Inclusion of binary proxy variables in logistic regression improves treatment effect estimation in observational studies in the presence of binary unmeasured confounding variables |
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| Authors: | Cornelius Rosenbaum Qingzhao Yu Sarah Buzhardt Elizabeth Sutton Andrew G. Chapple |
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| Affiliation: | 1. Biostatistics Program, School of Public Health, LSU Health Sciences Center, New Orleans, Louisiana, USA;2. Department of Obstetrics and Gynecology, Louisiana State University Health Sciences Center, Baton Rouge, Louisiana, USA;3. Woman's Hospital Research Center, Woman's Hospital, Baton Rouge, Louisiana, USA;4. Department of Interdisciplinary Oncology, School of Medicine, LSU Health Sciences Center, New Orleans, Louisiana, USA |
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| Abstract: | We present a simulation study and application that shows inclusion of binary proxy variables related to binary unmeasured confounders improves the estimate of a related treatment effect in binary logistic regression. The simulation study included 60,000 randomly generated parameter scenarios of sample size 10,000 across six different simulation structures. We assessed bias by comparing the probability of finding the expected treatment effect relative to the modeled treatment effect with and without the proxy variable. Inclusion of a proxy variable in the logistic regression model significantly reduced the bias of the treatment or exposure effect when compared to logistic regression without the proxy variable. Including proxy variables in the logistic regression model improves the estimation of the treatment effect at weak, moderate, and strong association with unmeasured confounders and the outcome, treatment, or proxy variables. Comparative advantages held for weakly and strongly collapsible situations, as the number of unmeasured confounders increased, and as the number of proxy variables adjusted for increased. |
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| Keywords: | proxy variables confounding adjustment logistic regression |
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