Robust Frailty Models using Heavy-Tailed Distributions

Frailty models have been widely used for analyzing correlated survival data. For the inference a simple frailty distribution such as normal or gamma has been specified. However, the estimation of frailty parameter is sensitive to the misspecification of frailty distribution. This problem can be overcome by using a heavy-tailed distribution such as t-distribution. Thus, we propose the robust frailty models allowing heavy-tailed distributions. For the inference of the proposed model we develop the hierarchical-likelihood approach that avoids the integration used in the standard marginal likelihood approach. For the demonstration the numerical study is presented.