Parametric Estimation of the Mean Number of Events in the Presence of Competing Risks

Recurrent events, for example, hospitalizations or drug prescriptions, are common in time-to-event research. One useful summary measure of the recurrent event process is the mean number of events. Methods for estimating the mean number of events exist and are readily implemented for situations in which the recurrent event is the only possible outcome. However, estimation gets more challenging in the competing risk setting, in which methods are so far limited to nonparametric approaches. To this end, we propose a postestimation command for estimating the mean number of events in the presence of competing risks by jointly modeling the intensity function of the recurrent event and the survival function for the competing events. The proposed method is implemented in the R-package JointFPM which is available on CRAN. Simulations demonstrate low bias and good coverage in scenarios where the intensity of the recurrent event does not depend on the number of previous events. We illustrate our method using data on readmissions after colorectal cancer surgery included in the frailtypack package for R. Estimates of the mean number of events can be used to augment time-to-event analyses when both recurrent and competing events exist. The proposed parametric approach offers estimation of a smooth function across time as well as easy estimation of different contrasts which is not available using a nonparametric approach.