Log-normal frailty models fitted as Poisson generalized linear mixed models.

Area of Science:

• Biostatistics
• Survival Analysis
• Statistical Modeling

Background:

• The equivalence between survival models with piecewise constant hazards and Poisson regression is established.
• This equivalence extends to clustered survival data, allowing frailty models to be treated as generalized linear mixed models (GLMMs).
• GLMMs offer readily available statistical theory and software for fitting frailty models, though with limitations on baseline hazard flexibility and data size.

Purpose of the Study:

• To extend simulations of frailty models using a more realistic Gompertz baseline hazard.
• To compare the proposed Poisson GLMM approach with competing models.
• To introduce the %PCFrailty SAS macro for applying the Poisson GLMM to frailty models.

Main Methods:

• Simulations were conducted using a Gompertz baseline hazard function.
• The Poisson generalized linear mixed model approach was implemented using the novel %PCFrailty SAS macro.
• Performance was evaluated against competing models, particularly focusing on scenarios with varying events per piece.

Main Results:

• Simulations demonstrated favorable results for the shared frailty model under the Gompertz hazard.
• The %PCFrailty macro yielded accurate parameter estimates, particularly when there were at least 4 events per piece.
• The approach proved effective for analyzing clustered survival data.

Conclusions:

• The Poisson generalized linear mixed approach for log-normal frailty models, implemented via the %PCFrailty macro, offers significant advantages.
• These advantages include more flexible modeling of fixed and random effects.
• The method provides exact maximum likelihood estimation and reliable variance parameter estimation for clustered survival data analysis.