Multivariate frailty models for multi-type recurrent event data and its application to cancer prevention trial

Multi-type recurrent event data arise in many situations when two or more different event types may occur repeatedly over an observation period. For example, in a randomized controlled clinical trial to study the efficacy of nutritional supplements for skin cancer prevention, there can be two types of skin cancer events occur repeatedly over time. The research objectives of analyzing such data often include characterizing the event rate of different event types, estimating the treatment effects on each event process, and understanding the correlation structure among different event types. In this paper, we propose the use of a proportional intensity model with multivariate random effects to model such data. The proposed model can take into account the dependence among different event types within a subject as well as the treatment effects. Maximum likelihood estimates of the regression coefficients, variance-covariance components, and the nonparametric baseline intensity function are obtained via a Monte Carlo Expectation Maximization (MCEM) algorithm. The expectation step of the algorithm involves the calculation of the conditional expectations of the random effects by using the Metropolis-Hastings sampling. Our proposed method can easily handle recurrent event data that have more than two types of events. Simulation studies were used to validate the performance of the proposed method, followed by an application to the skin cancer prevention data.