A simulation procedure based on copulas to generate clustered multi-state survival data

Generating survival data with a clustered and multi-state structure is useful to study finite sample properties of multi-state models, competing risks models and frailty models. We propose a simulation procedure based on a copula model for each competing events block, allowing to introduce dependence between times of different transitions and between those of grouped subjects. The effect of simulated frailties and covariates can be added in a proportional hazards way.In order to mimic information from real data, we also propose a method for the tuning of parameters via 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 on 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. The results demonstrated that data simulated according to our proposed method have characteristics very close to the target values.