Abstract
Modeling events requires accounting for differential follow-up duration, especially when combining randomized and observational studies. Although events occur at any point over a follow-up period and censoring occurs throughout, most applied researchers use odds ratios as association measures, assuming follow-up duration is similar across treatment groups. We derive the bias of the rate ratio when incorrectly assuming equal follow-up duration in the single study binary treatment setting. Simulations illustrate bias, efficiency, and coverage and demonstrate that bias and coverage worsen rapidly as the ratio of follow-up duration between arms moves away from one. Combining study rate ratios with hierarchical Poisson regression models, we examine bias and coverage for the overall rate ratio via simulation in three cases: when average arm-specific follow-up duration is available for all studies, some studies, and no study. In the null case, bias and coverage are poor when the study average follow-up is used and improve even if some arm-specific follow-up information is available. As the rate ratio gets further from the null, bias and coverage remain poor. We investigate the effectiveness of cardiac resynchronization therapy devices compared with those with cardioverter-defibrillator capacity where three of eight studies report arm-specific follow-up duration.