Cinelli & Hazlett (2020) sensitivity summary for a causal effect — causal_sensitivity

Computes the Robustness Value (RV): the minimum partial R-squared (on both exposure and outcome, with the observed adjustments partialed out) that an unobserved confounder U would need to have to bring the estimate to zero (q = 1) or reduce it by a fraction q of its magnitude. Also reports the RV at 5% significance (RV_q): the minimum R-squared to push the t-ratio below the critical value.

Usage

causal_sensitivity_summary(effect, se, df, q = 1, alpha = 0.05)

Arguments

effect: Numeric; point estimate of the causal effect.
se: Numeric; standard error of the estimate.
df: Numeric; degrees of freedom (n - k - 1).
q: Numeric; the fraction of the estimate we want to neutralise. q = 1 is zero-out; q = 0.5 is half-reduction.
alpha: Significance level for RV_alpha (default 0.05).

Value

Named list with rv, rv_alpha, t_stat, and a verbal interpretation.

Details

Interpretation: if RV = 0.10, then any confounder explaining more than 10 percent of the residual variance in both X and Y (jointly) would be enough to kill the effect. Small RV = fragile estimate.

Examples

# A 2SLS effect of beta = 0.008, SE = 0.003, df = 1080:
causal_sensitivity_summary(0.008, 0.003, 1080)
#> $effect
#> [1] 0.008
#> 
#> $se
#> [1] 0.003
#> 
#> $df
#> [1] 1080
#> 
#> $t_stat
#> [1] 2.666667
#> 
#> $rv
#> [1] 0.07791866
#> 
#> $rv_alpha
#> [1] 0.02120882
#> 
#> $q
#> [1] 1
#> 
#> $alpha
#> [1] 0.05
#> 
#> $interpretation
#> [1] "An unobserved confounder explaining 7.8% of the residual variance in BOTH X and Y would suffice to zero out the estimate. At the 95% significance threshold, 2.1% is enough to make the result statistically insignificant."
#>