Cost-sensitive performance metric for comparing multiple ordinal classifiers

The surge of interest in personalized and precision medicine during recent years has increased the application of ordinal classification problems in biomedical science. Currently, accuracy, Kendall's τb , and average mean absolute error are three commonly used metrics for evaluating the effectiveness of an ordinal classifier. Although there are benefits to each, no single metric considers the benefits of predictive accuracy with the tradeoffs of misclassification cost. In addition, decision analysis that considers pairwise analysis of the metrics is not trivial due to inconsistent findings. A new cost-sensitive metric is proposed to find the optimal tradeoff between the two most critical performance measures of a classification task - accuracy and cost. The proposed method accounts for an inherent ordinal data structure, total misclassification cost of a classifier, and imbalanced class distribution. The strengths of the new methodology are demonstrated through analyses of three real cancer datasets and four simulation studies. The new cost-sensitive metric proved better performance in its ability to identify the best ordinal classifier for a given analysis. The performance metric devised in this study provides a comprehensive tool for comparative analysis of multiple (and competing) ordinal classifiers. Consideration of the tradeoff between accuracy and misclassification cost in decisions regarding ordinal classification problems is imperative in real-world application. The work presented here is a precursor to the possibility of incorporating the proposed metric into a prediction modeling algorithm for ordinal data as a means of integrating misclassification cost in final model selection.