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Dynamically weighted evolutionary ordinal neural network for solving an

imbalanced liver transplantation problem

Article  in  Artificial intelligence in medicine · February 2017

DOI: 10.1016/j.artmed.2017.02.004

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Artificial Intelligence in Medicine 77 (2017) 1–11

Contents lists available at ScienceDirect

Artificial Intelligence in Medicine

j o ur na l ho mepage: www.elsev ier .com/ locate /a i im

ynamically weighted evolutionary ordinal neural network forolving an imbalanced liver transplantation problem

anuel Dorado-Morenoa,∗, María Pérez-Ortizb, Pedro A. Gutiérreza, Rubén Ciriac,avier Briceñoc, César Hervás-Martíneza

Department of Computer Science and Numerical Analysis, University of Córdoba, Campus Universitario de Rabanales, “Albert Einstein Building”,hird Floor, 14071 Córdoba, SpainDepartment of Quantitative Methods, Universidad Loyola Andalucía, Escritor Castilla Aguayo 4, 14004 Córdoba, SpainLiver Transplantation Unit, Reina Sofía Hospital, Av. Menéndez Pidal, 14004 Córdoba, Spain

r t i c l e i n f o

rticle history:eceived 21 July 2016eceived in revised form 17 January 2017ccepted 5 February 2017

eywords:rtificial neural networksrdinal classification

mbalanced classificationurvival analysisiver transplantation

a b s t r a c t

Objective: Create an efficient decision-support model to assist medical experts in the process of organallocation in liver transplantation. The mathematical model proposed here uses different sources of infor-mation to predict the probability of organ survival at different thresholds for each donor–recipient pairconsidered. Currently, this decision is mainly based on the Model for End-stage Liver Disease, whichdepends only on the severity of the recipient and obviates donor–recipient compatibility. We thereforepropose to use information concerning the donor, the recipient and the surgery, with the objective ofallocating the organ correctly.Methods and materials: The database consists of information concerning transplants conducted in 7 dif-ferent Spanish hospitals and the King’s College Hospital (United Kingdom). The state of the patients isfollowed up for 12 months. We propose to treat the problem as an ordinal classification one, where wepredict the organ survival at different thresholds: less than 15 days, between 15 and 90 days, between90 and 365 days and more than 365 days. This discretization is intended to produce finer-grain survivalinformation (compared with the common binary approach). However, it results in a highly imbalanceddataset in which more than 85% of cases belong to the last class. To solve this, we combine two approaches,a cost-sensitive evolutionary ordinal artificial neural network (ANN) (in which we propose to incorporatedynamic weights to make more emphasis on the worst classified classes) and an ordinal over-samplingtechnique (which adds virtual patterns to the minority classes and thus alleviates the imbalanced natureof the dataset).Results: The results obtained by our proposal are promising and satisfactory, considering the overallaccuracy, the ordering of the classes and the sensitivity of minority classes. In this sense, both the dynamiccosts and the over-sampling technique improve the base results of the considered ANN-based method.Comparing our model with other state-of-the-art techniques in ordinal classification, competitive resultscan also be appreciated. The results achieved with this proposal improve the ones obtained by other state-of-the-art models: we were able to correctly predict more than 73% of the transplantation results, witha geometric mean of the sensitivities of 31.46%, which is much higher than the one obtained by othermodels.

Conclusions: The combination of the proposed cost-sensitive evolutionary algorithm together with theapplication of an over-sampling technique improves the predictive capability of our model in a significantway (especially for minority classes), which can help the surgeons make more informed decisions aboutthe most appropriate recipient for an specific donor organ, in order to maximize the probability of survivalafter the transplantation and therefore the fairness principle.

© 2017 Elsevier B.V. All rights reserved.

∗ Corresponding author.E-mail address: i92domom@uco.es (M. Dorado-Moreno).

ttp://dx.doi.org/10.1016/j.artmed.2017.02.004933-3657/© 2017 Elsevier B.V. All rights reserved.

dx.doi.org/10.1016/j.artmed.2017.02.004http://www.sciencedirect.com/science/journal/09333657http://www.elsevier.com/locate/aiimhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.artmed.2017.02.004&domain=pdfmailto:i92domom@uco.esdx.doi.org/10.1016/j.artmed.2017.02.004

2 Intelligence in Medicine 77 (2017) 1–11

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. Introduction

Liver transplantation is an accepted treatment for patientsho present end-stage liver disease. However, transplantation is

estricted by the lack of suitable donors, where this imbalanceetween supply and demand results in significant waiting listeaths. With the objective of approaching this problem, severalechniques have been proposed to find a better system to prioritizeecipients on the waiting list. The first attempt at developing a sys-em is the Donor Risk Index [1], which establishes the quantitativeisk associated to the surgery considering only donor information.he opposite methodology, and the pillar of the current allocationolicy, is the Model for End-stage Liver Disease (MELD) [2], whichnly considers the severity of the recipient.

Nonetheless, the above-mentioned methods cannot be consid-red good predictors of graft failure after transplantation, becausehey only take into account either characteristics of donors orecipients (but not both). Rana et al. [3] created a scoring systemo predict recipient survival three months after liver transplan-ation using information of both donor and recipient. Dutkowskit al. recently proposed a balance of risk score [4] also basedn donor and recipient characteristics. A rule-based system issed to determine graft survival one year after transplantation

n [5,6] using donor, recipient and transplanted organ character-stics. These studies show that artificial neural networks (ANN)erform better at this task than the rest of scores, showing veryood predictive capabilities at a higher time threshold. In this sense,ew trends in biomedicine have considered the use of machine

earning to approach different problems related to patient sur-ival [7–10] resulting in remarkable applications for science andedicine [11,12], which motivates their study in future work.ote that generally, donors are assigned to the candidates under

he greatest-risk according to MELD. Clearly, this policy does notllow the liver transplant team to match the donor to the recipientccording to principles of fairness and benefit, which could lead to aisk of unconscious gaming when trying to match marginal donorso urgent candidates [13].

This paper considers a liver transplantation dataset with datarom 1406 surgeries performed in seven Spanish transplant unitsnd the King’s College Hospital (UK). As stated before, this datasetncludes characteristics of donors, recipients and surgery, with theim of developing and constructing a global system for predictingraft survival, by means of artificial intelligence techniques. Thelassification problem is addressed using an ordinal classificationoint of view since the classes are ordered taking into account theime leading up to liver failure (in case of failure). The classes con-idered for the dataset are: (1) graft loss before the first 15 days,2) loss between 15 days and 89 days, (3) loss between 90 days and65 days, and (4) graft survival after 365 days. The 3-month and-year thresholds have been highlighted by experts as being theost pertinent in early graft loss [14,3,15–17]. As can be observed

n Fig. 1, these thresholds are also justified by the change of therend of cumulative frequencies of graft losses after 15, 90 and 365ays.

Several issues are usually taken into account in order to exploithe presence of this order when applying ordinal classification tech-iques. These issues can be all simplified in the following premise:he class ordering should be considered in all the processes for con-tructing the classification model, which involves the classificationraining strategy, the metrics to evaluate the performance of thelassifiers and even the preprocessing of the dataset.

To clarify the difference between standard classification and

rdinal classification, consider the problem of classifying villinjuries (Marsh classification) given the labels: {normal state, mildtrophy, marked atrophy, complete atrophy}. Clearly, an ordermong the categories can be appreciated, and there are also some

Fig. 1. Graph showing the cumulative frequency of graft loss. Note that a regressionanalysis is not feasible because of the high number of organs which survived the365 day threshold (for which, we do not have a label).

misclassification errors that should be more penalized. For exam-ple, misclassifying a complete atrophy with a normal state shouldbe far more penalized than misclassifying it as a marked atro-phy. Since this is a common learning issue, several approacheshave been proposed to tackle this paradigm in the domain of pat-tern recognition and machine learning over the years, the firstwork applying logistic regression dating back to 1980 [18]. Thisissue has generally been addressed by transforming ordinal scalesinto numeric values and solving the problem as one of standardregression or multinomial classification. However, as said, thereare several problems within this approach: on the one hand, thefact that, without a priori knowledge, the distance between dif-ferent classes is unknown, thus the assumption of equidistantlabels when performing standard regression may not hold; onthe other hand, as nominal classification does not consider thisorder information, misclassification errors are treated equally.Nonetheless, other works have approached the paradigm consider-ing the order information by means of threshold methods [19–21],which are based on the idea that some underlying real-valuedoutcomes exist (also called latent variable), although they areunobservable.

The liver transplantation problem tackled in this paper presentsand ordinal and highly imbalanced nature, which leads to a dif-ficulty in classifying minority classes, which are, in fact, themost important ones for this application (the ones associated toorgan failure). Imbalanced classification has been the focus of manymachine learning researchers in the past years, given the hindrancethat it usually poses for the learning machine. This paradigm isusually approached using a cost-sensitive approach (i.e. modifyingthe classification method) or using a resampling strategy (over-sampling the minority class or under-sampling the majority one).In our case, because of the complexity of the dataset, we propose tocombine these two common approaches in imbalanced learning:a cost-sensitive method and an over-sampling technique (both ofwhich are focused on ordinal classification problems). More specif-ically, a new fitness function is proposed for an evolutionary ordinalclassification algorithm [22], which dynamically updates theweights of the classes considering the worst classified class in eachgeneration. This classifier is used in conjunction with a recently

proposed algorithm for data over-sampling in ordinal domains [23].Note that an ordinal version of this dataset has also been consideredin a previous research [13]. However, in this paper, we improve theperformance of our previously developed method by proposing a

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ew evolutionary ANN technique, complement the study with andditional experiment and study the best model obtained in thexperiments.

The rest of the paper is organized as follows: Section 2 presentshe materials used for this paper, introducing evolutionary ANNsnd the dataset considered. Then, Section 3 explains the article pro-osal, including the model and the dynamic costs used, as well ashe methods used for ordinal over-sampling. Section 4 presentsnd discusses the database and the experimental results. Finally,he last section summarizes the main contributions of the paper,utlining some conclusions.

. Materials

This section presents the dataset used and provides a brief intro-uction about evolutionary ANNs.

.1. Dataset description

A multi-centered retrospective analysis was made of 7 Spanishiver transplant units. Recipient, donor and surgery characteris-ics were reported at the time of transplant. Patients undergoingartial, split or living-donor liver transplantation and patientsndergoing combined or multi-visceral transplants were excludedrom the study. Liver transplantation units were homogeneouslyistributed throughout Spain. The dataset constructed has 634 pat-erns (donor–recipient pairs) corresponding to the years 2007 and008. The proportion of combined transplant was 2.3% in bothohorts. The proportion of partial grafts was 0.9% and 9.1% in thepanish and British cohort, respectively. The few cases of com-ined transplantation were those of liver and kidney, which, ineveral series, have been reported to not decrease the outcomef the liver graft. We decided to include the partial graft but nothe living donor grafts because of two main reasons. Firstly, livingonation is performed in a very well-selected manner, with excel-

ent donors and with no cold ischemia time. These grafts could be tremendous bias. Besides, only King’s College and not the Span-sh cohort performs right-lobe adult-to-adult liver transplantation.econdly, partial adult grafts (pediatrics were excluded) have veryimilar results to whole grafts (see European liver transplantationegistry 2016). The only ones with worse outcomes are the full-eft-full-right splits, which are not included in these cohorts (onlyxtended rights). Probably, combined liver transplants (which, inact, are very few) may not be ruled by any allocation program, ashey have specific D–R matching rules. However, extended rightobe splits should account as whole grafts and, thus, be allocatedccordingly.

In addition, the dataset was completed with information aboutonor–recipient pairs from the King’s College Hospital (London),o perform a supranational study of donor–recipient allocation iniver transplantation. To obtain a similar number of patterns, onlyeported pairs of recipients over eighteen years of age betweenanuary 2002 and December 2010 were included. Thus, a datasetontaining 858 English donor–recipient pairs was collected. Inrder to merge the datasets, several variables were selected, 16ecipient variables, 17 donor variables and 5 surgically related vari-bles, as shown in Table 1.

All patients were followed from the date of transplant untileath, graft loss or completion of the first year after the liver trans-lant. The final dataset was comprised of 1406 patterns.

To solve the donor–recipient matching problem, the cumulativerequency of cases according to the dependent variable is repre-ented in Fig. 1. As can be checked, the dataset shows a significantegree of imbalance. The imbalance ratio (IR) is a measure of the

igence in Medicine 77 (2017) 1–11 3

imbalance degree of a class with respect to the rest of classes andis defined as:

IR(q) =∑

j /= qNjQ · Nq (1)

where Q is the number of classes and Nq is the number of patternsin class q. The IRs for the different classes are IR(C1) = 4.43, IR(C2) =5.12, IR(C3) = 5.12 and IR(C4) = 0.04.

2.2. Artificial neural networks and evolutionary algorithms

ANNs were created in the 50s, and are still under study dueto their high computational power. In [24], it is demonstratedthat they are universal approximators, i.e., they are capable ofapproximating any continuous function with a single hidden layer,provided they have enough neurons. This and other characteristicsmake them a very attractive option for researchers in the field ofartificial intelligence. Furthermore, they have been widely used inapplications for medicine such as [25–28].

ANNs need a training phase in order to adjust their weights,and thus, correctly model the output function. Generally, to trainthem, gradient descent algorithms (such as Backpropagation [29] orirProp [30]) are used, but there are other alternatives, such as evolu-tionary algorithms (EAs). EAs are computationally more expensivethan a gradient descent approach, but they are also much moreflexible when training an ANN [31].

With EAs [32], we can perform any operation on the neural net-work, e.g., deleting, modifying or adding a link, deleting or addingnew neurons, etc. Moreover, we can also establish a fitness functiondepending on the aspect of the problem considered. These featuresmake EAs able to optimize both the structure and weights of thenetworks [33,34] at the same time, focusing on those aspects ofthe problem that we pay interest to. Many researchers have shownthat EAs perform well for global searching, because they are capa-ble of finding promising regions in the whole search space, whilegradient descent methods perform a local search.

Finally, a widely used technique is the hybridization of EAs withgradient descent ones [35] in order to find a first optimal per-forming a global search, and then, optimize it using a local searchprocedure.

3. Methods

This section describes the ordinal ANN model, the classificationalgorithm proposed and the over-sampling techniques used to dealwith the imbalanced nature of the data.

The goal in ordinal classification is to assign an input vector xto one of J discrete classes Cj, j ∈ {1, . . ., J}, where there exists agiven ordering among the labels C1 ≺ C2 ≺ · · · ≺ CJ , ≺ denoting thisorder information. Hence, the objective is to find a prediction rule,C : X → Y, by using an i.i.d. training sample X = {xi, yi}Ni=1, where Nis the number of training patterns, xi ∈ X, yi ∈ Y, X ⊂ Rk is the k-dimensional input space, and Y = {C1, C2, . . ., CJ} is the label space.

3.1. Proposed ordinal ANN classifier

An adaptation of the Proportional odds model (POM) [18] toartificial neural networks is used in this work. POM is the extensionof binary logistic regression for dealing with ordered categories.Our adaptation is based on two elements: the first one is a second

hidden linear layer with only one node whose inputs are the non-linear transformations of the first hidden layer. The task of this nodeis to project the values into a line, in order to impose an order. Apartfrom this one-node linear layer, an output layer is included with one

4 M. Dorado-Moreno et al. / Artificial Intelligence in Medicine 77 (2017) 1–11

Table 1Main characteristics of the dataset: features considered, number of patterns and classes, etc.

Attribute name Number of patterns: 1406; number of classes: 4; number of features: 38

Type Value

RecipientAge Numeric [18,76]Gender Binary 0 = male; 1 = femaleBody mass index Numeric [14,68.3]Diabetes mellitus Binary 0 = absence; 1 = presenceArterial hypertension Binary 0 = absence; 1 = presenceDialysis at transplant Binary 0 = absence; 1 = presenceEtiology Nominal 0 = virus C cirrhosis; 1 = alcohol; 2 = virus B cirrhosis;

3 = fulminant hepatic failure; 4 = primary biliary cirrhosis;5 = primary sclerosing cholangitis; 6 = others

Portal thrombosis Ordinal 0 = no; 1 = partial; 2 = completeWaiting list time Numeric [0,1978]MELD (inclusion) Numeric [1,46]MELD (at transplant) Numeric [5,50]TIPS at transplant Binary 0 = absence; 1 = presenceHepatorrenal syndrome Binary 0 = absence; 1 = presenceUpper abdominal surgery Binary 0 = absence; 1 = presencePretransplant status performance Nominal 0 = at home; 1 = hospitalized; 2 = hospitalized in ICU;

3 = hospitalized in ICU with mechanical ventilationCytomegalovirus Binary 0 = absence; 1 = presence

DonorAge Numeric [10,86]Gender Binary 0 = male; 1 = femaleBody mass index Numeric [14.38,53.35]Diabetes mellitus Binary 0 = absence; 1 = presenceArterial hypertension Binary 0 = absence; 1 = presenceCause of exitus Nominal 0 = brain trauma; 1 = cerebral vascular accident; 2 = anoxia;

3 = deceased vascular after cerdiac death; 4 = othersHospitalization length in ICU Numeric [0,58]Hypotension episodes Binary 0 = absence; 1 = presenceHigh inotropic drug use Binary 0 = absence; 1 = presenceCreatinine plasma level Numeric [0.1,9.5]Sodium plasma level Numeric [98,187]Aspartate transaminase level Numeric [1,1090]Alanine aminotransferase plasma level Numeric [2,1400]Total bilirubin Numeric [0.06,4.2]Hepatitis B Binary 0 = absence; 1 = presenceHepatitis C Binary 0 = absence; 1 = presenceCytomegalovirus Binary 0 = absence; 1 = presence

Operative factorsMulti-organ harvesting Binary 0 = no; 1 = yesCombined transplant Binary 0 = no; 1 = yesComplete or partial graft Binary 0 = no; 1 = yesCold ischemia time Ordinal 0 = 12 hAB0 compatible transplant Binary 0 = no; 1 = yes

The end-point variable is the time leading up to liver failure: (1) before 15 days, (2) between 15 days and 3 months, (3) between 3 months and a year and (4) no graft failurepA t of 5

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resented after the first year.ll nominal and ordinal variables are transformed into binary ones, resulting in a se

ias for each class, whose objective is to set the optimum thresholdso classify the patterns in the class they belong to.

The structure of our model is shown in Fig. 2 which has twoain parts. The part at the bottom is formed by sigmoidal unit (SU)

eurons, where x = (x1, . . ., xk), is the vector of input variables, and is the number of variables in the database. W = {w1 . . . wM} is theatrix of weights of the connections from the input nodes to the

idden SU nodes (for each neuron, wj = {wj0, wj1, . . .wjk}, wj0 beinghe bias of the neuron), and � is the sigmoidal function.

The upper part of the figure shows a single node in the secondidden layer, which is the one that performs the linear transfor-ation of the POM model. Its result, f(x, �), where � = {W, ˇ1, . . .,

M}, is connected, together with a second bias, to the output layer,here J is the number of classes, and ˇ00, . . ., ˇ

J−10 are the thresh-

lds for the different classes. These J − 1 thresholds are able toeparate the J classes, but they have to fulfill the order constrainthown in the figure. Finally, the output layer obtains the outputsf the model, fj(x, �, ˇ

j0), for j ∈ {1, . . ., J − 1}. These outputs are

5 variables.

transformed into a probability (gj(x, �, ˇj0)), using the POM model

structure. gj(x, �, ˇj0) is the probability that each pattern has to

belong to the different classes, and the class with the greatest prob-ability is the one selected by the neural network. More details aboutthis neural network model and the corresponding model equationscan be checked in [36].

3.2. Training algorithm and proposed fitness function

In this section, the hybrid algorithm used to optimize the struc-ture and weights of the ANN is described. The aim of the proposedalgorithm is, firstly, to design an ANN with optimal structure, andsecondly, to calculate the optimal weights for the problem being

solved. It is a hybrid EA, in which, each G generations, the bestANN model is extracted and optimized by a gradient descent algo-rithm using the output error of the ANN. Later, that optimized ANNmodel is included in the next generation of the EA. In this way,

M. Dorado-Moreno et al. / Artificial Intell

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Fig. 2. Neural network model used for ordinal classification.

he algorithms hybridization follows a Darwinian principle [37].he algorithm is based on the proposed in [38], where the mainifference resides in the dynamic treatment of the class weights.

As this problem is of unbalanced ordinal nature, both algorithmsthe EA and the gradient descent mechanism), must be specificallydapted, so the following modification of the Mean Squared ErrorMSE) function is proposed, both for the fitness evaluation of theA and for the gradient descent error:

(�, ˇ0) = −1N

N∑i=1

J∑j=1

IM(Cj) · c(yi, j) · (gj(x, �, ˇj0) − y(j)i

)2, (2)

here several symbols must be clarified. yi = (y(0)i , y(1)i

, . . ., y(J)i

) is

1-of-J encoding vector of the label from pattern xi (i.e. y(j)i

= 1f the pattern xi belongs to class j, and 0 otherwise), yi is the cor-esponding index (i.e. yi = argj(y(j)i = 1)), ˇ0 = (ˇ10, . . ., ˇ

J−10 ) and �

re the vector of biases and the vector of parameters of the rankingunction, respectively, and c(yi, j) is an ordinal cost function in theollowing form:

(yi, j) ={

(J/2)(J − 1), if yi = j,|yi − j|, if yi /= j.

his cost function gives higher importance to the errors of the clas-ifier as the number of classes between predicted and true ranksncreases. For example, if a pattern is predicted to be a member oflass C1 and its true rank is class C4, the absolute difference woulde 3, which is a high cost. On the other hand, if a pattern is predicted

o be in class C3 and its true rank is class C4, the difference woulde only 1, a considerably smaller error than in the first case. Thisodification of the error function helps us reduce the magnitude

f the errors of the classifier in the ordinal scale, e.g. avoiding that

igence in Medicine 77 (2017) 1–11 5

patterns of class “365 days”. The value(J/2)(J − 1) corresponds to the maximum sum of the costs for a class(i.e. the sum of the costs for the extreme classes), in order to forcethe error of correctly classifying a pattern to be 0. Moreover, wemust also consider the imbalance dataset problem, so we considera dynamic cost (IM(Cj)). These dynamic weights substitute the staticweights proposed in [38], where the weights are fixed beforehandbased on the number of patterns per class.

In this paper, we propose to initialize the costs for each classinversely proportional to the number of patterns per class:

IM(Cj) =1 − NjN∑Jj=11 −

NjN

= N − NjN(J − 1) , j = 1, . . ., J,

where Nj corresponds to the number of patterns of class j. Thiscorresponds to the normalized imbalance ratio of the class. Thiswill give higher cost to the classes with less patterns, penalizingtheir misclassification more than the misclassification of patternsfrom the majority class.

There has been some attempts to modify the MSE metric tobe applied in imbalanced problems, e.g. in [39], where they set afixed cost based on the overlapping ratio and class distribution ratioobtaining competitive results. In our case, these costs are updatedevery G generations, based on the minimum sensitivity of the bestmodel for the worst and the best classified classes (with indexesp and q, respectively), in this way, the costs adapt to the currentclassification performance, instead of being fixed by some initialparameters:

p = argj min(Sj), q = argj max(Sj), j ∈ 1, . . ., J,IM(Cp)′ = IM(Cp)(1 − ˛)IM(Cq)′ = IM(Cq)(1 + ˛)where p and q the indexes of the worst and best classified classes,respectively, and ̨ is a value in the range [0, 1] which is set by theuser to configure the updating rate and Sj is the sensitivity of the jthclass for the best model of the population (i.e. the ratio of patternscorrectly predicted as belonging to the jth class). These sensitivitiesare obtained as:

Sj =100Nj

Nj∑i=1

(I(y∗i = yi)), j ∈ 1, . . ., J, (3)

where y∗i

is the label predicted by the model, yi is the correct label,Nj is the number of patterns in the jth class and I(·) is the indicatorfunction, returning 0 if the condition is false and 1 otherwise.

The idea is to make the EA focus on the class which has moreproblems to be correctly classified. This can be considered as an evo-lutionary (or dynamic) cost that will force the misclassified class,however small it may be, to have a strong impact on the fitnessfunction. A flowchart of the algorithm is shown in Fig. 3, whereLS ind . denotes local search individual, EA ind . evolutionary algo-rithm individual, the maximum number of generations is equal to150 and the value of G is 50 generations.

First, the ANNs population of the EA is initialized randomly andthe mutation operators, both structural (optimize weights) andparametric (optimize structure), are applied. Every generation, thepopulation is updated, maintaining the 10% of the best individualsfor the next generation, thus being an elitist algorithm. Every G = 50generations, the best individual of the population is taken and it isoptimized by the iRProp+ [40] algorithm, a local search method. Inthis way, the derivatives of the weighted error (see Eq. (2)) are usedto further improve the model (please, check more details about this

algorithm and the corresponding derivatives in [31,36]).

Once the best individual is optimized by the gradient descentalgorithm, that model is included again in the population. Thebest evolutionary and gradient descent solutions (Best Evo and

6 M. Dorado-Moreno et al. / Artificial Intelligence in Medicine 77 (2017) 1–11

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est iRProp+, respectively) are recorded. Then, the EA continuesearching for optimal ANN solutions for the problem until the nextradient descent optimization. Finally, in the last generation, theest models from all the reports obtained during the evolutionaryrocess is obtained and returned as the final solution.

The implementation of the ANN model and the training algo-ithm was based on neural net evolutionary programming (NNEP), aava framework for neural network evolution, which can be foundn KEEL environment.1.

.3. Ordinal over-sampling

As stated before, the ordinal nature of the classes should be takennto account even for preprocessing the data. In this sense, threever-sampling techniques in the context of ordinal classificationre used in this paper as a preprocessing step for the dataset [23].he main intuition behind this method is that the ordering struc-ure of the classes can be exploited when generating new syntheticatterns. A synthetic pattern in this case corresponds to a virtualonor–recipient pair, which we create to balance the class distribu-ion and make the classifier pay more attention to minority classes.hese virtual pairs are created using the information of other pairs,o new synthetic patterns are not totally virtual, but rather basedn the combination of two donors and two recipients. The order isxploited considering a neighborhood graph between the classes,hich aims to capture the underlying manifold of the ordinal label-

ng space. New patterns are generated on the paths that preservehe ordinal structure of this manifold and create a spatial continuityn the input space.

Roughly speaking, the over-sampling techniques consideredake use of different graph operations to create a representative

ata-driven manifold that exploits the order of the classes. Thetrategies tested in this paper are:

Ordinal graph-based over-sampling via neighborhood infor-mation using a probability function for the intra-class edges(OGO-NI). In this case, the manifold structure is constructed based

1 http://keel.es/.

e proposed EA.

on a simple neighborhood analysis, and new synthetic patternsare created using a probabilistic approach.

• Ordinal graph-based over-sampling via shortest paths using aprobability function for the intra-class edges (OGO-SP). The man-ifold is constructed using the previous mentioned neighborhoodanalysis, but it is refined computing the shortest paths in thegraph.

• Ordinal graph-based over-sampling via interior shortest paths(OGO-ISP). The technique for constructing the graph is the samethan in OGO-SP but, in this case, the probabilistic approach forconstructing new patterns is also used.

Further details about these methods can be consulted in [23].The software used for performing oversampling was developed inMATLAB and can be downloaded from our research group website.2

4. Results

This section presents the experimental part of this paper, wherenine different classification methodologies have been compared forthe purpose of predicting survival time post-transplant.

4.1. Evaluated methodologies

To tackle this donor–recipient allocation problem, the method-ology described in Section 3.2 has been referred to as Dynamicimbalanced ordinal neural network (DIM-ORNET). The experi-ments in this paper have been designed to compare severalmethodologies with this proposal:

• Ordinal neural network (ORNET). The original algorithm pre-sented in [22], where the fitness function is the one presentedin Section 3.2 without considering the cost IM(Cj).

•

Imbalanced ordinal neural network (IM-ORNET). In this case thefitness function is the one presented in Section 3.2, withoutconsidering the dynamic update of the costs (i.e. the methoddiscussed in [38]).

2 http://www.uco.es/grupos/ayrna/GBOforOR.

http://keel.es/http://keel.es/http://keel.es/http://keel.es/http://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforORhttp://www.uco.es/grupos/ayrna/GBOforOR

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the errors into account, although it led to reasonable results forminority classes. AMAE, however, mixes both ideas, and althoughthe GMS could be zero, minority classes are ordered in a better man-ner, which is the main purpose of the application. Nonetheless, the

M. Dorado-Moreno et al. / Artificial

Support vector classifier using the one-versus-one approach(SVC) [41], a state-of-the-art nominal classification methodology.Tree methodologies, which are gaining popularity in medicalapplications, because of their interpretability and good perfor-mance. Specifically, we considered Random forests (RF) [42] andGradient boosted trees (GBT) [43].Proportional odds model (POM) [18], i.e. a standard ordinal logis-tic regression method.Extreme learning machine for ordinal regression (ELMOR) [44],which corresponds to the adaptation to ordinal classification of avery popular non-iterative neural network training method.Error Correcting output codes with the utility cascade modeland Support vector machines (ECSVM), which is the methodpreviously proposed in [13] for tackling the same classificationproblem.Kernel discriminant leaning for ordinal regression (KDLOR) [19],which applies discriminant learning in the context of ordinal clas-sification.Reduction scheme for ordinal classification using Support vectormachines (REDSVM) [45], which approaches ordinal classifica-tion based on an augmented binary classification problem, usingSVMs.

As can be seen, seven of the eight methods considered for com-arison are ordinal, although only ECSVM considers the imbalancedature of the dataset, given the low amount of works that dealimultaneously with both problems.

.2. Evaluation metrics

Several measures can be considered for evaluating ordinal clas-ifiers. The most common ones in machine learning are the Meanbsolute error (MAE) and the Mean zero-one error (MZE) [46], beingZE = 1 − Acc, where Acc is the accuracy or correct classification

ate. However, these measures may not be the best option, forxample, when measuring performance in the presence of classmbalance [47], and/or when the costs of different errors vary

arkedly. The accuracy (Acc) is defined by:

cc = 100N

N∑i=1

(I(y∗i = yi)),

here I(·) is the zero-one loss function, yi is the desired output forattern xi, y∗i is the prediction of the model and N is the total num-er of patterns in the dataset. Acc values vary from 0 to 100, and

t represents global performance in the classification task. How-ver, it does not take the category order into account, and it is notecommended for imbalanced datasets.

The geometric mean of the sensitivities of each class (GMS) isn average of the percentages of correct classification individuallybtained for each class:

MS = J√√√√ J∏

j=1Sj,

here the sensitivities are obtained using Eq. (3).The average mean absolute error (AMAE) [47] is the mean of

AE classification errors throughout the classes, where MAE is theverage absolute deviation of the predicted class from the true classin number of categories on the ordinal scale). It is able to mitigatehe effect of imbalanced class distributions. Let MAEj be the MAEor a given jth class:

igence in Medicine 77 (2017) 1–11 7

MAEj =1Nj

Nj∑i=1

|O(yi) − O(y∗i )|, 1 ≤ j ≤ J,

where O(Cj) = j, 1 ≤ j ≤ J, i.e. O(yj) is the order of class label yj. Then,the AMAE measure can be defined in the following way:

AMAE = 1J

J∑j=1

MAEj.

MAE values range from 0 to J − 1, as do those of AMAE.These three performance metrics briefly summarize the most

important aspects of confusion matrices: Acc giving an idea of theglobal performance, GMS focusing on the performance of minorityclasses and AMAE reflecting the mean magnitude of errors in theordinal scale.

4.3. Experimental setting

For evaluating the results, a stratified 10-fold technique has beenused to divide the data, and the results have been taken as the meanand standard deviation of the measures for the test sets over the 10obtained models.

The parameters for all methods (except for the ORNET method-ologies) have been chosen using a nested 5-fold cross-validationover the training set (independent of the 10-fold technique). Thefinal parameter combination was the one which obtained, in mean,the best average performance for the 5 validation sets of this nested5-fold cross-validation, where the metric used was the AMAE. Thetest sets were never used during model selection.

The parameters used during model selection are now specified.The kernel selected for all the kernel methods (SVC, ECSVM, KDLOR

and REDSVM) was the Gaussian one, K(x, y) = exp(

− ‖x−y‖2�2

),

where � is the kernel width. For every tested kernel method, thekernel width was tuned within the range � ∈ {10−3, 10−2, . . ., 103},as well as the cost parameter associated to SVM-based methods,C ∈ {10−3, 10−2, . . ., 103}. For the ELMOR methodology, the sig-moidal units were used, and the number of hidden neurons wasselected within the values H ∈ {5, 10, 20, 30, 40, 50, 60, 70, 80,90, 100}. The cross-validation procedure used for these methods isclarified in Fig. 4.

The AMAE metric was used for model selection for all thesemethods because cross-validating by Acc led to very poor resultsin this application (poor results in terms of the minority classes).Cross-validating by GMS does not take the ordinal magnitude of

Fig. 4. Diagram of the 5-fold cross-validation used for SVC, ECSVM, KDLOR, REDSVMand ELMOR methodologies.

8 M. Dorado-Moreno et al. / Artificial Intelligence in Medicine 77 (2017) 1–11

Table 2Average and standard deviation (mean ± st. dev) of Acc, GMS and AMAE results forthe test sets.

Method Input features Acc (%) GMS (%) AMAE

DIM-ORNET Donor 81.70 ± 2.05 0.00 ± 0.00 1.522 ± 0.063DIM-ORNET Recipient 81.27 ± 1.64 0.00 ± 0.00 1.492 ± 0.074DIM-ORNET Donor + surgery 80.00 ± 1.21 0.00 ± 0.00 1.478 ± 0.065

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Table 4Average and standard deviation (mean ± st. dev) of Acc, GMS and AMAE results forthe test sets.

Method Preprocessing Acc (%) GMS (%) AMAE

ORNET Original 71.84 ± 3.15 0.00 ± 0.00 1.393 ± 0.078ORNET OGO-NI 66.24 ± 3.05 5.03 ± 10.74 1.396 ± 0.116ORNET OGO-SP 66.74 ± 3.21 4.4 ± 9.27 1.431 ± 0.089ORNET OGO-ISP 68.23 ± 4.96 2.62 ± 8.28 1.393 ± 0.078IM-ORNET Original 84.85 ± 0.91 0.00 ± 0.00 1.501 ± 0.002IM-ORNET OGO-NI 69.08 ± 3.54 5.29 ± 11.17 1.367 ± 0.072IM-ORNET OGO-SP 71.13 ± 2.99 7.47 ± 12.08 1.354 ± 0.113IM-ORNET OGO-ISP 66.95 ± 6.09 2.66 ± 8.41 1.421 ± 0.092DIM-ORNET Original 77.09 ± 2.76 7.55 ± 11.33 1.365 ± 0.099DIM-ORNET OGO-NI 71.84 ± 2.58 14.97 ± 13.17 1.259 ± 0.079DIM-ORNET OGO-SP 75.35 ± 2.97 13.52 ± 12.99 1.313 ± 0.112DIM-ORNET OGO-ISP 70.37 ± 4.03 10.98 ± 13.23 1.332 ± 0.110ELMOR Original 85.21 ± 0.27 0.00 ± 0.00 1.500 ± 0.000ELMOR OGO-NI 62.09 ± 3.94 0.00 ± 0.00 1.336 ± 0.063ELMOR OGO-SP 64.58 ± 2.87 2.13 ± 6.72 1.294 ± 0.101ELMOR OGO-ISP 61.39 ± 8.81 0.00 ± 0.00 1.322 ± 0.087ECSVM Original 66.28 ± 4.08 2.28 ± 7.20 1.333 ± 0.109ECSVM OGO-NI 83.00 ± 1.67 0.00 ± 0.00 1.493 ± 0.057ECSVM OGO-SP 83.00 ± 2.16 0.00 ± 0.00 1.503 ± 0.044ECSVM OGO-ISP 83.00 ± 1.25 0.00 ± 0.00 1.503 ± 0.041KDLOR Original 50.50 ± 3.96 5.22 ± 11.05 1.355 ± 0.159KDLOR OGO-NI 54.56 ± 4.31 2.79 ± 8.81 1.206 ± 0.064KDLOR OGO-SP 54.70 ± 4.85 0.00 ± 0.00 1.240 ± 0.078

TA

DIM-ORNET Recipient + surgery 76.45 ± 1.69 0.00 ± 0.00 1.439 ± 0.066DIM-ORNET All variables 77.09 ± 2.76 7.55 ± 11.33 1.365 ± 0.099

se of AMAE or GMS usually leads to worse results for Acc (which isbvious, given the imbalanced nature of the data). Finally, it shouldlso be mentioned that because of the definition of the set of thresh-lds in KDLOR (these are not optimized, they are set to the middleoint between two consecutive and projected classes), this methodsually obtains better results for minority classes and worse resultsor global Acc.

For the ORNET methodologies, the hidden layer was composedy sigmoidal basis functions, where the minimum number of hid-en neurons was 20 and the maximum was set to 30. The maximumumber of hidden neurons was always set to 10 units more to givehe EA enough freedom to search for the optimum classifier. Theopulation size and the number of generations were set to 500. ForIM-ORNET G is 500 and ̨ to 0.05.

Several works in the literature have considered the over-ampling of classes that present an imbalanced ratio (IR) higherhan 1.5 [48,49]. This threshold (IR = 1.5) is used, given that it isuggested in the literature that it is the point from which the imbal-nce of the data starts to hamper the learning phase. We use thishreshold to decide if a class is imbalanced with respect to the restf classes. Once that we have decided this, we compute the num-er of necessary patterns to include, so that the IR of that class is

ower than the initial threshold. This is, we add new patterns untile consider that the class is balanced. In this case, we over-sample

he first three classes of the dataset, which present a pattern dis-ribution of {69, 75, 64}, as opposed to the majority class which isomposed of 1198 patterns.

.4. Results

As a first experiment and in order to analyze the necessity ofonsidering both donor and recipient characteristics for this appli-ation, different versions of the original dataset have been createdombining these blocks of features. In this way, we test the impor-ance of each block and verify if all of them are relevant for the

odel, or if we can solve the problem avoiding some of the char-cteristics, making the model simpler.

The proposed model has been trained and generalized with eachf the new datasets, obtaining the test results shown in Table 2.ote that all the results included in this table are obtained using

he original version of the test sets, the oversampling method being

nly applied to the training sets. The characteristics consideredre those shown in Table 1, where All variables corresponds to allhe features, Donor and Recepient characteristics corresponds tohe ones considered in this table, and Surgery characteristics are

able 3ccumulated test confusion matrices for each variable group tested from the 10-fold exp

KDLOR OGO-ISP 54.27 ± 5.33 3.05 ± 9.63 1.224 ± 0.085The best result is in bold face and the second best result is in italics.

those related to Operative factors. It can be seen that the resultsobtained with a single block of variables (both when using onlydonor or recipient characteristics) are not suitable for the problem,because they both classify nearly all the patterns as belonging tothe majority class (GMS = 0% and AMAE = 1.50, i.e. a trivial classi-fier, which however leads to a very high Acc). This effect is usuallychecked by considering the Area Under the ROC curve (AUC), butthis evaluation metric is restricted to binary classification prob-lems. There are some extensions of ROC to multi-class problems,such as [50,51], which seem attractive because of the benefits ofROC analysis, but their exponential computational complexity asfunction of the number of classes is very restrictive [52,53]. Thatbeing the reason why we consider GMS in this paper (comple-mented by AMAE to check the magnitude of the errors). It is clearhow adding information about the surgery is necessary to improvethe results, surpassing the AMAE = 1.50 limit, which means thatminority classes are starting to be differentiated from the majorityone. In conclusion, observing the results corresponding to considerall features, which lead to a reasonable AMAE and a GMS differ-ent from 0%, all the variables analyzed in Section 2 are necessaryto provide a suitable model to solve the organ allocation problem.These comments about the variable sets are reinforced by the con-fusion matrices shown in Table 3, where it can be observed thatall variables are needed in order to correctly classify at least somepatterns from all classes.

Once we have validated these three sources of information,we include an experiment that tests different algorithms for thisproblem. In this sense, Table 4 shows the results obtained forthe different algorithms considered with the four versions of the

erimental design.

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M. Dorado-Moreno et al. / Artificial

ataset (the original one and three versions obtained by applyinghe three over-sampling methods to the different training sets, asresented in Section 3.3). Observing the results in Table 4, differentethods can be emphasized depending on the evaluation metric

onsidered. In this dataset, it is important to obtain a trade-offetween all the metrics included, aiming at an accurate model thatlso respects the classification and order of minority classes. Notehat a GMS = 0% means that at least one class is always misclassified,nd this is the case of SVC, POM, REDSVM and tree methodologiesRF and GBT), so they are not included in the table. If we only focusn Acc, the best model is obtained by ELMOR using the originalataset, but this result, examining GMS and AMAE scores, showshat nearly all the patterns are classified in the predominant classthe majority one). Note that most classifiers are in this case trivialnes (especially the ones not included in the table), showing theifficulty of the considered application.

It can be seen that the application of the different over-samplingechniques improves the GMS results and obviate trivial models inome cases. This is especially true when combined with the evolu-ionary ordinal neural network methodologies (ORNET, IM-ORNETnd DIM-ORNET). It can also be seen that the results obtained byIM-ORNET improve those obtained for the same problem in pre-ious studies (ECSVM [13] and IM-ORNET [38]). Furthermore, these of dynamic weights in the evolution improve the results in thisataset for both GMS and AMAE.

The best AMAE model is obtained by KDLOR using the OGO-NIechnique. The corresponding GMS score is 2.79% in average (whichs, at least, higher than 0%), and whose AMAE shows that this classi-er tends to respect the order of the label space (i.e., generally,

t does not misclassify a pattern belonging to class 0 in class 3,or example) at the cost, however, of sacrificing Acc, whose resultround 50% is not acceptable. In this way, the classifier is biasedgainst predicting almost all patterns as belonging to intermediatelasses (which indeed minimizes AMAE). Note that the combina-ion of ECSVM and the over-sampling approaches does not resultn a satisfactory result. This is due to the formulation of this clas-ifier, in which the imbalanced nature of the data is already takennto account, which is the reason why, in the original data, ECSVMerforms better than in the over-sampling case (where the data isalanced by the introduction of synthetic examples). When com-ining DIM-ORNET with the OGO-ISP over-sampling technique, theodel with the best trade-off is obtained (i.e. a relatively high Acc,

he best result in GMS and an acceptable AMAE).In conclusion, it can be affirmed that the dynamic weight pro-

osal improves the results of the base algorithm in most cases,btaining a GMS higher than 5% considering the three over-ampling techniques and competitive Acc and AMAE.

.5. Interpretation of the best model obtained

For model interpretation, we select the best algorithm (DIM-RNET with OGO-NI) and we extract information from the bestNN model among the 10 folds. The results obtained in this case are

he following: Acc = 73.57%, GMS = 31.46% and AMAE = 1.155, whichre very competitive.

To interpret the ANN model used, we consider the number ofimes that each variable has been used in the model and the mean ofhe absolute values of the associated ANN-weights. In this case, theariables that have a mean weight higher than the average and thatre selected more times than the average are: etiology (recipient),ortal thrombosis (recipient, no), MELD (inclusion and at trans-lant), hepatorrenal syndrome (recipient), gender (donor), body

ass index (donor), cause of exitus (donor), sodium plasma level

donor), aspartate transaminase level (donor), hepatitis C (donor),ulti-organ harvesting (surgery), combined transplant (surgery),

omplete or partial graft (surgery) and cold ischemia time (surgery).

igence in Medicine 77 (2017) 1–11 9

It can be appreciated that selected features belong either to therecipient, donor or surgery, which emphasizes the need of using allthese sources of information. Concerning the selected features, itcan be seen that there are different conditions (portal thrombosis,hepatorrenal syndrome and hepatitis C) which are important forthe prediction of organ survival post-transplant.

Two of the features selected also belong to the factors ofexpanded criteria donors (donors with extreme values of age, daysin the intensive care unit (ICU), inotrope usage, body mass index(BMI) and cold ischemia time), characteristics that result in anincreased risk of recipient and/or graft losses compared to the riskassociated with the use of livers from non-extended criteria donors[54,55].

Moreover, the variables that are selected fewer times than themean and that also present a mean weight lower than the meanare: gender (recipient), dyalisis at transplant (recipient), pretrans-plant status performance (recipient), diabetes mellitus (donor),hypotension episodes (donor), high inotropic drug use (donor),gender (donor), alanine aminotransferase plasma level (donor) andcytomegalovirus (donor).

Finally, to conclude the interpretability of the model, it must benoted that, as this is a threshold-based model, the output of the ANNmodel for every transplant can be observed, giving us informationabout the robustness of the result. If the output of a pattern is farenough from the class border (threshold), the medical expert canassume that the result is more robust, while in the opposite case,where the output of a pattern is close to a class border, that patterncould jump to the next (or previous, depending on which borderthe pattern is) class easily. This will also help the expert in his/herdecisions.

5. Discussion and conclusions

This paper tackles the problem of developing an organ allo-cation system in liver transplantation using machine learning. Tosupport the medical expert with finer-grain information, the classi-fication problem is considered from an ordinal classification pointof view, where 4 classes are used, discretizing the time leadingup to organ failure. More specifically, the dataset is composed ofdonor–recipient pairs of 7 transplantation units in Spain and onehospital in the United Kingdom, and considers characteristics of thedonor, the recipient and the surgery. The classification problem istackled by an ordinal evolutionary ANN that takes into account theimbalanced nature of the data by the definition of a dynamic fitnessfunction. This method is considered in conjunction with an ordi-nal over-sampling approach. The good synergy of these strategieswidely used for imbalanced classification is shown in the results ofour paper.

From the results in the experiments of this paper, several con-clusions can be extracted. First of all, some of the methodologieshave been discarded, which, due to the complexity of the problemconsidered, obviated one of the classes in the dataset, most of themobtaining trivial classifiers. This usually results in an outstandingAcc score, given that 85% of the patterns belong to the majorityclass, while these classifiers are useless for prediction. Moreover,it can be observed that the use of an ordinal over-sampling tech-nique improves the results in imbalanced domains with respect tothe original dataset (not only in the proposed methodology, butalso in the other methodologies tested). In this case, our proposalof combining ordinal over-sampling (to palliate the unbalance ofthe pattern distribution) with the idea of adding a dynamic fitness

to the EA (which helps the model to give more importance to theworst classified class at the moment) results in the best results.As said, the proposal (DIM-ORNET) also improves the results withrespect to previous works, obtaining a good balance in performance

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0 M. Dorado-Moreno et al. / Artificial

or all the metrics considered (concerning the overall classification,he classification of minority classes and the ordering of the data).

As stated before, the results obtained by the complete set of usedethodologies indicate the complexity of the problem dealt within

his study in which the proposal was able to obtain reasonably goodesults.

This model could be tested in the practice analyzing the result ofach transplant performed (i.e. without changing the current policyut analyzing if the model predicts the survival accurately in a realorld scenario). Note that this approach does not intend to sub-

titute the medical professional, but rather provide him/her withn accurate prediction model which serves as a decision-supportystem. Moreover, our model can also be complemented with theELD score, to also consider other factors, such as the severity of

he recipient.Future research lines comprise the acquisition of more data to

reate a supranational dataset and the simulation of the model in more controlled environment to analyze its behavior.

cknowledgements

This work has been partially subsidized by the TIN2014-54583-2-1-R and the TIN2015-70308-REDT projects of the Spanishinisterial Commission of Science and Technology (MINECO,

pain), FEDER funds (EU), the P11-TIC-7508 project of the “Juntae Andalucía” (Spain), the PI-0312-2014 project of the “Fundaciónública andaluza progreso y salud” (Spain) and the PI15/01570roject (Spain, “Proyectos de Investigación en Salud”). Manuelorado-Moreno’s research has been subsidized by the FPU Predoc-

oral Program of the Spanish Ministry of Education, Culture andport (MECD), grant reference FPU15/00647.

We would also like to thank Astellas Pharma Company for theirartial support in the data acquisition.

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