Meta-analysis of rate ratios with differential follow-up by treatment arm: inferring comparative effectiveness of medical devices

Journal Statistics in Medicine
Authors Kunz, Laura; Normand, Sharon-Lise; Sedrakyan, Art
Year Published 2015
Link to article


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 followup 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. Copyright © 2015 John Wiley & Sons, Ltd.

Combining randomized trial data to estimate heterogeneous treatment effects

Authors  Hatfield, Laura; Kramer, Daniel;  Normand, Sharon-Lise
Year Published 2015
Link to white paper


Heart failure arises, progresses, and responds to therapy differently in different people. Yet clinical trials often lack power to estimate treatment effects for subgroups, or enforce eligibility criteria that exclude some patients entirely. Combining information across trials increases power for subgroup estimates and expands generalizibility. However, naively pooling patient-level data sacrifices the benefits of randomization, and pooling study-level estimates must consider trial heterogeneity.We develop and illustrate approaches for combining information across trials to estimate effects in men and women with heart failure who are treated with implantable cardioverter-defibrilliator (ICD) alone or in combination with cardiac resynchronization therapy (CRT-D). We consider individual- and trial-level factors that may confound or mediate subgroup treatment effects. For example, ischemic disease is more common in men; could this explain why women appear to benefit more from CRT-D than men?Our Bayesian models estimate sex-specific treatment effects across trials, accounting for uncertainty, confounding, and mediation. We find that with a very small number of heterogeneous studies, hierarchical modeling offers few benefits over conventional effect pooling,producing wider credible intervals but little shrinkage. We also find little evidence for residual confounding within subgroups, but some evidence of interactions between left bundle branch blockage and ischemic etiology in the sex-specific treatment effects, suggesting further study.


LAH and SLN are supported by contract DHHS/FDA-223201110172C and grant 1U01FD004493-01 from the Center for Devices and Radiological Health, US Food and Drug Administration.DBK is supported by a Paul B. Beeson Career Development Award (NIA K23AG045963).

Multiple Outcomes and Multiple Sources of Evidence

Journal  Circulation: Cardiovascular Quality Outcomes
Authors Normand, Sharon-Lise T.
Year Published 2011
Link to Publication



This issue contains 2 articles in our planned Statistical Primer on Methods or Interpretation Series. The goals of our series are to (1) familiarize cardiovascular outcomes researchers with design and analytic problems encountered in outcomes research, (2) point to potential solutions, and (3) introduce modern analytic approaches. The series’ inaugural article discussed approaches for handling missing data—approaches that have existed for several decades but have not been fully embraced by outcomes researchers. The second article focused on the “landmark analysis, an analytic approach in which patients having treatment-censoring events before a “landmark” time are excluded from analysis. In this issue, Teixeira-Pinto and Mauri address the problem of multiple outcomes, and Kwok and Lewis discuss the use of Bayesian hierarchical models.