Bootstrap confidence intervals for the optimal cutoff point to bisect estimated probabilities from logistic regression

Abstract

To classify estimated probabilities from a logistic regression model into two groups (e.g., yes or no, disease or no disease), the optimal cutoff point or threshold is crucial. While various methods have been proposed for estimating such a threshold, statistical inference is not generally available. To tackle this issue, we put forward several bootstrap based methods, including the conventional nonparametric bootstrap standard errors and the quantile interval. Special emphasis is placed on a more precise bagging estimator of the optimal cutoff point, for which a confidence interval can be obtained via the recently proposed infinitesimal jackknife method. We investigate the empirical performance of the proposed methods by simulation and illustrate their use via the analysis of a fertility data set concerning seminal quality prediction.