Survival Analysis with Poisson Random Effect Model

Abstract

Assuming the event hazard function to be of a piecewise constant form, survival analysis can be performed by Poisson regression. While this approach is less common compared to, for example, Cox proportional hazard regression, it offers flexible parametric modeling of the baseline hazard, and extension to models containing multiple time-dependent covariates and random effects can be conducted under the framework of generalized linear/nonlinear models. Due to these advantages, long-term follow-up analysis of a cohort study often relies on Poisson regression. The aim of this article is to formulate Poisson survival regression analysis and investigate its estimation properties by simulation. In particular, focus is on the impact of stratification of the main time-scale factor, the estimation performance under various situations including time-dependent covariates or random effects, and comparison with other methods such as Cox regression. A real data application to a large-scale cohort study is shown, which is followed by discussion about situations where Poisson survival regression might be most effective and future extensions.