Statistica Sinica 17(2007), 1643-1656

COMPARISON BETWEEN ESTIMATES OF THE

POTENTIAL PROPORTION WITH AND

WITHOUT STANDARDIZATION FOR A

NON-CONFOUNDER

Xueli Wang$^{1,2}$, Zhi Geng$^2$, Qiang Zhao$^{2,3}$ and Qi Qiao$^2$

$^1$Beijing University of Posts and Telecommunications, $^2$Peking University

and $^3$Shandong Normal University

Abstract: A covariate 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 populations. Standardization for a confounder can reduce confounding bias, but that for a non-confounder cannot. A question argued by many authors asks whether or not standardization of a non-confounder can improve the precision of estimation. This paper discusses the hypothetical or potential proportion of individuals in the exposed population who would have developed the disease had they not been exposed. It is shown that the precision of estimation of the hypothetical proportion cannot usually be improved by using standardization for a non-confounder, no matter how one re-categorizes the non-confounder.

Key words and phrases: Adjustment, causal inference, confounder, confounding, potential-outcome model, precision, standardization.