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.
Keywords: biased sampling; empirical likelihood; goodness‐of‐fit; logistic regression model; score test.
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