The relative risk or prevalence ratio is a natural and familiar summary of association between a binary outcome and an exposure or intervention. For rare events, the relative risk can be approximately estimated by logistic regression. For common events estimation is more difficult. We review proposed estimation algorithms for relative risk regression. Some of these give inconsistent estimates or invalid standard errors. We show that the methods that give correct inference can be viewed as arising from a family of quasilikelihood estimating functions for the same generalized linear model, differing in their efficiency and in their robustness to outlying values of the predictors. We give recommendations for fitting relative risk regression models in various popular statistical systems.
Epidemiology | Statistical Models
Lumley, Thomas; Kronmal, Richard; and Ma, Shuangge, "Relative Risk Regression in Medical Research: Models, Contrasts, Estimators, and Algorithms" (July 2006). UW Biostatistics Working Paper Series. Working Paper 293.