Confounding by Indication Simulator

Sicker patients get the more aggressive operation, so the aggressive operation looks harmful. Adjust, stratify, and watch the sign flip.

causal inference
confounding
adjustment
treatment effect

True effect

-2.000

Crude difference

2.013

confounded

Adjusted for measured L

-0.975

Residual bias

1.025

Outcome vs. measured severity, by treatment

Partial (conservative)Radical (aggressive)

Treatment contrast within severity strata

Stratum detail

Empty or near-empty cells signal a positivity violation: within that stratum the data cannot speak to the contrast.
Severity quintile	n radical	n partial	Within-stratum difference
Q1	25.000	95.000	0.780
Q2	35.000	85.000	-0.908
Q3	59.000	61.000	-1.438
Q4	74.000	46.000	-0.664
Q5	94.000	26.000	0.061

Sign reversal is the point

Set the true effect to −2 (beneficial) and push indication strength above 2. The crude difference becomes positive: the operation that helps appears to harm, purely because it was reserved for the patients who were already worse off.