Estimating the burden of recurrent events in the presence of competing risks: the method of mean cumulative count

Abstract

Cumulative incidence has been widely used to estimate the cumulative probability of developing an event of interest by a given time, in the presence of competing risks. When it is of interest to measure the total burden of recurrent events in a population, however, the cumulative incidence method is not appropriate because it considers only the first occurrence of the event of interest for each individual in the analysis: Subsequent occurrences are not included. Here, we discuss a straightforward and intuitive method termed "mean cumulative count," which reflects a summarization of all events that occur in the population by a given time, not just the first event for each subject. We explore the mathematical relationship between mean cumulative count and cumulative incidence. Detailed calculation of mean cumulative count is described by using a simple hypothetical example, and the computation code with an illustrative example is provided. Using follow-up data from January 1975 to August 2009 collected in the Childhood Cancer Survivor Study, we show applications of mean cumulative count and cumulative incidence for the outcome of subsequent neoplasms to demonstrate different but complementary information obtained from the 2 approaches and the specific utility of the former.

Keywords: cumulative incidence; disease burden; mean cumulative count; recurrent events.

Figure 1.

A visual representation of a hypothetical study that has a recurrent-event outcome. A dashed line represents the follow-up period of each individual. A solid circle represents the occurrence of the event of interest, an open circle represents censoring, and a cross represents the occurrence of the competing-risk event.

Figure 2.

Estimated MCC curves and CumI curves based on data from the Childhood Cancer Survivor Study (26 pediatric oncology centers in the United States and Canada), 1975–2009. A) Mean cumulative count curves and 95% confidence intervals calculated by the bootstrap percentile method, stratified by whether received radiation treatment (RT group) or not (no RT group); B) cumulative incidence curves and 95% confidence intervals, stratified by RT group and no RT group. Gray shading represents 95% confidence intervals. CumI, cumulative incidence; MCC, mean cumulative count; RT, radiation therapy.