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A study was presented where the authors used multivariable logistic regression to assess association between a risk factor and an incident disease outcome. The association was statistically significant. However they knew they had unmeasured confounders.

From what I can gather, they created a simulated covariate with a certain effect size which, even when added to the model, did not alter the statistical significance of the association between the risk factor and outcome. They concluded that even if there was an unmeasured confounder, as long as its association with the outcome did not have an effect size greater than the simulated variable, the overall model would remain significant.

Can anyone familiar with this method please direct me to an introductory text or at least its name? Is this an automated/interative technique where the maximum effect size of this unmeasured covariate can be tested to maintain overall model significance? How can they know if/how the unmeasured confounder interacts with other covariates in the model?

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    $\begingroup$ See Liu, Karamoto, & Stuart (2013) (DOI:10.1007/s11121-012-0339-5) for a review of sensitivity analyses for unmeasured confounding, including the method you described. $\endgroup$
    – Noah
    Nov 7 '17 at 6:11
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The method that I was referring to, and have since learnt, is called the "E value" described here. It allows assessment of how robust associations are to potential unmeasured or uncontrolled confounding.

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