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

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.