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

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

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