In cohort studies with common outcomes, the odds ratio estimated from a logistic regression analysis is often interpreted as an indirect estimate of the risk ratio. In such settings, the odds ratio will be farther from the null than the risk ratio. Direct and unbiased estimates of the risk ratio may be obtained from a log binomial model fit by maximum likelihood. When the maximum likelihood log binomial model fails to converge (as is common) or provides predicted probability estimates or upper confidence limits greater than 1.0, various approaches have been suggested, but each has drawbacks, as we describe. We propose a novel Bayesian approach for the estimation of the risk ratio from the log binomial model that addresses drawbacks of existing approaches. Posterior computation can be accomplished easily using the WinBUGs code provided.
From the aDepartment of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC; bLineberger Comprehensive Cancer Center, The University of North Carolina at Chapel Hill, Chapel Hill, NC; and cDepartment of Epidemiology, The University of North Carolina at Chapel Hill, Chapel Hill, NC.
Submitted 10 September 2009; accepted 28 April 2010.
Supported by NCI grant CA16086 and NIH grants P30-AI-50410, R03-AI-071763, R01-AA-01759, and P30-AI-50410. The MACS is supported by the National Institute of Allergy and Infectious Diseases, with additional supplemental funding from the National Cancer Institute, UO1-AI-35042, 5-MO1-RR-00052 (GCRC), UO1-AI-35043, UO1-AI-35039, UO1-AI-35040, UO1-AI-35041. Website available at: http://www.statepi.jhsph.edu/macs/macs.html.
Data in this manuscript were collected by the Multicenter AIDS Cohort Study with centers (Principal Investigators) at The Johns Hopkins Bloomberg School of Public Health (Joseph B. Margolick, Lisa P. Jacobson), Howard Brown Health Center, Feinberg School of Medicine, Northwestern University, and Cook County Bureau of Health Services (John P. Phair, Steven M. Wolinsky), University of California, Los Angeles (Roger Detels), and University of Pittsburgh (Charles R. Rinaldo).
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Correspondence: Haitao Chu, Division of Biostatistics, The University of Minnesota, A460 Mayo Building, MMC 303, Minneapolis, MN 55455. E-mail: firstname.lastname@example.org.