A note on two novel easy-to-interpret feature effect measures for partial dependence plots in a classification setting

Classification of observations into one of several distinct categories is a common task in applied statistics, traditionally performed using parametric statistical models such as logistic regression. These parametric models are, however, often outperformed in terms of prediction accuracy by black box supervised learning models (BBSLMs). A drawback of BBSLMs is the lack of easy-to-interpret feature effect measures similar to the odds ratio (OR) for logistic regression models. The present paper derives two novel feature effect measures based on partial dependence plots for binary classification using BBSLMs: the relative risk of marginal effects (RRME) and the odds ratio of marginal effects (ORME). The performance and interpretation of these new measures are illustrated in an application studying the risk of death within 48 hours of admission among individuals admitted to hospital with a myocardial infarction. The BBSLMs are shown to have better predictive ability than the logistic regression models, with the RRME:s and ORME:s of death for the main risk factor anterior infarct both being 1.8, comparable to the OR of 1.9 for the logistic regression model. The RRMEs and ORMEs are also shown to be more robust in terms of being applicable also for observations with missing values for some features.