Propensity Score Matching (PSM)

The propensity score is the conditional probability of receiving a treatment given a set of observed baseline covariates. It is typically estimated using a logistic regression model where treatment assignment is the dependent variable and all measured confounders are independent variables.

• Reduces a high-dimensional vector of covariates to a single scalar summary
• Balances the distribution of observed confounders between treatment groups
• Satisfies the balancing score property: conditional on the score, treatment assignment is independent of observed covariates

Once propensity scores are estimated, treated units are matched to untreated units with similar scores. Common algorithms include:

• Nearest Neighbor Matching: Each treated unit is paired with the untreated unit having the closest propensity score, with or without a caliper (maximum allowable distance)
• Optimal Matching: Minimizes the total within-pair difference in propensity scores across all pairs simultaneously
• Kernel Matching: Each treated unit is matched to a weighted average of all untreated units, with weights inversely proportional to score distance

After matching, researchers must verify that the matching procedure successfully balanced the distribution of covariates between groups. Key diagnostics include:

• Standardized Mean Differences (SMD): An SMD below 0.1 after matching is generally considered acceptable balance
• Variance Ratios: The ratio of variances between treated and control groups should approach 1.0
• Love Plots: Visual displays comparing covariate balance before and after matching
• Kolmogorov-Smirnov Tests: Assess equality of entire distributions, not just means

PSM requires sufficient overlap in the propensity score distributions of treated and untreated groups. The region of common support is where causal inference is valid.

• Units outside the common support region must be trimmed or discarded
• Extreme propensity scores (near 0 or 1) indicate near-deterministic treatment assignment and violate the positivity assumption
• Trimming can reduce generalizability but improves internal validity by ensuring comparisons are only made between comparable units

PSM only balances observed confounders. Sensitivity analysis assesses how strongly an unmeasured confounder would need to influence both treatment assignment and outcome to nullify the estimated treatment effect.

• Rosenbaum Bounds: Quantifies the magnitude of hidden bias required to alter causal conclusions
• Gamma (Γ): A measure of the odds of differential treatment assignment due to unobserved covariates; values close to 1 indicate high sensitivity
• Essential for regulatory submissions and clinical evidence generation where randomization is absent

In biomarker identification, PSM is used to control for confounding when comparing outcomes between patients with and without a specific biomarker expression.

• Matches patients on age, sex, disease stage, comorbidities, and prior treatments
• Enables estimation of the Average Treatment Effect on the Treated (ATT) for biomarker-guided therapy selection
• Often combined with survival analysis to compare time-to-event outcomes in matched cohorts
• Addresses confounding by indication where biomarker-positive patients systematically differ from biomarker-negative patients

A technique for estimating causal effects when unobserved confounding is present. An instrument (e.g., a genetic variant in Mendelian Randomization) must satisfy three conditions: it is associated with the treatment, affects the outcome only through the treatment, and shares no confounders with the outcome. Unlike PSM, which relies on observed covariates, IV methods can recover causal effects even with hidden bias.

A quasi-experimental design that estimates treatment effects by comparing the change in outcome over time between treated and control groups. DiD assumes parallel trends: that both groups would have followed the same trajectory absent treatment. While PSM matches on static covariates, DiD leverages temporal variation, making it ideal for policy evaluations where randomization is impossible.

A class of models for estimating causal effects of time-varying treatments in the presence of time-dependent confounding. MSMs use inverse probability of treatment weighting (IPTW) to create a pseudo-population where treatment assignment is independent of covariates. This addresses a critical PSM limitation: PSM handles only point-in-time treatments, while MSMs model dynamic treatment regimes.

A framework for designing observational studies by explicitly specifying the protocol of a hypothetical randomized trial and then emulating it with observational data. Steps include defining eligibility criteria, treatment strategies, time zero, and follow-up. This approach clarifies causal questions and reduces design biases that PSM alone cannot address, such as immortal time bias.

A systematic distortion that arises when conditioning on a common effect of two variables. For example, if both treatment and outcome influence study inclusion, analyzing only included patients induces a spurious association. PSM can inadvertently introduce collider bias if the propensity score model includes variables affected by the exposure, violating causal identification assumptions.

A graphical representation of causal assumptions where nodes represent variables and directed edges represent direct causal effects. DAGs encode conditional independence relationships and identify which variables must be controlled for (or left uncontrolled) to estimate an unbiased causal effect. They are essential for selecting covariates in a PSM model and avoiding collider or mediator adjustment.