Survival analysis using a scale change random effects model

Frailty models are effective in broadening the class of survival models and inducing dependence in multivariate survival distributions. In proportional hazards, the random effect multiplies the hazard function. The scale-change model incorporates unobserved heterogeneity through a random effect that enters the baseline hazard function to change the time scale. We interpret this random effect as frailty, or other unobserved risks that create heterogeneity in the population. This model produces a wide range of shapes for univariate survival and hazard functions. We extend this model to multivariate survival data by assuming that members of a group share a common random effect. This structure induces association among the survival times in a group and provides alternative association structures to the proportional hazards frailty model. We present parametric and semiparametric estimation techniques and illustrate these methods with an example.