Decision Support Multi-objective evolutionary algorithm for donor–recipient decision system in liver transplants Manuel Cruz-Ramírez a,⇑ , César Hervás-Martínez a , Juan Carlos Fernández a , Javier Briceño b , Manuel de la Mata b a Department of Computer Science and Numerical Analysis, University of Córdoba, Spain b Liver Transplantation Unit, Hospital Reina Sofía, CIBERehd, Córdoba, Spain article info Article history: Received 20 October 2011 Accepted 4 May 2012 Available online 15 May 2012 Keywords: Artificial neural networks Generalised radial basis function Liver transplantation Multi-objective evolutionary algorithms Organ allocations Rule-based system abstract This paper reports on a decision support system for assigning a liver from a donor to a recipient on a waiting- list that maximises the probability of belonging to the survival graft class after a year of transplant and/or minimises the probability of belonging to the non-survival graft class in a two objective framework. This is done with two models of neural networks for classification obtained from the Pareto front built by a multi-objective evolutionary algorithm – called MPENSGA2. This type of neural network is a new model of the generalised radial basis functions for obtaining optimal values in C (Correctly Classified Rate) and MS (Minimum Sensitivity) in the classifier, and is compared to other competitive classifiers. The decision support system has been proposed using, as simply as possible, those models which lead to making the cor- rect decision about receptor choice based on efficient and impartial criteria. Ó 2012 Elsevier B.V. All rights reserved. 1. Introduction Today, hepatic transplantation is a well-accepted treatment for patients with terminal liver disease, but transplantation is strongly limited by the availability of suitable liver donors. The imbalance between supply and demand unfortunately results in many waiting-list deaths. Several efforts have been made to expand the donor pool and to prioritise recipients on the waiting-list better. The use of extended criteria donors (donors with extreme values of age, days in the intensive care unit, existence of inotropes, BMI and cold ischaemia time) as well as the adoption of the Model for End-stage Liver Disease (MELD) score [1] for prioritisation are good examples of these attempts worldwide. In recent years, more relaxed criteria have been used for donors, with an accompanying increased risk in recipient and/or graft losses in comparison to livers from non-extended criteria donors [2]. The MELD score model (based on the sickest-first principle) is the cornerstone of the current allocation policy and has been widely validated [3]. These methods have been developed to esti- mate the risk of death, taking into consideration the underlying disease and urgency of the receiving patient and assuming that all donor livers carry the same risk of failure, whereas, in general, this assumption is not true. However, the combination of multiple marginal factors can mean the loss of the graft [4], so these risks should be carefully analysed. Thus, these methods are poor predic- tors of mortality following transplants, because they have not jointly considered the characteristics of the donor, recipient and transplant. Based on this concept, Feng [5] has proposed a donor risk index (DRI), aimed at establishing the quantitative risk associ- ated with the sole use of combinations of donor characteristics. Predicting the first 1-year post-transplant survival graft could potentially play a critical role in understanding and improving the matching procedure between the recipient, the donor and the transplant. Our objective is to devise a liver allocation system, based on donor, recipient and transplant matching, that predicts recipient survival 1 year following liver transplantation. There are numerous motivations for developing this system: (1) current selection/allocation systems are based on the risk of waiting-list patient deaths and do not recognise distinctions in donor organ quality; (2) efforts to increase the number of organ donations are likely to result in a relatively high proportion of extended criteria donors; (3) matching donors and recipients may offer the prospect of predicting outcome at the time when a specific donor liver is allocated to a specific recipient; (4) differences in local acceptance rates and policies may be diminished; and (5) overall outcome and efficacy may improve. This liver allocation system will be developed using Machine Learning and Soft Computing methods, specifically Evolutionary Artificial Neural Networks (ANNs) [6,7]. ANNs have been an object 0377-2217/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2012.05.013 ⇑ Corresponding author. Address: Department of Computer Science and Numer- ical Analysis, University of Córdoba, Rabanales Campus, Albert Einstein Building 3rd Floor, 14071 Córdoba, Spain. Tel.: +34 957 218 349; fax: +34 957 218 630. E-mail address: mcruz@uco.es (M. Cruz-Ramírez). European Journal of Operational Research 222 (2012) 317–327 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor