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.

中文翻译：

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校准的敏感性分析，用于匹配的观察性研究，并应用于二手烟暴露对儿童血铅水平的影响

我们进行了一项匹配的观察性研究，以调查儿童二手烟与血铅水平之间的因果关系。我们的第一个分析假设没有不可估量的混杂，这表明二手烟有害。但是，与其他有关二手烟影响的观察性研究一样，不可衡量的混杂是我们研究中的一个问题。敏感性分析询问结论对假设的未测混杂因子U有多敏感。例如，在我们的研究中，一个潜在的无法衡量的混杂因素是孩子上的是公立学校还是私立学校。匹配观察研究中常用的敏感性分析采用最坏情况的观点，即假设在每个匹配集中，都将未测量的混杂因素分配为使偏倚更糟：在匹配对中，血铅水平较高的孩子总是参加公立学校和另一所私立学校。这种最坏情况下分配ù不对应于任何实际的分布ü在人口中，很难与观察到的协变量进行比较。我们提出了一种解决这些问题的新的灵敏度分析方法。我们将新方法应用到我们的研究中，发现为了解释二手烟暴露与血铅水平之间的关系是非因果关系，未衡量的混杂因素必须比任何衡量的混杂因素更大。