A simulation study of different correlated frailty models and estimation strategies

Frailty models are becoming more and more popular in the area of multivariate survival analysis. In particular, shared frailty models are often used despite their limitations. To overcome the disadvantages of shared frailty models numerous correlated frailty models were established during the last decade. In the present study we examine correlated frailty models, especially the behavior of the parameter estimates when using different estimation strategies. Three different frailty models are considered: the gamma model and two versions of the log-normal model. The traditional maximum likelihood procedure of parameter estimation in the gamma case with an explicit available likelihood function is compared with maximum likelihood methods based on numerical integration and a Bayesian approach using MCMC methods with the help of a comprehensive simulation study. A strong dependence between the two parameter estimates (variance and correlation of frailties) in the multivariate correlated frailty model is detected and analyzed in detail.