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Compute E-value to assess bias due to unmeasured confounder.

Source: R/confounders.evalue.R
confounders.evalue.Rd

Help to quantify the evidence strength for causality in presence of unmeasured confounding. The E-value is the minimum strength of association that an unmeasured confounder would need to have with both the exposure and the outcome, conditional on the measured covariates, to fully explain away a specific exposure-outcome association.

Usage

confounders.evalue(
  est,
  lower_ci = NULL,
  upper_ci = NULL,
  sd = NA,
  type = c("RR", "ORc", "HRc", "diff_RR", "diff_OR"),
  true_est = 1
)

Arguments

est

Point estimate for the effect measure. For difference in continuous outcomes, it is the standardized effect size (i.e. mean of the outcome divided by its standard deviation).

lower_ci

Lower limit of the confidence interval for the association (relative risk, odds ratio, hazard ratio, incidence rate ratio, risk difference).

upper_ci

Upper limit of the confidence interval for the association (relative risk, odds ratio, hazard ratio, incidence rate ratio, risk difference).

sd

For difference in continuous outcomes, the standard error of the outcome divided by its standard deviation.

type

Choice of effect measure (relative risk, and odds ratio or hazard ratio for rare outcomes i.e. < 15 outcome -- ORc; hazard ratio for common outcome i.e. > 15 difference in continuous outcomes, RR approximation -- diff_RR; difference in continuous outcomes, OR approximation -- diff_OR).

true_est

True estimate to assess E-value for. Default to 1 on risk scale to assess against null value. Set to a different value to assess for non-null hypotheses.

Value

A matrix with the observed point estimate and closest confidence interval to the null hypothesis, expressed as a relative risk, and their corresponding E-value.

References

VanderWeele T.J and Ding P. Sensitivity analysis in observational research: Introducing the E-value. Annals of Internal Medicine 2017;167:268-274.

Examples

# The data for this example come from:
# Victoria C.G., Smith P.G., Vaughan J.P., Nobre L.C., Lombardi C., Teixeira A.M.
# et al.
# Evidence for protection by breast-feeding against infant deaths from infectious
# diseases in Brazil.
# Lancet 1987;2:319-22.
confounders.evalue(est = 3.9, type = "RR")
#> 
#> --E-value--
#>          Point estimate   CI closest to H_0
#>      RR:       3.900000                    
#> E-value:       7.263034                    

# The data for this example come from:
# Oddy W.H, Smith G.J., Jacony P. 
# A possible strategy for developing a model to account for attrition bias in a
# longitudinal cohort to investigate associations between exclusive breastfeeding and
# overweight and obesity at 20 years.
# Annals of Nutrition and Metabolism 2014;65:234-235.
confounders.evalue(est = 1.47, lower_ci = 1.12, upper_ci = 1.93, type = "ORc")
#> 
#> --E-value--
#>          Point estimate   CI closest to H_0
#>      RR:       1.212436            1.058301
#> E-value:       1.719944            1.306694

# The data for this example come from:
# Reinisch J., Sanders S., Mortensen E., Rubin D.B.
# In-utero exposure to phenobarbital and intelligence deficits in adult men.
# Journal of the American Medical Association 1995;274:1518-1525
confounders.evalue(est = -0.42, sd = 0.14, type = "diff_RR")
#> 
#> --E-value--
#>          Point estimate   CI closest to H_0
#>      RR:      0.6823586           0.8754651
#> E-value:      2.2914593           1.5453444