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Ordinal classification or ordinal regression are classification problems in which the labels have an ordered arrangement between them. Due to this order, alternative performance evaluation metrics are need to be used in order to consider the magnitude of errors. This paper presents an study of the use of a multi-objective optimization approach in the context of ordinal classification. We contribute a study of ordinal classification performance metrics, and propose a new performance metric, the Maximum Mean Absolute Error (MMAE). MMAE considers per-class distribution of patterns and the magnitude of the errors, both issues being crucial for ordinal regression problems. In addition we empirically show that some of the performance metrics are competitive objectives, which justifies the use of multi-objective optimization strategies. In our case, a multi-objective evolutionary algorithm optimizes a artificial neural network ordinal model with different pairs of metrics combinations, and we conclude that the pair of the Mean Absolute Error (MAE) and the proposed MMAE is the most favorable. A study of the relationship between the metrics of this proposal is performed, and the graphical representation in the 2 dimensional space where the search of the evolutionary algorithm takes place is analyzed. The results obtained show a good classification performance, opening new lines of research in the evaluation and model selection of ordinal classifiers.

In 2014, we reported a model for donor-recipient (D-R) matching in liver transplantation (LT) based on artificial neural networks (ANNs) from a Spanish multicenter study (Model for Allocation of Donor and Recipient in España [MADR-E]). The aim is to test the ANN-based methodology in a different European health care system in order to validate it. An ANN model was designed using a cohort of patients from King's College Hospital (KCH; n = 822). The ANN was trained and tested using KCH pairs for both 3- and 12-month survival models. End points were probability of graft survival (correct classification rate [CCR]) and nonsurvival (minimum sensitivity [MS]). The final model is a rule-based system for facilitating the decision about the most appropriate D-R matching. Models designed for KCH had excellent prediction capabilities for both 3 months (CCR-area under the curve [AUC] = 0.94; MS-AUC = 0.94) and 12 months (CCR-AUC = 0.78; MS-AUC = 0.82), almost 15% higher than the best obtained by other known scores such as Model for End-Stage Liver Disease and balance of risk. Moreover, these results improve the previously reported ones in the multicentric MADR-E database. In conclusion, the use of ANN for D-R matching in LT in other health care systems achieved excellent prediction capabilities supporting the validation of these tools. It should be considered as the most advanced, objective, and useful tool to date for the management of waiting lists. Liver Transplantation 24 192-203 2018 AASLD.

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