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Model-checking techniques for stratified case-control studies.

Patrick G Arbogast1, D Y Lin

  • 1Department of Biostatistics, Vanderbilt University, S-2323 Medical Center North, Nashville, TN 37232-2158, USA. patrick.arbogast@vanderbilt.edu

Statistics in Medicine
|October 30, 2004
PubMed
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We developed new graphical and numerical methods to check logistic regression models for stratified case-control data. These methods use cumulative residuals to assess covariate form, link function, and overall model fit, proving effective in simulations.

Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical Modeling

Background:

  • Logistic regression is widely used for analyzing case-control studies.
  • Assessing model adequacy is crucial for reliable epidemiological findings.
  • Existing methods may not fully capture model misspecification in stratified data.

Purpose of the Study:

  • To introduce novel graphical and numerical methods for evaluating logistic regression model adequacy.
  • To specifically address the challenges posed by stratified case-control data.
  • To provide tools for assessing covariate functional form, link function, and overall model fit.

Main Methods:

  • Methods based on the cumulative sum of residuals (CUSUM) applied to covariates and linear predictors.
  • Utilizing the weak convergence of the cumulative residual process to a Gaussian process.

Related Experiment Videos

  • Approximating the null distribution via Monte Carlo simulation for comparison.
  • Visual and analytical comparisons of observed residuals against simulated null distributions.

    • Main Results:

    • The proposed CUSUM-based methods effectively detect deviations from the assumed logistic model.
    • Simulations confirm the practical utility and performance of the methods.
    • The methods allow detailed examination of individual components of the logistic model.

    Conclusions:

    • The developed methods offer a robust approach to assessing logistic regression adequacy in stratified case-control studies.
    • These tools enhance the reliability of epidemiological analyses by ensuring appropriate model specification.
    • The study provides a practical framework for model diagnostics in biostatistical research.