Modified Poisson and Least-Squares Regressions for Binary Outcome Data Analyses

Abstract

Logistic regression has been widely applied in clinical and epidemiological studies as a standard method for multivariate analysis of binary outcome data. However, the odds-ratio is not directly interpretable effect measure and only can be interpreted as an approximation of risk-ratio when the event frequency is low. Many recent reporting guidelines recommend using directly interpretable effect measures, and thus, the modified Poisson and least-squares regressions have been widely adopted in practice to address this issue. Using these methods, valid estimates of risk ratio and risk difference can be obtained through simply fitting Poisson and least-squares regressions to binary outcome data. In this article, we provide theoretical review of these methods and show why these regression analyses can provide consistent risk ratio and risk difference estimators within the framework of estimating equation theory. We also provide a tutorial for actual data analyses using these methods by R package “rqlm” released on CRAN. In addition, we review recent methodological studies concerning these regression methods for further analyses.