Calibrating sensitivity analyses to observed covariates in observational studies

In medical sciences, statistical analyses based on observational studies are common phenomena. One peril of drawing inferences about the effect of a treatment on subjects using observational studies is the lack of randomized assignment of subjects to the treatment. After adjusting for measured pretreatment covariates, perhaps by matching, a sensitivity analysis examines the impact of an unobserved covariate, u, in an observational study. One type of sensitivity analysis uses two sensitivity parameters to measure the degree of departure of an observational study from randomized assignment. One sensitivity parameter relates u to treatment and the other relates u to response. For subject matter experts, it may be difficult to specify plausible ranges of values for the sensitivity parameters on their absolute scales. We propose an approach that calibrates the values of the sensitivity parameters to the observed covariates and is more interpretable to subject matter experts. We will illustrate our method using data from the U.S. National Health and Nutrition Examination Survey regarding the relationship between cigarette smoking and blood lead levels.