Effciency comparison between mean and log-rank tests for recurrent event time data

Recurrent event time data are common in biomedical follow-up studies, in which a study subject may experience repeated occurrences of an event of interest. In this paper, we evaluate two popular nonparametric tests for recurrent event time data in terms of their relative effciency. One is the log-rank test for classical survival data and the other a more recently developed nonparametric test based on comparing mean recurrent rates. We show analytically that, somewhat surprisingly, the log-rank test that only makes use of time to the first occurrence could be more effcient than the test for mean occurrence rates that makes use of all available recurrence times, provided that subject-to-subject variation of recurrence times is large. Explicit formula are derived for asymptotic relative effciencies under the frailty model. The findings are demonstrated via extensive simulations.