Competing risk model with bivariate random effects for clustered survival data

Competing risks are often observed in clinical trial studies. As exemplified in two data sets, the bone marrow transplantation study for leukaemia patients and the primary biliary cirrhosis study, patients could experience two competing events which may be correlated due to shared unobservable factors within the same cluster. With the presence of random hospital/cluster effects, a cause-specific hazard model with bivariate random effects is proposed to analyse clustered survival data with two competing events. This model extends earlier work by allowing random effects in two hazard function parts to follow a bivariate normal distribution, which gives a generalized model with a correlation parameter governing the relationship between two events due to the hospital/cluster effects. By adopting the GLMM formulation, random effects are incorporated in the model via the linear predictor terms. Estimation of parameters is achieved via an iterative algorithm. A simulation study is conducted to assess the performance of the estimators, under the proposed numerical estimation scheme. Application to the two sets of data illustrates the usefulness of the proposed model.