Unmeasured confounding may undermine the validity of causal inference withobservational studies. Sensitivity analysis provides an attractive way topartially circumvent this issue by assessing the potential influence ofunmeasured confounding on the causal conclusions. However, previous sensitivityanalysis approaches often make strong and untestable assumptions such as havinga confounder that is binary, or having no interaction between the effects ofthe exposure and the confounder on the outcome, or having only one confounder.Without imposing any assumptions on the confounder or confounders, we derive abounding factor and a sharp inequality such that the sensitivity analysisparameters must satisfy the inequality if an unmeasured confounder is toexplain away the observed effect estimate or reduce it to a particular level.Our approach is easy to implement and involves only two sensitivity parameters.Surprisingly, our bounding factor, which makes no simplifying assumptions, isno more conservative than a number of previous sensitivity analysis techniquesthat do make assumptions. Our new bounding factor implies not only thetraditional Cornfield conditions that both the relative risk of the exposure onthe confounder and that of the confounder on the outcome must satisfy, but alsoa high threshold that the maximum of these relative risks must satisfy.Furthermore, this new bounding factor can be viewed as a measure of thestrength of confounding between the exposure and the outcome induced by aconfounder.
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