Comparison of algorithms to generate event times conditional on time-dependent covariates

The Cox proportional hazards model with time-dependent covariates (TDC) is now a part of the standard statistical analysis toolbox in medical research. As new methods involving more complex modeling of time-dependent variables are developed, simulations could often be used to systematically assess the performance of these models. Yet, generating event times conditional on TDC requires well-designed and efficient algorithms. We compare two classes of such algorithms: permutational algorithms (PAs) and algorithms based on a binomial model. We also propose a modification of the PA to incorporate a rejection sampler. We performed a simulation study to assess the accuracy, stability, and speed of these algorithms in several scenarios. Both classes of algorithms generated data sets that, once analyzed, provided virtually unbiased estimates with comparable variances. In terms of computational efficiency, the PA with the rejection sampler reduced the time necessary to generate data by more than 50 per cent relative to alternative methods. The PAs also allowed more flexibility in the specification of the marginal distributions of event times and required less calibration.