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Robust Poisson likelihood estimation for frailty Cox models: A simulation study
Authors:Adel Elghafghuf  Henrik Stryhn
Affiliation:1. Department of Statistics, Faculty of Science, University of Misurata, Misurata, Libya;2. Centre for Veterinary Epidemiological Research, University of Prince Edward Island, Charlottetown, PE, Canada;3. Centre for Veterinary Epidemiological Research, University of Prince Edward Island, Charlottetown, PE, Canada
Abstract:Frailty models can be fit as mixed-effects Poisson models after transforming time-to-event data to the Poisson model framework. We assess, through simulations, the robustness of Poisson likelihood estimation for Cox proportional hazards models with log-normal frailties under misspecified frailty distribution. The log-gamma and Laplace distributions were used as true distributions for frailties on a natural log scale. Factors such as the magnitude of heterogeneity, censoring rate, number and sizes of groups were explored. In the simulations, the Poisson modeling approach that assumes log-normally distributed frailties provided accurate estimates of within- and between-group fixed effects even under a misspecified frailty distribution. Non-robust estimation of variance components was observed in the situations of substantial heterogeneity, large event rates, or high data dimensions.
Keywords:Frailty models  Misspecification of frailty distribution  Poisson maximum likelihood  Simulation study  Time-to-event data
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