How strong would an unmeasured confounder have to be

The E-value of VanderWeele and Ding (2017): the minimum strength of association, on the risk-ratio scale, that an unmeasured confounder would need with BOTH the exposure and the outcome to explain away an observed risk ratio.

Usage

evalue_rr(rr, lo = NULL, hi = NULL, true = 1)

Arguments

rr

Observed risk ratio, greater than 0. Protective effects (below 1) are inverted first, as the measure is symmetric.

lo, hi

Optional confidence limits on the same scale. The limit nearer the null is the one used.

true

The value to move the estimate to. Defaults to 1, the null.

Value

A named numeric vector: evalue_point and, when limits are given, evalue_limit.

Details

It answers the question a covariate list cannot: not whether the analysis adjusted for the right things, but how much unmeasured confounding it would take to move the result to nothing. An E-value of 1.2 says very little would be needed; an E-value of 5 says a confounder five times more common in the exposed group AND five times more associated with the outcome would have to have gone unnoticed.

The E-value for the confidence limit is the one to report alongside it: a large point-estimate E-value with a limit E-value of 1 means the interval already includes no effect, and no confounding is needed at all.

References

VanderWeele, T. J., and Ding, P. (2017). Sensitivity Analysis in Observational Research: Introducing the E-Value. Annals of Internal Medicine 167(4), 268-274. doi:10.7326/M16-2607

See also

capsule_falsify() for controls that use the data, where this uses none.

Examples

# a risk ratio of 2 needs a confounder associated by 3.41 with both
evalue_rr(2)
#> evalue_point 
#>     3.414214 

# a protective effect is inverted, so 0.5 gives the same answer
evalue_rr(0.5)
#> evalue_point 
#>     3.414214 

# an interval that already includes the null needs nothing
evalue_rr(2, lo = 0.9, hi = 4.4)
#> evalue_point evalue_limit 
#>     3.414214     1.000000 

# and a strong result with a limit well above the null is harder to
# explain away
evalue_rr(3, lo = 2.1, hi = 4.3)
#> evalue_point evalue_limit 
#>     5.449490     3.619868