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

Area of Science:

• Biostatistics
• Statistical Modeling
• Epidemiology

Background:

• Logistic regression is widely used for binary outcomes with continuous covariates.
• Existing methods for change-point detection in logistic regression have limitations.
• Density ratio models offer an alternative framework for analyzing covariate distributions.

Purpose of the Study:

• To adapt density ratio modeling for change-point logistic regression.
• To develop novel statistical tests for change-point detection and logistic model validation.
• To evaluate the performance of proposed methods using simulations and real-world data.

Main Methods:

• Equivalence between logistic regression and two-sample density ratio models was utilized.
• Maximal score-type tests were developed for change-point detection.
• A Kolmogorov-Smirnov type test was proposed for logistic model assumption validation.
• Estimation and inference methods for the density ratio model were investigated.

Main Results:

• The density ratio modeling framework enables effective change-point analysis in logistic regression.
• Proposed maximal score-type tests demonstrate power in detecting change points.
• The Kolmogorov-Smirnov type test provides a tool for assessing logistic model fit.
• Simulation studies confirm the finite-sample performance of the developed methods.

Conclusions:

• The proposed change-point logistic regression approach using density ratio modeling is a valuable statistical tool.
• The developed tests offer improved methods for detecting structural breaks and validating model assumptions.
• The methodology is applicable to various fields, including HIV-1 transmission and oral cancer research.