What is Propensity Score?
Propensity Score is the conditional probability of receiving a treatment given observed pre-treatment covariates, `e(X)=P(A=1|X)`, and is a balancing score used to design or analyze observational comparisons.
Quick Facts
| Specification | Official Specification |
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How It Works
Build the score from pre-treatment causal knowledge
Include variables needed to control measured confounding and strong outcome predictors when justified by the design; exclude treatment consequences. Predictive feature selection or a high treatment-classification AUC is not the objective. Rosenbaum and Rubin's original paper defines the score, its balancing property, and the strong-ignorability conditions behind causal adjustment.
Choose the transformation that matches the estimand
Matching commonly creates a treated-like comparison population and often targets ATT; ATE weighting uses 1/e(X) for treated and 1/(1-e(X)) for controls; overlap weighting emphasizes units with plausible assignment to either group. Trimming, calipers, replacement, and normalization alter the target population or finite-sample behavior and must be reported.
Judge balance and overlap, not classification accuracy
Austin's propensity-method review emphasizes balance diagnostics after applying the chosen design. Inspect covariate standardized differences, score distributions, extreme weights, Effective Sample Size, retained population, and key slices. Good measured balance does not address unmeasured confounding, bad outcome timing, hidden treatment versions, or interference.
Key Characteristics
- Equals treatment probability conditional on observed baseline covariates
- Balances measured covariate distributions at the true score
- Is not an outcome probability or treatment-effect estimate
- Supports matching, stratification, weighting, and design diagnostics
- Requires overlap and no-unmeasured-confounding assumptions for causal use
- Must be evaluated through post-design balance rather than predictive AUC
Common Use Cases
- Matching treated users to comparable untreated users
- Creating ATE or ATT inverse-probability weights
- Checking common support before observational effect estimation
- Designing an outcome-blind observational comparison
- Diagnosing which covariate slices remain unbalanced
Example
Loading code...Frequently Asked Questions
What does a Propensity Score predict?
It predicts treatment assignment from observed pre-treatment covariates. It does not predict the outcome, treatment benefit, or probability of success. Those are different quantities and require outcome data or causal estimands.
How is a Propensity Score different from IPS?
The Propensity Score is the conditional treatment probability. Inverse Propensity Scoring or weighting transforms that probability into weights for a declared estimand. A score may also support matching or stratification without inverse weights.
Should a Propensity Score model maximize AUC?
No. Its design objective is covariate balance in the matched or weighted sample. Very strong treatment discrimination can indicate weak overlap and extreme weights. Assess standardized differences and support after applying the chosen design.
Does Propensity Score matching remove all confounding?
No. It can balance observed covariates represented by a suitable score. It cannot balance unmeasured common causes, repair measurement error, correct treatment or outcome timing, or create comparable controls where no support exists.
What should be reported in a Propensity Score analysis?
Report the causal estimand, treatment and time zero, covariate rationale, score model, overlap, matching or weighting rule, trimming and normalization, pre/post balance, retained population, Effective Sample Size, uncertainty method, and sensitivity to hidden confounding.