A Semiparametric Two‐Sample Density Ratio Model With a Change Point

Abstract

The logistic regression model for a binary outcome with a continuous covariate can be expressed equivalently as a two‐sample density ratio model for the covariate. Utilizing this equivalence, we study a change‐point logistic regression model within the corresponding density ratio modeling framework. We investigate estimation and inference methods for the density ratio model and develop maximal score‐type tests to detect the presence of a change point. In contrast to existing work, the density ratio modeling framework facilitates the development of a natural Kolmogorov–Smirnov type test to assess the validity of the logistic model assumptions. A simulation study is conducted to evaluate the finite‐sample performance of the proposed tests and estimation methods. We illustrate the proposed approach using a mother‐to‐child HIV‐1 transmission data set and an oral cancer data set.