title: Meta-analysis of rate ratios with differential follow-up by treatment arm: inferring comparative effectiveness of medical devices.
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.
authors.affiliation: Office of Biostatistics Research, National Heart, Lung, and Blood Institute, Bethesda, 20892, MD, U.S.A.|Department of Biostatistics, Harvard School of Public Health, Boston, 02115, MA, U.S.A.
authors.forename: Lauren M
authors.initials: LM
authors.lastname: Kunz
authors.affiliation: Department of Biostatistics, Harvard School of Public Health, Boston, 02115, MA, U.S.A.|Department of Health Care Policy, Harvard Medical School, Boston, Massachusetts, 02115, U.S.A.
authors.forename: Sharon-Lise T
authors.initials: SL
authors.lastname: Normand
authors.affiliation: Weill Cornell Medical College of Cornell University and New York Presbyterian Hospital, New York, 10065, NY, U.S.A.
authors.forename: Art
authors.initials: A
authors.lastname: Sedrakyan
mesh_terms: D015982:Bias; D058409:Cardiac Resynchronization Therapy Devices; D003198:Computer Simulation; D017147:Defibrillators, Implantable; D004812:Epidemiologic Methods; D004864:Equipment and Supplies; D005500:Follow-Up Studies; D006801:Humans; D015201:Meta-Analysis as Topic; D016017:Odds Ratio; D016012:Poisson Distribution; D012044:Regression Analysis
keywords: aggregated data; bayesian; comparative effectiveness