From 7c8ae95d6f7fb127147b0c21387f3a3c43253601 Mon Sep 17 00:00:00 2001 From: Daniel Ibsen Date: Wed, 29 May 2024 06:21:17 +0200 Subject: [PATCH] added ref to e-value --- ...sal-mediation-analysis-sensitivity-analysis.qmd | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/sessions/causal-mediation-analysis-sensitivity-analysis.qmd b/sessions/causal-mediation-analysis-sensitivity-analysis.qmd index 95d7834..fbdf9f8 100644 --- a/sessions/causal-mediation-analysis-sensitivity-analysis.qmd +++ b/sessions/causal-mediation-analysis-sensitivity-analysis.qmd @@ -252,8 +252,8 @@ levels *A* = *a* and *A* = *a*^\*^. Once we have calculated the bias term **B~*mult*~(*c*)**, we can estimate our risk ratio controlling only for *C* (if the outcome is rare, fit a logistic regression) and we divide our estimate by -**B~*mult*~(*c*)** to get the corrected estimate for risk ratio—that is, -what we would have obtained if we had adjusted for *U* as well. +**B~*mult*~(*c*)** to get the corrected estimate for risk ratio---that +is, what we would have obtained if we had adjusted for *U* as well. Under the simplifying assumptions of (A8.1.1) and (A8.1.2b), we can also obtain corrected confidence intervals by dividing both limits of the @@ -429,7 +429,7 @@ Once we have calculated the bias term $B^{CDE}_{mult}(m|c)$, we can estimate the *CDE* risk ratio controlling only for *C* (if the outcome is rare), we fit a logistic regression) and we divide our estimate and confidence intervals by the bias factor $B^{CDE}_{mult}(m|c)$ to get the -corrected estimate for CDE risk ratio and its confidence interval—that +corrected estimate for CDE risk ratio and its confidence interval---that is, what we would have obtained if we had adjusted for *U* a well. We have to specify the two prevalences of *U*, namely $P(U = 1|a,m, c)$ @@ -573,14 +573,14 @@ uc_sens - The E-value is the minimum strength of association, on the risk ratio scale, that an unmeasured confounder would need to have with both the treatment and the outcome to fully explain away a specific - treatment–outcome association, conditional on the measured - covariates. + treatment--outcome association, conditional on the measured + covariates @vanderweele_sensitivity_2017. - A large E-value implies that considerable unmeasured confounding would be needed to explain away an effect estimate. - A small E-value implies little unmeasured confounding would be needed to explain away an effect estimate. - -(Tyler J VanderWeele 2017) ::: + +## References