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

Abstract

We conducted a matched observational study to investigate the causal relationship between second-hand smoke and blood lead levels in children. Our first analysis that assumes no unmeasured confounding suggests evidence of a detrimental effect of second-hand smoke. However, unmeasured confounding is a concern in our study as in other observational studies of second-hand smoke’s effects. A sensitivity analysis asks how sensitive the conclusion is to a hypothesized unmeasured confounder U. For example, in our study, one potential unmeasured confounder is whether the child attends a public or private school. A commonly used sensitivity analysis for matched observational studies adopts a worst-case perspective, which assumes that, in each matched set, the unmeasured confounder is allocated to make the bias worst: in a matched pair, the child with higher blood lead level always attends public school and the other private school. This worst-case allocation of U does not correspond to any realistic distribution of U in the population and is difficult to compare with observed covariates. We proposed a new sensitivity analysis method that addresses these concerns. We apply the new method to our study and find that, to explain away the association between second-hand smoke exposure and blood lead levels as non-causal, the unmeasured confounder would have to be a bigger confounder than any measured confounder.