Simulation of clustered multi-state survival data based on a copula model

Generating survival data with a clustered and multi-state structure is useful to study multi-state models, competing risks models and frailty models. Simulations should allow to introduce dependence between times of different transitions and between those of grouped subjects. At the same time they should allow to control the probability of each competing event, the median time to each transition, the effect of covariates and the type and magnitude of heterogeneity. We propose a simulation procedure based on a copula model for each competing events block, allowing to specify the marginal distributions of time variables. The effect of simulated frailties and covariates can be added in a proportional hazards way. The tuning of parameters is done by numerical minimization of a criterion function based on the ratios of target and observed values of median times and of probabilities of competing events. An example is provided of simulation of data mimicking those from a multicenter study on head and neck cancer, where the interest is in studying both time to local relapses and to distant metastases before death. We show that our proposed method reaches very good convergence to the target values