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Goodness-of-fit tests in proportional hazards models with random effects.

Wenceslao González-Manteiga1, María Dolores Martínez-Miranda2, Ingrid Van Keilegom3

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This study introduces a new method for testing covariate effects in Cox proportional hazards models with random effects, crucial for analyzing clustered and censored survival data.

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Area of Science:

  • Biostatistics
  • Survival Analysis
  • Statistical Modeling

Background:

  • Analyzing clustered and right-censored survival data is common in biomedical and veterinary research.
  • Cox proportional hazards models with random effects are frequently used for such data.
  • Assessing the functional form of covariate effects is critical for accurate model interpretation.

Purpose of the Study:

  • To develop and evaluate a statistical test for the functional form of covariate effects in random effects Cox models.
  • To compare parametric and nonparametric approaches for estimating covariate effects under different hypotheses.
  • To provide a robust method for analyzing complex survival data.

Main Methods:

  • Utilized the full marginal likelihood for model estimation under both null (parametric) and alternative (nonparametric) hypotheses.
  • Employed orthogonal expansions for estimating nonparametric covariate effects.
  • Applied a bootstrap method to approximate the distribution of the likelihood ratio test statistic.

Main Results:

  • The proposed testing procedure demonstrates good performance in simulation studies.
  • The method effectively distinguishes between parametric and nonparametric covariate effects.
  • The likelihood ratio statistic, approximated via bootstrapping, provides a reliable test.

Conclusions:

  • The developed testing procedure offers a valuable tool for assessing covariate effect functional forms in complex survival data.
  • The method is applicable to real-world datasets from biomedical and veterinary fields.
  • This approach enhances the reliability and interpretability of survival analyses involving random effects.