Modeling Dependence in Survival Times using Log-Skew Normal Shared Frailties

Abstract

In survival studies, event times under a common influence are often grouped together in clusters. The association between and within these clusters can be studied using frailty models where randomness in the data or heterogeneity arising due to unknown covariates is described using a frailty variable. In shared frailty models, frailty value is common or shared for all observations within a cluster while it is conditionally independent for different clusters. In this article, we consider a model whose baseline distribution is Weibull and shared frailties follow log skew-normal distribution. This distribution increases flexibility of the model as it allows the frailty term to be positively or negatively skewed and estimation of skewness parameter enables us to comment on dependence structure of the random component. A simulation study is performed and Bayesian estimates of treatment effects, variance and skewness of frailty term are obtained using Metropolis-Hastings algorithm. It is shown that while bias and expected loss for estimates of all parameters reduce as dataset size increases, frailty parameters are more efficiently estimated when the random component is considered to be skewed. The model is also applied to two real-life datasets where positive and negative skewness is observed in the frailty term.