Modeling Patients as Dynamical Systems: Evaluating the Efficiency of Kidney Transplantation through Multi-Stage Data Envelopment Analysis
Santos Arteaga FJ
Di Caprio D
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*Purpose: The occurrence of kidney graft loss is determined by a large set of variables interacting across the different stages of the transplantation process. This dynamic structure can be analyzed as a multidimensional network setting encompassing the behavior of these variables at every stage of the transplantation process. The resulting model should allow us to classify the patients based on their evolution through the process, identify the main variables leading to a potential graft loss on a per patient basis and generate clusters of patients based on the relations arising between their characteristics and the variables determining the potential success or failure of the transplant. *Methods: We focus on living donor kidney transplant (LDKT) in order to homogenize at least for one type of transplant. We implement a decision-engineering approach and model kidney transplant patients as dynamical network systems. As such, patients undergo three stages determining the potential causes for the loss of a graft after undergoing a transplant. The first stage consists of the pre-transplant conditions and is composed by 10 variables, ranging from immunological incompatibilities to the potential reasons leading to a kidney failure. The second stage describes the state of the patient at the time of the transplant and contains four variables, including different medications that may be administered when the transplant takes place. The third stage describes the post-transplant evolution and deals with 10 variables – accounting, among others, for the emergence of rejection episodes or the development of tumors. Two additional dynamical variables monitoring the renal function at different times throughout the process are also considered. We design a slacks-based three-stage Data Envelopment Analysis (DEA) model with parallel transformations to evaluate the resulting multi-stage dynamical system. *Results: 486 LDKT patients from our institution were evaluated within the 2006-2015 period with an average follow-up time of 44.64±30.9 months. The resulting evaluation matrix consists of 486 rows identifying the patients and 38 columns accounting for the different variables: 24 of them correspond to the three main stages of the transplantation process, 12 columns include the observations from the two renal function variables considered and the two final columns describe the output variables, namely, graft loss and its causes. The results displayed in this matrix allow us to identify and categorize clusters of patients based on the effects of different subsets of variables on their evolution through the transplantation process and the potential loss of the graft. We must note that the parametric approach inherent to standard regression methods does not allow to perform this type of analysis. The non-parametric quality of DEA allows to identify – on a per patient basis – each and every characteristic where an inefficiency arises relative to the reference benchmark defined by the whole set of data across all variables. *Conclusions: The efficiency matrix derived from the dynamic network DEA model implemented in the current study provides fertile ground on which to perform further analyses, ranging from standard correlation tests across specific variables to the use of neural networks so as to cluster the patients according to any subset of characteristics highlighted by the model.
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