H-likelihood Approaches for Random-Effect Survival Models

Abstract

The beauty of the likelihood is that once the statistical model is specified parametrically or nonparametrically, the associated inference procedures for the parameters of interest are rather straightforward. Statistical models have been enriched and actively extended in the literature by allowing random unknowns such as frailties in addition to fixed unknowns, namely parameters. The hierarchical (or h-) likelihood (Lee and Nelder, 1996) obviates the need for intractable integrations over the frailty terms required to obtain the (marginal) likelihood and it provides a statistically efficient procedure for various random-effects models such as generalized linear mixed models and semi-parametric frailty models. In this talk, we review recent works on extensions of the h-likelihood to time-to-event data (survival data), which overcomes various challenges due to incomplete observations caused by censoring, truncation and competing events, and present further extensions of existing works, such as complicated structured frailties and joint models. In particular, we show that the h-likelihood approach gives a useful methodology for interval estimation of the individual frailty and variable selection of covariates in the general class models with frailties. We also demonstate via the h-likelihood how to make inference various random-effect survival models using time-to-event data from clinical studies including multi-center clinical trials. Key words: competing risks models; frailty models; random effect; h-likelihood; marginal likelihood