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added ref to e-value
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danielibsen committed May 29, 2024
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14 changes: 7 additions & 7 deletions sessions/causal-mediation-analysis-sensitivity-analysis.qmd
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Expand Up @@ -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 ratiothat 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
Expand Down Expand Up @@ -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 intervalthat
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 $P(U = 1|a,m, c)$
Expand Down Expand Up @@ -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
treatmentoutcome 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

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