Bayesian bivariate cure rate models using Gaussian copulas

We propose a joint model for multiple time-to-event outcomes where the outcomes have a cure structure. When a subset of a population is not susceptible to an event of interest, traditional survival models cannot accommodate this type of phenomenon. For example, for patients with melanoma, certain modern treatment options can reduce the mortality and relapse rates. Traditional survival models assume the entire population is at risk for the event of interest, i.e., has a non-zero hazard at all times. However, cure rate models allow a portion of the population to be risk-free of the event of interest. Our proposed model uses a novel truncated Gaussian copula to jointly model bivariate time-to-event outcomes of this type. In oncology studies, multiple time-to-event outcomes (e.g., overall survival and relapse-free or progression-free survival) are typically of interest. Therefore, multivariate methods to analyze time-to-event outcomes with a cure structure are potentially of great utility. We formulate a joint model directly on the time-to-event outcomes (i.e., unconditional on whether an individual is cured or not). Dependency between the time-to-event outcomes is modeled via the correlation matrix of the truncated Gaussian copula. A Markov Chain Monte Carlo procedure is proposed for model fitting. Simulation studies and a real data analysis using a melanoma clinical trial data are presented to illustrate the performance of the method and the proposed model is compared to independent models.