Some Results About Standardization for a Non Confounder in Estimators of (log) Relative Risk

Confounding is very fundamental to the design and analysis of studies of causal effects. A variable is not a confounder if it is not a risk factor to disease or if it has the same distribution in the exposed and unexposed population. Whether or not to adjust for a non confounder to improve the precision of estimation has been argued by many authors. This article shows that if C is a non confounder, the pooled and standardized (log) relative risk estimators are asymptotic normal distributions with the mean being the true (log) relative risk, and that the asymptotic variance of the pooled (log) relative risk estimator is less than that of the stratified estimator.