A comparison of estimation methods for relative risk in binary response

Abstract

The odds ratio and relative risk are usually the indices of interest in public health and medical studies. The odds ratio can be obtained using logistic regression in case-control studies. In cohort studies, however, the odds ratio should not be replaced with relative risk. This can cause overestimation or underestimation of the treatment effect in the study under some conditions. In this paper, we compare multiple methods to estimate the appropriate relative risk in a binary response. The odds ratio can be obtained using logistic regression. With an incidence of the outcome of more than10%, the odds ratio should not be replaced with the relative risk. Log-binomial regression has become an alternative to logistic regression for the analysis. However, it fails to converge at a high incidence. The Poisson regression using a sandwich variance estimator outperforms in estimating the relative risk directly in terms of MLEs and the convergence problem. It is reliable in terms of simulation results. Data from a diabetes study are used to illustrate the different methods.