Statistical methods for multivariate interval-censored recurrent events.

Multi-type recurrent event data arise when two or more different kinds of events may occur repeatedly over a period of observation. The scientific objectives in such settings are often to describe features of the marginal processes and to study the association between the different types of events. Interval-censored multi-type recurrent event data arise when the precise event times are unobserved, but intervals are available during which the events are known to have occurred. This type of data is common in studies of patients with advanced cancer, for example, where the events may represent the development of different types of metastatic lesions which are only detectable by conducting bone scans of the entire skeleton. In this setting it is of interest to characterize the incidence of the various types of bone lesions, to estimate the impact of treatment and other covariate effects on the development of new lesions, and to understand the relationship between the processes generating the bone lesions. We develop joint models for multi-type interval-censored recurrent events which accommodate dependencies between different types of events and enable one to examine the covariate effects via regression. However, since the marginal likelihood resulting from the multivariate random effect model is intractable, we describe a Gibbs sampling algorithm to facilitate model fitting and inference. We use generalized estimating equations for estimation and inference based on marginal models. The finite sample properties of the marginal approach are studied via simulation. The estimates of both the regression coefficients and the variance-covariance parameters are shown to have negligible bias and 95 per cent confidence intervals based on the asymptotic variance formula are shown to have excellent empirical coverage probabilities in all of the settings considered. The application of these methods to data from a trial of women with advanced breast cancer provides insight into the clinical course of bone metastases in this population.