This thesis presents an overview of frailty models in survival analysis for modelling unobserved heterogeneity in survival times. The frailty model is a generalization of Cox's proportional hazard model, where a shared unobserved quantity called frailty describes a positive correlation among the survival times. The frailty term describes the common risks, acting as a factor on the hazard function.

In this thesis, we investigate a score test based on the mixture of chi-square distributions for testing homogeneity of individuals in recurrent event data using a shared frailty model, which is equivalent to testing whether the variance component in a frailty model is zero.

Simulation studies are conducted to assess the empirical level and power of the score test under correctly specified and misspecified random effects, and to study the finite-sample properties in terms of biases and mean squared errors of the estimators