Estimating risk ratio using modified Poisson regression for cohort studies with binary outcomes

Risk ratio is usually the parameter of interest in epidemiologic and medical studies. Poisson regression model is an approach used to directly estimate risk ratio. When Poisson regression is applied to binomial data, the error for the estimated risk ratio will be overestimated. In other words, Poisson regression is likely to compute a confidence interval that is conservative. In this paper we aim at devising a modified Poisson regression method to rectify this problem.

To illustrate modified Poisson regression, a simple 2-by-2 contingency table was used. Simple computation was performed to estimate variance. We compared ordinary and modified Poisson regression models by actual data from a study on predictors of coronary artery disease.

Application of ordinary and modified Poisson regression methods resulted in an estimated relative risk of 1.68 for hypercholesterolemia. The confidence intervals provided by these two methods were 1.005-2.82 and 1.05-2.68, respectively. The confidence interval provided by the modified Poisson regression was 10 percent narrower than that obtained by the ordinary method.

Applying modified Poisson regression to cohort studies with binary data, compared with ordinary Poisson regression, reduces variance and increases precision of the estimated risk ratio. This method might result in different findings from ordinary Poisson regression for borderline statistical significance.