  Multi-type recurrent events are often encountered in medical applications
when two or more different event types could repeatedly occur over an
observation period. For example, patients may experience recurrences of
multi-type nonmelanoma skin cancers in a clinical trial for skin cancer
prevention. The aims in those applications are to characterize features of the
marginal processes, evaluate covariate effects, and quantify both the
within-subject recurrence dependence and the dependence among different event
types. We use copula-frailty models to analyze correlated recurrent events of
different types. Parameter estimation and inference are carried out by using a
Monte Carlo expectation-maximization (MCEM) algorithm, which can handle a
relatively large (i.e., three or more) number of event types. Performances of
the proposed methods are evaluated via extensive simulation studies. The
developed methods are used to model the recurrences of skin cancer with
different types.
