ipw-causal-inference

name

ipw-causal-inference

description

Use when the user needs inverse probability weighting (IPW) or inverse probability of treatment weighting (IPTW) for causal inference from observational data, including propensity-score weighting, stabilized weights, ATE or ATT estimation via weighting, an introduction to marginal structural models, positivity/overlap diagnostics, weight trimming and truncation, effective sample size, Horvitz-Thompson and Hajek estimators, and covariate balance after weighting using weighted standardized mean differences. Applies to Python, R, Stata, or SQL-backed analytics workflows for observational treatment effect studies.

Inverse Probability Weighting (IPW)

Use this skill for observational treatment effect questions where the user wants to reweight units by the inverse of their treatment probability to build a pseudo-population in which treatment is independent of measured confounders, then estimate ATE or ATT on that pseudo-population.

Workflow

1. Define the estimand before code:

   • Treatment, outcome, unit of analysis, time window, and eligible population.
   • Target estimand: ATE for the whole population, or ATT for the effect on treated units.
   • Confounders must be pre-treatment variables only; never condition on mediators, colliders, or outcome-derived features.

2. Estimate the propensity score:

   • Estimate e(x) = P(T = 1 | X) with logistic regression, regularized logistic regression, gradient boosting, or another calibrated classifier.
   • Calibration matters more than raw discrimination; the weights depend on the predicted probabilities, not on classification accuracy.
   • Inspect the propensity distribution by treatment arm before constructing any weights.

3. Construct the weights:

   • For ATE, weight treated units by 1 / e(x) and control units by 1 / (1 - e(x)).
   • For ATT, weight treated units by 1 and control units by e(x) / (1 - e(x)), reweighting controls to look like the treated population.
   • Prefer stabilized weights: multiply the ATE numerator by the marginal treatment probability, so treated weight is P(T=1) / e(x) and control weight is P(T=0) / (1 - e(x)). Stabilization shrinks weight variance without changing the target estimand.

4. Check positivity and extreme weights:

   • Verify positivity/overlap: every unit should have 0 < e(x) < 1 with adequate support in both arms; near-deterministic propensities break IPW.
   • Inspect the weight distribution: report the maximum weight, the ratio of max to mean, and the share of total weight carried by the top few units.
   • Trim units in the tails of the propensity distribution, or truncate (Winsorize) weights at percentile cutoffs such as the 1st/99th, when a few units would otherwise dominate. Document any trimming/truncation because it changes the estimand slightly.

5. Estimate the treatment effect:

   • Use the Hajek (self-normalizing) estimator, i.e. weighted means normalized by the sum of weights in each arm, which is more stable than the raw Horvitz-Thompson sum.
   • Equivalently, fit a weighted outcome regression of the outcome on treatment (the marginal structural model in its simplest form).
   • Report uncertainty with the bootstrap (refitting the propensity model inside each replicate) or a robust/sandwich variance; naive unweighted standard errors understate uncertainty.

6. Validate balance and stability:

   • Report weighted standardized mean differences (weighted SMD) for every covariate; aim for absolute weighted SMD below 0.1.
   • Report the effective sample size (ESS) per arm; a large drop versus the nominal count signals weight concentration and unstable estimates.
   • Try alternative propensity specifications, stabilized versus unstabilized weights, and several trimming thresholds; report how the estimate moves.

Reporting Checklist

• Estimand (ATE or ATT), inclusion criteria, treatment timing, and outcome window.
• Propensity model and covariates, with justification that they are pre-treatment confounders.
• Positivity/overlap diagnostics and the propensity distribution by arm.
• Weight type (ATE vs ATT, stabilized vs unstabilized), weight summary statistics, and the maximum weight.
• Any trimming or truncation rule applied and how many units it affected.
• Weighted SMD balance table before and after weighting.
• Effective sample size per arm.
• Treatment effect estimate with bootstrap or robust confidence interval.
• Sensitivity analyses and unmeasured-confounding caveats.

Guardrails

• Extreme weights inflate variance: a handful of near-zero or near-one propensities can dominate the estimate and produce wide, unstable intervals.
• Positivity is the binding assumption: if some covariate region has no treated (or no control) units, the effect there is not identified and weighting will extrapolate silently.
• A misspecified propensity model biases pure IPW with no internal warning; consider doubly robust estimation (AIPW) when feasible, which stays consistent if either the propensity or the outcome model is correct.
• Always stabilize weights and inspect ESS; unstabilized weights routinely have far larger variance for the same point estimate.
• Good predictive propensity scores are not the goal; covariate balance after weighting is.
• IPW adjusts only for observed confounders and does not address unmeasured confounding.