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

## TL;DR

This paper introduces a parametric method to estimate the average number of recurring events when competing risks are present, using a new R package for implementation.

## Contribution

A novel parametric approach for estimating mean recurrent events under competing risks, implemented in the R package JointFPM.

## Key findings

- The method shows low bias and good coverage in simulations when the event intensity is independent of prior events.
- The proposed approach allows for smooth function estimation over time and easy contrast estimation, which nonparametric methods lack.
- The method is demonstrated using real-world data on hospital readmissions after colorectal cancer surgery.

## Abstract

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.