A hot-deck multiple imputation procedure for gaps in longitudinal data on recurrent events

We consider the analysis of longitudinal data sets that include times of recurrent events, where interest lies in variables that are functions of the number of events and the time intervals between events for each individual, and where some cases have gaps when the information was not recorded. Discarding cases with gaps results in a loss of the recorded information in those cases. Other strategies such as simply splicing together the intervals before and after the gap potentially lead to bias. A relatively simple imputation approach is developed that bases the number and times of events within the gap on matches to completely recorded histories. Multiple imputation is used to propagate imputation uncertainty. The procedure is developed here for menstrual calendar data, where the recurrent events are menstrual bleeds recorded longitudinally over time. The recording is somewhat onerous, leading to gaps in the calendar data. The procedure is applied to two important data sets for assessing the menopausal transition, the Melbourne Women's Midlife Health Project and the TREMIN data. A simulation study is presented to assess the statistical properties of the proposed procedure. Some possible extensions of the approach are also considered.