Double‐robust estimation of an exposure‐outcome odds ratio adjusting for confounding in cohort and case‐control studies

<jats:title>Abstract</jats:title><jats:p>Modern epidemiologic studies often aim to evaluate the causal effect of a point exposure on the risk of a disease from cohort or case‐control observational data. Because confounding bias is of serious concern in such non‐experimental studies, investigators routinely adjust for a large number of potential confounders in a logistic regression analysis of the effect of exposure on disease outcome. Unfortunately, when confounders are not correctly modeled, standard logistic regression is likely biased in its estimate of the effect of exposure, potentially leading to erroneous conclusions. We partially resolve this serious limitation of standard logistic regression analysis with a new iterative approach that we call ProRetroSpective estimation, which carefully combines standard logistic regression with a logistic regression analysis in which exposure is the dependent variable and the outcome and confounders are the independent variables. As a result, we obtain a correct estimate of the exposure‐outcome odds ratio, if either thestandard logistic regression of the outcome given exposure and confounding factors is correct, or the regression model of exposure given the outcome and confounding factors is correct but not necessarily both, that is, it is double‐robust. In fact, it also has certain advantadgeous efficiency properties. The approach is general in that it applies to both cohort and case‐control studies whether the design of the study is matched or unmatched on a subset of covariates. Finally, an application illustrates the methods using data from the National Cancer Institute's Black/White Cancer Survival Study. Copyright © 2010 John Wiley & Sons, Ltd.</jats:p>