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Sensitivity Analysis for Omitted Variable Bias (E-value & RV)

confounding_strength.Rd

Implements the E-value of VanderWeele & Ding (2017) and the robustness value / bias formula of Cinelli & Hazlett (2020) to quantify how much unmeasured confounding would be needed to explain away a causal estimate.

Usage

confounding_strength(
  estimate,
  se,
  df = Inf,
  benchmark_covariates = NULL,
  data = NULL,
  outcome = NULL,
  treatment = NULL,
  alpha = 0.05
)

Arguments

estimate

Numeric. The point estimate of the causal effect (from any model).

se

Numeric. The standard error of the estimate.

df

Numeric. Residual degrees of freedom. Use Inf for large samples. Default Inf.

benchmark_covariates

Character vector or NULL. Names of observed covariates to use as benchmarks (requires data, outcome, and treatment). Optional.

data

Data frame or NULL. Required when benchmark_covariates is specified.

outcome

Character or NULL. Outcome variable name in data.

treatment

Character or NULL. Treatment variable name in data.

alpha

Numeric. Significance level for the CI-based E-value. Default 0.05.

Value

A named list:

e_value

Named numeric: e_value (for the point estimate) and e_value_ci (for the confidence limit closer to the null).

robustness_value

Named numeric: rv_q0 (to explain away the point estimate) and rv_qa (to explain away the CI bound).

sensitivity_df

Data frame of bias-adjusted estimates across a grid of r2dz (0–0.5) × r2yz (0–0.5) partial R² values.

plot

A ggplot2 contour plot showing the sensitivity surface.

Details

Sensitivity Analysis for Omitted Variable Bias

Computes sensitivity measures for assessing robustness of a causal estimate to unobserved confounding:

  • E-value (VanderWeele & Ding 2017): the minimum strength of association (on a risk-ratio scale) that an unmeasured confounder would need with both the treatment and the outcome to fully explain away the observed effect.

  • Robustness value (Cinelli & Hazlett 2020): the minimum partial R² that the confounder would need to explain in both the treatment and the outcome to drive the estimate to zero (or the null).

  • Bias-adjusted contour plot: estimated effect across a grid of partial R² values for the confounder's association with treatment (r²[dz|x]) and outcome (r²[yz|x]).

No dependency on sensemakr is required; all computations use base R.

References

VanderWeele, T. J., & Ding, P. (2017). Sensitivity analysis in observational research: Introducing the E-value. Annals of Internal Medicine, 167(4), 268-274.

Cinelli, C., & Hazlett, C. (2020). Making sense of sensitivity: Extending omitted variable bias. Journal of the Royal Statistical Society: Series B, 82(1), 39-67.

Examples

# Simulated linear regression
set.seed(42)
n  <- 500
x  <- rnorm(n)
y  <- 0.4 * x + rnorm(n)
m  <- lm(y ~ x)
sm <- summary(m)

est <- coef(m)["x"]
se  <- coef(sm)["x", "Std. Error"]
df_r <- m$df.residual

sens <- confounding_strength(estimate = est, se = se, df = df_r)
print(sens$e_value)
#>    e_value.x e_value_ci.x 
#>     16.91304     12.97937 
print(sens$robustness_value)
#>    rv_q0.x      rv_qa 
#> 0.30650970 0.08425162 
sens$plot