STATISTICAL METHODS FOR ADAPTIVE DESIGNS - S4 - Friede... · 2017-11-14 · STATISTICAL METHODS FOR ADAPTIVE DESIGNS. Workshop on flexible designs for diagnostic studies. Göttingen,

STATISTICAL METHODS FOR ADAPTIVE DESIGNS

Workshop on flexible designs for diagnostic studiesGöttingen, 6-7 November 2017

Tim FriedeDepartment of Medical StatisticsUniversity Medical Center GöttingenGöttingen, Germany

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Collaborative work with Nigel Stallard, Nick Parsons and Thomas Homburg (Warwick)“BIostatistische Methoden zur effizienten Evaluation von Individualisierten Therapien (BIMIT)” funded by BMBF

WP C: Tim Friede, Marius Placzek, Roland Gera (Göttingen); Heinz Schmidli (Novartis)

"Innovative methodology for small populations research" (InSPiRe) funded by EU's FP7 (HEALTH 2013 – 602144)

WP3 led by Martin Posch (Vienna)“Identification und confirmation of biomarker-defined populations in the personalized pharmacotherapy” co-funded by BfArM

PIs Tim Friede, Jürgen Brockmöller (UMG), Norbert Benda, Julia Stingl (BfArM)

ACKNOWLEDGEMENTS

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MotivationLearning and confirming in clinical development

Overview of statistical methods for adaptive designsTreatment selection in adaptive designs

Comparison of methodsCase study in secondary progressive MSInterim decisions and early outcomes

Subgroup selection in adaptive designsMotivation: Biomarkers, Personalised medicineAdaptive enrichment designsInternal pilot studies in adaptive enrichment designs

OUTLINE

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LEARNING VS. CONFIRMING

Drug development process as two learning / confirming cycles (Sheiner, 1997)

First learning / confirming cycle (Phase I-IIa)

Learning about tolerated dose (Phase I)

Then confirming of efficacy of selected dose in selected group of patients (Phase IIa)

Second learning / confirming cycle (Phase IIb-III, IV)

Learning about optimal use in respresentativepatients (Phase IIb)

Then confirming of acceptable benefit / risk ratio (Phase III)

Traditionally separate studies for learning and confirming

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Drug development very expensive and risky with many compounds failing in late development phases

Adaptive designs recognized as a way to improve efficiency of drug development

FDA Critical Path Initiative

Industry led initiatives such as PhARMA working group

Combining trials of different phases into one study, e.g. adaptive seamless phase II/III design

Adaptations of interest include: treatment (or dose) selection, subgroup selection, sample size reestimation

ADAPTIVE SEAMLESS DESIGNS (ASD)

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sample size re-estimation

treatment (or dose) selection (combining Ph IIb/ III)

subgroup selection (predefined, possibly based on genomic biomarkers)

changing objectives, e.g. switching between non-inferiority and superiority

change of primary endpoint or analysis, . . .

ADAPTATIONS IN LATE STAGE CLINICAL TRIALS

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OUTLINE

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STATISTICAL METHODOLOGY FOR ASDrepeated testing

classical group sequential designs (e.g. Jennison & Turnbull 1999)

combining pre/ post adaptation data

(recursive) combination test (Brannath et al, 2002), conditional error function approach (Müller & Schäfer, 2001)

multiple hypotheses

closed test principle (Marcus et al, 1976), Bonferroni, . . .

combinations of these approaches in ASDs: e.g. weighted inverse normal method and closed test principle

COMBINATION TEST AND CLOSURE PRINCIPLE

Figure taken from Bretz et al (2006) Biometrical Journal

e.g. weighted inverse normal combinationfunction

Stage 1 data only

Stage 2 data only

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OUTLINE

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COMPARISON OF METHODS FOR TREATMENT SELECTION IN ADAPTIVE DESIGNS

Classical Dunnett

Single stage test

Combination test (Bretz et al, 2006)

Intersection hypotheses tested by Dunnett test

Inverse normal combination function

Adaptive Dunnett (Koenig et al, 2008)

Conditional error function approach based on Dunnett test

Group-sequential approach (Stallard & Friede, 2008)

Test statistic at the final analysis is the sum of the largest test statistics based on the data from each stage of the trial

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Under the global null hypothesis (Friede & Stallard, 2008)

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Under alternatives (Friede & Stallard, 2008)

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ADAPTIVE SEAMLESS PHASE II/III DESIGNIN SECONDARY PROGRESSIVE MS

Chataway et al (2011) MSJ

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ADAPTIVE SEAMLESS PHASE II/III DESIGNIN SECONDARY PROGRESSIVE MS

Chataway et al (2011) MSJ

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Sometimes the primary endpoint only available after long-term follow-up and recruitment relatively fast:

Adaptations need to be based on early outcome data

Example: PFS and OS in oncology (Jenkins et al, 2011)

Complete follow-up

Stage 1: Patients recruited before adaptation (regardless whether their follow-up extends beyond the interim analysis)

Stage 2: Patients recruited after adaptation

Discontinued follow-up

Conservative imputation of test statistic

Reference: Friede et al (2011)

ADAPTATIONS BASED ON EARLY OUTCOMES

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ADAPTIVE SEAMLESS PHASE II/III DESIGN IN SECONDARY PROGRESSIVE MS

Type I error rate control Sample size savings

Chataway et al (2011) MSJFriede et al (2011) SiM

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If for at least some patients early and primary outcomes are available, interim decisions can be improved by integrating the data of those patients from whom only early outcomes are available.

Further readingStallard N (2010). A confirmatory seamless phase II/III clinical trial design incorporating short-term endpoint information. Statistics in Medicine 29: 959–971.

Kunz CU, Friede T, Parsons N, Todd S, Stallard N (2015) A comparison of methods for treatment selection in seamless phase II /III clinical trials incorporating information on short-term endpoints. Journal of Biopharmaceutical Statistics 25: 170-189.

Kunz CU, Friede T, Parsons N, Todd S, Stallard N (2014) Data-driven treatment selection for seamless phase II/III trials incorporating early-outcome data. Pharmaceutical Statistics 13: 238–246.

INCORPORATING SHORT-TERM ENDPOINTS

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OUTLINE

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Definition by the Biomarkers Definitions Working Group (2001)

„A characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention.“

Very general definition

WHAT ARE BIOMARKERS?

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Biomarkers are used …

to diagnose diseases (or certain subtypes)

to predict disease course or response to treatment

to stratify populations

to monitor patients

as endpoints in clinical trials

WHAT ARE BIOMARKERS USED FOR?

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For an overview refer to recent systematic literature review by Ondra et al. (2015) on methods for subgroup identification and confirmation in clinical trials

Exploratory subgroup identification

attracted a lot of attention over the past years

several methods proposed

Here we assume …Biomarker-defined subgroup identified in exploratory study

Subgroup to be confirmed by independent data

Confirmation of treatment effect in selected population

SUBGROUP IDENTIFICATION

STRATIFIED MEDICINE

F S

Full population Sub-population

HYPOTHESES AND TEST STATISTICS

Subpopulation with prevalence

Denote standardised test statistics for testing , (no effect in full/subpopulation) by and

Under (no effect in full and subpopulation):

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Extension to several nested subgroups: prevalences ,

Under (no effect in any population)

Note: same structure as in group-sequential designs

HYPOTHESES AND TEST STATISTICS

Spiessens & Debois (2011) CCT

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In case of normally distributed data

Reference distributions for hypothesis tests

MVN: multivariate normal; MVT: multivariate T distr.; n total sample size; n(k) sample size of smallest subgroup; ksubgroups; k+1 hypotheses

NESTED SUBGROUPS: STATISTICAL ANALYSIS

Variances Equalacross subgroups

Unequalacross subgroups

Known ExactMVN

ExactMVN

Unknown ExactMVTdf=n - 2 (k+1)

Approx. / asympt.MVTdf=n(k) - 2 (k+1)

Placzek & Friede (2017) SMMR

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Practical applications: unknown and unequal variances most likely

NESTED SUBGROUPS: TYPE I ERROR RATES

Placzek & Friede (2017) SMMR

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Pocock (1977) Biometrika and Jennison and Turnbull (2000) propose (for group-sequential designs)

to calculate the critical values based on the multivariate normal distribution then to transform critical values to the corresponding boundary of the univariate t-distribution with n(i) – 2 degrees of freedom (based on actual sample size)Student’s t-tests to account for unknown variance using the critical values above

Note: (a) Ease of computation as multivariate normal distribution used (not multivariate t-distribution); (b) degrees of freedom vary across subgroups

ALTERNATIVE APPROACH

Graf et al (2017) (submitted)

Thresholds for hazard ratios (Jenkins et al., 2011)

ε-rule on z-statistics (Friede & Stallard, 2008; Kelly et al, 2005)

Bayesian decision tools (Brannath et al., 2009)

INTERIM SELECTION RULES

Table II from Jenkins et al (2011)

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ADAPTIVE ENRICHMENT DESIGN

F S

F and S

Futility stopping /Early success

S only (Enrichment)

F only

Stage 1 Stage 2

Interim analysis

Option

ENRICHMENT DESIGNS MORE POWERFUL

Friede et al. (2012) Stat Med

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Conditional error function approach by Friede et al (2012) based on (approximate) normal distribution of test statistics

Adapted to continuous data with unknown variances that might vary across subgroups using test strategies proposed in Placzek and Friede (2017) and Graf et al (2017)

CONDITIONAL ERROR FUNCTION APPROACH WITH CONTINUOUS ENDPOINTS

Placzek and Friede (2017) (in preparation)

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CONDITIONAL ERROR FUNCTION APPROACH WITH CONTINUOUS ENDPOINTS

Placzek and Friede (2017) (in preparation)

OPTIMAL TIME POINT FOR INTERIM ANALYSIS

Adaptive enrichment design with CEF approach

Simulation results for nsim=10,000 replications

n=400 subjects per group (treatment/placebo)

Under the alternative

Maximum in power after 40-50% of the subjects

0 0.2 0.4 0.6 0.8 1n1/N

0.55

0.65

0.75

0.85

pow

er

tau=0.5

tau=0.4

tau=0.3 eps=0 eps=1 eps=Inf

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Power / sample size depend among other quantities on nuisance parameters such as the variances of the outcomes in the subgroups and the prevalences of the subgroups. Knowledge of these nuisance parameters might be very scarce in the planning phase of such a trial resulting in a considerable risk of choosing an inappropriate sample size. These risks can be mitigated in an internal pilot study design

NESTED SUBGROUPS: INTERNAL PILOT STUDY

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Three step procedure:

Initial sample size calculation → N0

based on estimates of the standard deviation from previous studies

Sample size review

when n1=p N0 (e.g. p=1/2) patients completed the study

reestimation of sample size based on estimate of standard deviation from the n1 patients

Final analysis

based on all n1+n2 patients

INTERNAL PILOT STUDY (IPS) DESIGN (Wittes & Brittain,1990)

Early IA for blinded sample size reestimation

Later IA for enrichment decision / futility stopping (unblinding)

BSSR

Enrichment decision /Futility stopping

BLINDED SAMPLE SIZE REESTIMATION (BSSR) IN ADAPTIVE ENRICHMENT DESIGNS

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SOME REFERENCESBretz F, Schmidli H., König F, Racine A, Maurer W (2006) Confirmatory seamless phase II/III clinical trials with hypotheses selection at interim: General concepts. Biometrical Journal 48: 623–634.

Friede T, Parsons N, Stallard N (2012) A conditional error function approach for subgroup selection in adaptive clinical trials. Statistics in Medicine 31: 4309-4320.

Friede T, Parsons N, Stallard N, Todd S, Valdés-Márquez E, Chataway J, Nicholas R (2011) Designing a seamless phase II/III clinical trial using early outcomes for treatment selection: An application in multiple sclerosis. Statistics in Medicine 30: 1528-1540.

Friede T, Stallard N (2008) A comparison of methods for adaptive treatment selection. Biometrical Journal 50: 767-781.

Ondra T, Dmitrienko A, Friede T, Graf A, Miller F, Stallard N, Posch M (2015) Methods for identification and confirmation of targeted subgroups in clinical trials: A systematic review. Journal of Biopharmaceutical Statistics 26: 99-119.

Placzek M, Friede T (2017) Clinical trials with nested subgroups: Analysis, sample size determination and internal pilot studies. Statistical Methods in Medical Research (in press).

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STATISTICAL METHODS FOR ADAPTIVE DESIGNS - S4 - Friede... · 2017-11-14 · STATISTICAL METHODS FOR ADAPTIVE DESIGNS. Workshop on flexible designs for diagnostic studies. Göttingen,