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Goodness-of-fit tests for modified Poisson regression possibly producing fitted values exceeding one in binary

Yasuhiro Hagiwara1, Yutaka Matsuyama1

  • 1Department of Biostatistics, School of Public Health, The University of Tokyo, Japan.

Statistical Methods in Medical Research
|May 23, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces new goodness-of-fit tests for modified Poisson regression, a method for binary outcomes. The normalized residual sum of squares test is recommended for its reliable performance in assessing model fit.

Keywords:
Goodness-of-fit testlog-binomial regression modelmodified Poisson regressionprevalence ratiorisk ratio

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Statistical modeling

Background:

  • Modified Poisson regression is valuable for estimating risk and prevalence ratios in binary outcome analyses.
  • Existing goodness-of-fit tests are limited for modified Poisson regression, hindering model validation.
  • The unconstrained parameter space in modified Poisson regression can lead to fitted values exceeding 1, complicating standard test application.

Purpose of the Study:

  • To propose and evaluate novel goodness-of-fit tests specifically designed for modified Poisson regression.
  • To identify appropriate statistical tests for assessing the fit of modified Poisson models.
  • To address the limitations of existing goodness-of-fit tests in the context of modified Poisson regression.

Main Methods:

  • Development of several goodness-of-fit tests: modified Hosmer-Lemeshow with empirical variance, Tsiatis test, normalized Pearson chi-square tests (binomial and Poisson variance), and normalized residual sum of squares test.
  • Simulation studies to assess the performance of proposed tests regarding Type I error and power.
  • Application of the tests to cross-sectional cancer patient data.

Main Results:

  • The original Hosmer-Lemeshow and normalized Pearson chi-square tests with binomial variance are unsuitable for modified Poisson regression.
  • The normalized residual sum of squares test demonstrated robust performance in simulations, particularly for Type I error control and power against wrong link functions.
  • The proposed tests were successfully applied to real-world cross-sectional cancer data.

Conclusions:

  • The normalized residual sum of squares test is a reliable and recommended goodness-of-fit test for modified Poisson regression.
  • The study provides essential tools for validating modified Poisson models in epidemiological and biostatistical research.
  • Accurate model fit assessment is crucial for reliable estimation of risk and prevalence ratios.