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Matched observational studies are commonly used to study treatment effects innon-randomized data. After matching for observed confounders, there couldremain bias from unobserved confounders. A standard way to address this problemis to do a sensitivity analysis. A sensitivity analysis asks how sensitive theresult is to a hypothesized unmeasured confounder U. One method, known assimultaneous sensitivity analysis, has two sensitivity parameters: one relatingU to treatment assignment and the other to response. This method assumes thatin each matched set, U is distributed to make the bias worst. This approach hastwo concerning features. First, this worst case distribution of U in eachmatched set does not correspond to a realistic distribution of U in thepopulation. Second, sensitivity parameters are in absolute scales which arehard to compare to observed covariates. We address these concerns byintroducing a method that endows U with a probability distribution in thepopulation and calibrates the unmeasured confounder to the observed covariates.We compare our method to simultaneous sensitivity analysis in simulations andin a study of the effect of second-hand smoke exposure on blood lead levels inU.S. children.

A calibrated sensitivity analysis for matched observational studies with  application to the effect of second-hand smoke exposure on blood lead levels  in U.S. children