Bayesian design of clinical trials with multiple time-to-event outcomes subject to functional cure

With the continuous advancement of medical treatments, there is an increasing demand for clinical trial designs and analyses using cure rate models to accommodate a plateau in the survival curve. This is especially pertinent in oncology, where high proportions of patients, such as those with melanoma, lung cancer, and endometrial cancer, exhibit usual life spans post-cancer detection. A Bayesian clinical trial design methodology for multivariate time-to-event outcomes with cured fractions is developed. This approach employs a copula to jointly model the multivariate time-to-event outcomes. We propose a model that uses a Gaussian copula on the population survival function, irrespective of cure status. The minimum sample size required to achieve high statistical power while maintaining reasonable control over the type I error rate from a Bayesian perspective is identified using point-mass sampling priors. The methodology is demonstrated in simulation studies inspired by an endometrial cancer trial.