Abstract: Recurrent and terminal events are common outcomes for studying treatment effects in clinical studies. Existing approaches follow either a time-to-first event analysis approach or a recurrent event modeling approach. Recurrent event analyses are often restricted by independence assumptions on gap-times between events. Although time-to-first event analyses are not subject to this restriction, this analysis discards information that occurs beyond the initial event and is much less powerful for detecting treatment differences. We develop two new approaches for this data structure, motivated by less restrictive assumptions of time-to-first event analyses, that combine information from multiple follow-up intervals in determining treatment effects. Each approach follows behavior of short term outcomes during pre-specified intervals over time. The first testing procedure pools (correlated) short term ?-restricted outcomes from pre-specified intervals starting at times t_k,k=1,...,b, and compares estimated ?-restricted mean survival across treatment groups from this combined dataset. The second procedure calculates conditional ?-restricted means from those at risk at times t_k,k=1,...,b, and compares the area under a function of these by treatment. Variances calculations, taking into account correlation of short-term outcomes within individuals, linearize random components of the test statistics following Woodruff (1971) and more recently Williams (1995). Simulations compare the finite sample performance of our tests to the robust proportional rates model proposed by Lin et al. (2000) and the Ghosh and Lin (2000) test for recurrent events subject to death. In treatment effect patterns following proportional hazards, delayed treatment effect, short duration treatment effect and moderate duration effect the proposed methods perform favorably when compared to existing methods. These new analysis approaches also produce correct type I error rates when gap-times between events are correlated. The analysis approach is illustrated in data from a randomized trial of azithromycin in patients with chronic obstructive pulmonary disease (COPD).
