Constructed Second Control Groups and Attenuation of Unmeasured Biases

ABSTRACT

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.

Keywords:

• Attenuation of unmeasured biases
• Causal inference
• Observational study
• Second control group
• Sensitivity analysis

Supplementary Materials

The supplement provides a formal description of the matching algorithm used in the article to create balance on certain covariates and separation on others.

Funding

Supported by the Measurement, Methodology, and Statistics Program of the National Science Foundation and by Fellowship FA9550-11-C-0028 from the Department of Defense, Army Research Office, National Defense Science and Engineering Graduate (NDSEG) Fellowship Program, 32 CFR 168a4.