Bayesian Logistic Regression Modeling as a Flexible Alternative for Estimating Adjusted Risk Ratios in Studies with Common OutcomesCharles E Rose1*, Yi Pan1 and Andrew L Baughman2
- *Corresponding Author:
- Charles E Rose
Division of HIV/AIDS Prevention
National Center for HIV/AIDS
Viral Hepatitis, STD, and TB Prevention
Centers for Disease Control and Prevention
1600 Clifton Road NE, Mailstop E48, Atlanta
Tel: +1 404-639-3311
E-mail: [email protected]
Received date: October 02, 2015; Accepted date: October 14, 2015; Published date: October 21, 2015
Citation:Rose CE, Pan Y, Baughman AL (2015) Bayesian Logistic Regression Modeling as a Flexible Alternative for Estimating Adjusted Risk Ratios in Studies with Common Outcomes. J Biom Biostat 6:253. doi:10.4172/2155-6180.1000253
Copyright: ©2015 Rose CE, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Background: For cohort and cross-sectional studies, the risk ratio (RR) is the preferred measure of effect rather than an odds ratio (OR), especially when the outcome is common (>10%). The log-binomial (LB) and Poisson models are commonly used to estimate the RR; the OR estimated using logistic regression is often used to approximate the RR when the outcome is rare. However, regardless of the prevalence of the outcome, logistic regression predicted exposed and unexposed risks may be used to estimate the RR. Because maximum likelihood estimation is used to fit the logistic model, estimation of the SE of the RR is difficult. Methods: To overcome difficulty in estimation of the SE of the RR and provide a flexible framework for modeling, we developed a Bayesian logistic regression (BLR) model to estimate the RR, with associated credible interval (CIB). We applied the BLR model to a large hypothetical cross-sectional study with categorical variables and to a small hypothetical clinical trial with a continuous variable for which the LB method did not converge. Results of the BLR model were compared to those from several commonly used RR modeling methods. Results: Our examples illustrate the Bayesian logistic regression model estimates adjusted RRs and 95% CIBs comparable to results from other methods. Adjusted risks and risk differences were easily obtained from the posterior distribution. Conclusions: The Bayesian logistic regression modeling approach compares favorably with existing RR modeling methods and provides a flexible framework for investigating confounding and effect modification on the risk scale.