Estimation of the mean frequency function for recurrent events when ascertainment of events is delayed

In many large clinical trials there are delays between the time at which events occur and the time at which they are reported. Estimators of the mean frequency function for recurrent events that are currently used are inconsistent in these circumstances. We propose two new estimators to be used when events are reported with delay. One method is a basic inverse probability of censoring weighting approach, while the other explicitly estimates the distribution of the reporting delays. The asymptotic properties of these estimators are discussed and variance estimators are given. We examine the results of simulations comparing the new estimators to each other and to existing estimators that do not properly account for the delays. We also calculate some of these quantities using data from TNT, a clinical trial in which there were delays and events of interest were recurrent.