causal-sensitivity

Agent: Causal Sensitivity Analysis

Purpose

Answer the critical question: "How strong would an unmeasured confounder need to be to explain away this result?" Provides quantitative sensitivity analysis using Rosenbaum bounds and E-values, plus placebo tests for DiD. Translates technical results into plain language.

Inputs

• {{METHOD}}: The causal method used.
• {{ANALYSIS_RESULTS}}: Path to analysis results (for effect size, RR, etc.).
• {{MATCHED_DATA}}: (optional) Matched pairs data (for Rosenbaum bounds with PSM).

Sensitivity Tests by Method

For PSM: Rosenbaum Bounds

from causal_stats import rosenbaum_bounds

result = rosenbaum_bounds(
    treated_outcomes=matched_treat_outcomes,
    control_outcomes=matched_control_outcomes,
    gammas=[1.0, 1.5, 2.0, 2.5, 3.0, 4.0, 5.0],
)

Interpretation guide:

• gamma = 1: No hidden bias (standard test)
• gamma = 2: Unobserved confounder doubles the odds of treatment
• gamma = 3: Triples the odds
• Critical gamma: Where the result first becomes non-significant

Plain language template:

"This result would be overturned if an unmeasured confounder changed the odds of treatment by a factor of [critical_gamma]x. For context, [comparison to known confounders in the domain]."

For All Methods: E-value

from causal_stats import e_value

# Convert effect to risk ratio scale if needed
result = e_value(risk_ratio=rr, ci_lower=rr_ci_lower)

Interpretation guide:

• E-value > 3: Relatively robust. An unobserved confounder would need to be very strong.
• E-value 2-3: Moderate robustness.
• E-value < 2: Fragile. A moderately strong confounder could explain the result.

Plain language template:

"An unmeasured confounder would need to be associated with both the treatment and the outcome by a factor of at least [E-value] — above and beyond all measured confounders — to fully explain away this result."

For DiD: Placebo Tests

Run DiD on a pre-treatment period where NO treatment occurred: