Additive Logistic Models as Interpretable Likelihood-Ratio Scores for AUC-Based Classification

Abstract

Classification is a common statistical task in many areas. In order to ameliorate the performance of the existing methods, there are always some new classification procedures proposed. These procedures, especially those raised in the machine learning and data-mining literature, are usually complicated, and therefore extra effort is required to understand them and the impacts of individual variables in these procedures. However, in some applications, for example, pharmaceutical and medical related research, future developments and/or research plans will rely on the interpretation of the classification rule, such as the role of individual variables in a diagnostic rule/model. Hence, in these kinds of research, despite the optimal performance of the complicated models, the model with the balanced ease of interpretability and satisfactory performance is preferred. The complication of a classification rule might diminish its advantage in performance and become an obstacle to be used in those applications. In this paper, we study how to improve the classification performance, in terms of area under the receiver operating characteristic curve of a conventional logistic model, while retaining its ease of interpretation. The proposed method increases the sensitivity at the whole range of specificity and hence is especially useful when the performance in the high-specificity range of a receiver operating characteristic curve is of interest. Theoretical justification is presented, and numerical results using both simulated data and two real data sets are reported.