Statistics Papers

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Technical Report

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Publication Source

Journal of the American Statistical Association





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The informal folklore of observational studies claims that if an irrelevant observed covariate is left uncontrolled, say unmatched, then it will influence treatment assignment in haphazard ways, thereby diminishing the biases from unmeasured covariates. We prove a result along these lines: it is true, in a certain sense, to a limited degree, under certain conditions. Alas, the conditions are neither inconsequential nor easy to check in empirical work; indeed, they are often dubious, more often implausible. We suggest the result is most useful in the computerized construction of a second control group, where the investigator can see more in available data without necessarily believing the required conditions. One of the two control groups controls for the possibly irrelevant observed covariate, the other control group either leaves it uncontrolled or forces separation; therefore, the investigator views one situation from two angles under different assumptions. A pair of sensitivity analyses for the two control groups is coordinated by a weighted Holm or recycling procedure built around the possibility of slight attenuation of bias in one control group. Issues are illustrated using an observational study of the possible effects of cigarette smoking as a cause of increased homocysteine levels, a risk factor for cardiovascular disease. Supplementary materials for this article are available online.

Copyright/Permission Statement

This is an Accepted Manuscript of an article accepted by Taylor & Francis for publication in the Journal of the American Statistical Association and posted online 7 August 2015, available online:


attenuation of unmeasured biases, casual inference, observational study, second control group, sensitivity analysis



Date Posted: 25 October 2018

This document has been peer reviewed.