E-values: how strong an unmeasured confounder must be

The E-value of VanderWeele and Ding (2017): the smallest strength of association, on the risk-ratio scale, that an unmeasured confounder would need with both the treatment and the outcome to explain away an estimate; and that of the confidence limit nearer the null.

Usage

evlx(est, lo = NULL, hi = NULL, type = "rr", rare = FALSE, sd = NULL)

Arguments

est

The estimate: one positive ratio, or one standardised difference.

lo, hi

NULL or the confidence limits of a ratio.

type

"rr", "or", "hr" or "smd".

rare

TRUE when the outcome is rare (an odds or hazard ratio is then read as a risk ratio).

sd

NULL or the standard error of a standardised difference.

Value

A named numeric vector: rr (the estimate as a risk ratio), evalue and evlim (the limit's E-value; NA without limits).

Details

For a risk ratio RR >= 1 the E-value is RR + sqrt(RR (RR - 1)); a ratio below 1 is inverted first. An odds or hazard ratio is a risk ratio when the outcome is rare (rare = TRUE); otherwise an odds ratio is taken to sqrt(OR) and a hazard ratio to (1 - 0.5^sqrt(HR)) / (1 - 0.5^sqrt(1 / HR)). A standardised mean difference d is taken to exp(0.91 d), its limits to exp(0.91 d -+ 1.78 sd) from its standard error sd. The limit's E-value is 1 when the interval holds the null. These are the conversions of the 'EValue' package.

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

Examples

evlx(3.9, 1.8, 8.7)
#>       rr   evalue    evlim 
#> 3.900000 7.263034 3.000000 
evlx(0.8, 0.71, 0.91, type = "hr")
#>        rr    evalue     evlim 
#> 0.8567726 1.6088913 1.3360826 
evlx(0.5, type = "smd", sd = 0.1)
#>       rr   evalue    evlim 
#> 1.576173 2.529142 1.968037