Statistical Issues in Estimation of Adjusted Risk Ratio in Prospective Studies

Binary outcomes are common in prospective studies such as randomized controlled trials and cohort studies. Logistic regression is the most popular regression model for binary outcomes. Logistic regression yields an odds ratio that approximates the risk ratio when the risk of outcome is low. A consensus has been reached in an extensive argument in much of the literature that the risk ratio is preferred over the odds ratio for prospective studies. To obtain a model-based estimate of risk ratios, log-binomial regression has been recommended. However, this model may fail to converge and many methods have been provided as an alternative in these situations.

In this paper, we discuss the methods to obtain adjusted risk ratios in settings with independent and clustered data and we will review the results of comparisons between these methods based on simulation studies, especially a large simulation study which was conducted by the authors. We use hypothetical examples to show how log-Poisson regression with modified standard errors can be used to estimate risk ratio in practice using popular statistical software.

The potential misinterpretation of odds ratios should be considered by researchers, especially when the risk of the outcome is high. When researchers want to estimate the effect of exposure or intervention by controlling potential covariates, the misinterpretation of odds ratios can be avoided using regression models that can estimate risk ratios instead of logistic regression. The log-Poisson regression with modified standard errors can be considered to estimate risk ratios in both independent and clustered data settings.