Abstract: This paper proposes a simple technique for assessing the range of plausible causal conclusions from observational studies with a binary outcome and an observed categorical covariate. The technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response. A medical study of coronary artery disease is used to illustrate the technique.

INTRODUCTION AND NOTATION

Inevitably, the results of clinical studies are subject to dispute. In observational studies, one basis for dispute is obvious: since patients were not assigned to treatments at random, patients at greater risk may be over-represented in some treatment groups. This paper proposes a method for assessing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response. Despite their limitations, observational studies will continue to be a valuable source of information, and therefore it is prudent to develop appropriate methods of analysis for them.

Our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u, under several sets of assumptions about u. Both Cornfield et al. (1959) and Bross (1966) have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment, that is, whether the treatment effect, after adjustment for u could be zero.