PSM Causal Attribution
Propensity Score Matching — Isolating the True Causal Effect of Intervention
Propensity Score Matching (PSM) is the core quasi-experimental causal inference method. By statistically matching treatment and control groups on confounders (age, sex, baseline risk), it eliminates selection bias and isolates the true intervention effect, generating causally interpretable health effect estimates. ReHealth Core engineers this method to produce billable preventive care causal evidence in real-world settings.
📅 Last updated: April 2026
✍️ ReHealth Core Research Team
🔬 方法学文献与真实世界研究参考
Selection Bias: The Fatal Flaw of Correlation Evidence
People who actively participate in health management programs tend to have stronger health awareness, higher education, and more regular lifestyles. In other words, participants are already healthier before they join.
❌ Pre-match: Not Comparable
Treatment: 42yr, non-smoker, active
Treatment: 38yr, normal BMI
Control: 48yr, smoker, inactive
Control: 52yr, overweight
→
✅ Post-match: Comparable Groups
Treatment: 44yr, light smoker
Control (matched): 45yr, light smoker
✓ Now differences mainly from intervention
PSM in Three Steps
1
Calculate Each Patient's "Propensity Score"
For each patient (treatment and control), use logistic regression to estimate the probability of receiving the intervention given their covariates — the propensity score.
P(T=1 | X) = logistic(β₀ + β₁·age + β₂·BMI + β₃·risk_score + ...)
2
Match by Score, Eliminate Baseline Differences
For each patient in the treatment group, find the closest propensity score match in the control group (nearest neighbor matching). Set a caliper (0.2 × SD of propensity score) to ensure adequate matching quality. Verify matching: require SMD < 0.1 for all covariates.
SMD = |μ₁ - μ₀| / √((σ₁² + σ₀²)/2) < 0.1
3
Estimate Causal Effect (ATT)
Compare health outcomes between matched treatment and control groups to obtain the Average Treatment Effect on the Treated (ATT). Use Bootstrap resampling to calculate confidence intervals.
ATT = E[Y(1) - Y(0) | T=1] ≈ mean(Y_treated) - mean(Y_matched_control)
Reading PSM Output Metrics
| Metric | Meaning | Standard |
|---|
| ATT | Average Treatment Effect on the Treated. Average health change from intervention vs. no intervention. | Direction + CI not crossing zero = significant |
| 95% CI | 95% Confidence Interval of ATT. Reflects estimation uncertainty. | CI not containing zero = significant |
| SMD（匹配后） | Standardized Mean Difference. Measures post-match group comparability. | < 0.1 = Good match quality |
| Match Rate | Proportion of treatment group successfully matched. | > 80% = Good overlap |
| Bootstrap SE | Bootstrap standard error. Reflects ATT stability under resampling. | Smaller is more stable |
PSM Assumptions and Limitations
After controlling for all covariates, treatment assignment is independent of potential outcomes. In other words, all factors influencing treatment assignment are included in the propensity score model. PSM cannot control for unmeasured confounders like health consciousness.
Treatment and control groups must overlap in propensity score distribution — for every treated patient, there must be a comparable control. If groups are too different, PSM cannot produce valid matches.
PSM can only control observable covariates. Compared to RCTs, PSM is a second-best causal inference method. ReHealth Core clearly states this limitation in all reports and recommends PSM evidence as supplementary, not replacing RCTs.
Frequently Asked Questions
How does PSM differ from Randomized Controlled Trials (RCT)?
RCTs use random assignment to ensure group comparability on all characteristics — the gold standard for causal inference. PSM is the best alternative for real-world settings where random assignment isn't feasible, eliminating observable confounders through statistical matching. PSM's limitation is its inability to control for unobserved confounders.
What is SMD and how to assess matching quality?
SMD (Standardized Mean Difference) measures the standardized difference between groups on each variable. SMD < 0.1 is generally considered good matching quality. ReHealth Core requires all matching variables to achieve SMD < 0.1 post-match, otherwise it issues a warning and recommends expanding the control pool.
What does ATT (Average Treatment Effect) mean?
ATT (Average Treatment Effect on the Treated) represents the average health effect difference for those who actually received the intervention, compared to if they hadn't. For example, ATT can express the average outcome difference between an intervention group and matched controls. Its value is determined by project data, outcome definition, balance diagnostics, and study design, and should state limitations such as unobserved confounding.
Related Concepts
Key Takeaway
PSM's value lies not in statistical sophistication, but in answering the question actuaries truly care about: "After controlling for baseline differences, how much change did the intervention itself actually cause?" The answer to this question is the ticket to entry into the healthcare payment system.