The Cox shared frailty model with log-skew-normal frailties

Clustered survival data arise when groups of failure times share a common ingredient; typically, they refer to the same individual or individuals with a common factor. When the association between failure times within the same cluster is of interest, statistical methods called frailty models have been used. The frailty is an unobserved random component which affects the risk level, changing from cluster to cluster but shared by all observations within the same cluster. Various probability distributions have been proposed for the frailty term, with special emphasis on the gamma and log-normal distribution. Since adequate modelling of the frailty distribution is essential to properly investigate the dependence structure, we introduce a new class of frailty models with a flexible distribution form. Specifically, we adopt the skew-normal distribution for the log-transformed frailty, leading to an extension of the log-normal model. After presenting the methodology connected to this choice, we illustrate it with a case study of multiple myeloma patients with autologous stem cells transplantation.