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

Jiahui Feng1, Kin Yau Wong2,3, Chun Yin Lee2

  • 1Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, Canada.

Biometrical Journal. Biometrische Zeitschrift
|November 26, 2024

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel change-point logistic regression model using density ratio modeling. New tests are developed to detect change points and assess logistic model validity, showing promise in real-world data analysis.

Keywords:
biased samplingempirical likelihoodgoodness‐of‐fitlogistic regression modelscore test

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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.