologically induced changes in gastrointestinal transit, under fed and fasting conditions. The developed model featured a saturable first pass metabolism for paracetamol. This has typically not been accounted for when paracetamol is used as a marker for gastric emptying and it was demonstrated how this and other flaws in the traditional analysis of double marker studies can bias the interpretation.

A part of the secondary aim was to advance nonlinear mixed-effects mod-eling methodology with respect to the handling of censored observations.

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The M3 method was found to be the best option for handling censored ob-servations when occurring in three distinctly different ways. A practical way of acknowledging the presence of censored observations in VPCs was intro-duced and shown to strengthen the diagnostic value.

The concept of prediction and variability correction in VPCs was intro-duced and applied across many different models. pcVPCs were found to add diagnostic value in application to studies with adaptive dosing (e.g. thera-peutic drug monitoring) and allow for the pooling of data across different treatment strata (dose levels etc.) hence improving the possibility for diag-nosing random effects in mixed-effect models. In cases when not only the typical prediction varied between observations in a single bin, but when also the expected variability varied between observations, the pvcVPC was found to be a suitable diagnostic tool.

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Populärvetenskaplig sammanfattning

Det vanligaste sättet att administrera läkemedel är i tablettform. Det är natur-ligt med tanke på den bekvämlighet det erbjuder och att magtarmkanalen har en naturlig funktion i att absorbera näringsämnen. Absorption av läkemedel från magtarmkanalen är en komplicerad process med betydande variation mellan individer men också inom en individ från en gång till en annan. Att förstå och kunna förutsäga absorption är särskilt viktigt för tabletter med en långsam frisättning av läkemedel, s.k. depåtabletter. Depåtabletter används främst för att åstadkomma en längre duration av läkemedelseffekten. Magne-tic Marker Monitoring (MMM) är en teknik baserad på inmärkning av tablet-ter med magnetiskt material vilket gör dem till svaga magneter som kan de-tekteras med känsliga sensorer. MMM tekniken användas för att studera hur tabletter förflyttar sig genom magtarmkanalen och hur de på sin väg frisätter läkemedel. Samtidigt med data på tablettens position och storlek mäts kon-centrationen av läkemedel i blodet. En viktig del i den här avhandlingen handlar om utvecklandet av matematiska datormodeller för att analysera data från MMM studier. Modellerna har syftat till att beskriva hur en tablett för-flyttar sig i magtarmkanalen och förstå sambandet mellan tablettens position och den hastighet med vilken läkemedel frisätts. Vidare beskriver modeller-na med vilken hastighet och i vilken utsträckning läkemedel absorberas från magtarmkanalen till blodet samt hur detta varierar mellan individer och olika delar av magtarmkanalen. De utvecklade modellerna har använts för att för-utsäga koncentrationer av läkemedel i blodet för nyutvecklade depåtabletter.

Utvecklandet av modeller för absorptionsstudier har åskådliggjort behovet av, och lett till, vidareutveckling av metodologi för att undersöka hur väl en modell beskriver det som den är tänkta att beskriva. Detta kallas för modell-diagnostik och är ytterst viktigt för att kunna säkerställa att slutsatser och förutsägelser som görs med hjälp av en modell är pålitliga.

Liten ordlista: in vitro latin: "i glas", om experiment i en artificiell miljö t.ex. provrör in vivo latin: "i det levande", om experiment i en levande organism PK Farmakokinetik = vad kroppen gör med läkemedlet PD Farmakodynamik = vad läkemedlet gör med kroppen GI Gastrointestinalkanalen d.v.s. magtarmkanalen Pharmacometrics Farmakometri = vetenskap som syftar till att med dator-

modeller beskriva och förstå PK, PD och sjukdoms utveckling.

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Acknowledgments

The work presented in this thesis was carried out at the Department of Phar-maceutical Biosciences, Faculty of Pharmacy, Uppsala University and made possible by financial support from AstraZeneca R&D, Mölndal, Sweden.

I would like to express my sincere gratitude to all who, in one way or anoth-er, have contributed to this thesis. Thanks to:

My supervisor Prof. Mats Karlsson for being a never ending source of knowledge and inspiration. Especially thanks for sometimes letting me go my own way even though it often was a waste of time. I have never had a better work place and hope that I will have the privilege of collaborating with you many more times in the future.

My co-supervisor Dr. Hans Ericsson who did all the supervising already before I even started my PhD training. All that you taught me about pharma-cokinetics and drug development has been a very valuable during the last years and will continue to be in the years to come.

My sponsor Global Head Dr. Eva Bredberg, if it weren’t for you there would have been no job for me at AstraZeneca and no PhD in Uppsala. I am forever grateful for the decisions you have made on my behalf. To my sur-prise I haven’t received any orders on what to do next.

Dr. Erik Söderlind and Prof. Werner Weitschies for bringing Magnetic Marker Monitoring studies of oral absorption to my attention and for seeing the benefit of applying a model based approach for evaluating them.

My long time roommate Dr. Johan Wallin for many good discussions and happy times inside and outside of work. Many thanks also to your lovely wife Ida for always making me feel welcome during my visits to Mörtö.

My second roommate Åsa Johansson for letting me participate in and win the “DN news-quiz-challenge”. Your willingness to always laugh at my jokes has been blessing for a “funny-guy wannabe” like me.

My last roommate and dear friend Elodie Plan whom I cherish and respect deeply.

Professor Margareta Hammarlund-Uddenaes for creating a good work envi-ronment at the department and for giving me plenty of review experience.

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Co-authors; Dr. Ulf Eriksson, Dr. Sandra Visser, Dr. Ahmad Al-Saffar, Lin-nea Sjödin and Dr. Andrew Hooker for valuable input and patience.

Everyone at School of Natural Sciences at University of Kalmar (today Lin-naeus University) for giving me a solid start on my scientific journey. It was a very fun and rewarding time, and I never for a second regretted the choice to study at University of Kalmar. Particular thanks to Sara Göransson who remains in my memory as the most clever person I ever met.

My distinguished friend Dr. Paul “Hilda” Westwood for your sense of hu-mor and for your outstanding assistance with reading through the thesis. Anytime you want to go and see Håkan tickets are on me. Also feel free to bring Iggy if you like!

The former master students; David Khan, Anders Pettersson and Catharina Alm for forcing me to develop my communication and collaboration skills. I am sure you taught me more than I ever taught you.

Co-workers on projects not included in this thesis but nevertheless very im-portant to me; Emilie Henin for the excellent work with trying to make fur-ther use of the modeling approaches originating from the felodipine project, Camille Vong for your admirable efforts regarding the MCMP project, Joa-kim Nyberg for slowly making me appreciate optimal design and for endless good scientific input to all projects.

My mentor and badminton partner Dr. Jakob Ribbing for letting me win some sets but never a match and for giving lots of good advice.

My close colleague Angelica Quartino for all the coffee and discussions on life in general and thesis writing in particular. When you read this, your own book will be just days away and all our worrying will feel very distant.

My fellow AZ-Uppsala PhD colleague Markus Fridén for well needed non-pharmacometrician feedback on the thesis.

My friendliest of friends Waqas Sadiq for all the pancakes, fishing, chess and for being so extraordinarily friendly.

My halftime seminar opponents Dr. Urban Fagerholm and Dr. Mats Mag-nusson for helping me get on the right track.

The software developers and technical staff that made it all possible, includ-ing; Dr. Kajsa Harling, Pontus Philgren, Dr. Andrew Hooker, Dr. Lars Lindbom, Prof. Niclas Jonsson, Magnus Jansson and Jerker Nyberg.

The designer Sebastian Bähring for the right to use the cover picture.

ALL the present and former colleagues at the department for making most work days interesting, educational and funny!

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Also a big thank you to ALL my family and friends outside of work, in-cluding in particular;

Robert for reminding me of the value of fine art and for your great humor.

Tore for sharing a particular type of humor, for toasting the party and for insights in to the absurd world of politics and national economics.

Stefan for calling in the middle of the night and being the person I can call in the middle of the night.

Per for all the times you invite me along to larger as well as smaller events. In the future I will try to come with more initiatives of my own.

Lisa for all the sushi and good talks (is it my or your time to pay?)

Svenne for introducing me to “KostymRACEing” and reminding me that a “doktors hatt” is nothing compared to a “hatttrick”.

Jimmy for being a lousy KostymRACEare but a really good friend.

The dinner club with Henrik, Jonas, Anders and Fredrik for keeping the Kalmar spirit alive.

All my friends and former colleagues in Mölndal/Göteborg for not complete-ly forgetting me even though I am lousy at keeping in touch.

Dr. Martina for showing that a willful “Smålänning” can get through a PhD even though it was tough every once in a while.

Hela ”tjocka släkten” inklusive, Kaisa, Curt, Helena, Jens, Felix, Hannes, Ingelöv, Hanna, Malin, Tord, Margareta, Niklas, Helen, Felicia, Ellen, Cla-ra, Magnus, Berit, Petter, Tommie och Isa m.fl. för att ni alltid visat intresse för det jag gjort och att så många av er verkar vilja komma till min fest.

Min fina syster Lotta för att man alltid kan skylla på dig och att för att vi alltid har varandra.

Mina kära föräldrar för att ni kompletterar varandra så väl och för att ni väs-sat min förmåga att ifrågasätta och tänka självständigt men samtidigt alltid stöttat mig i allt vad jag företagit mig.

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