Propensity scores#

Executive summary

Propensity scores are the probability of being in the treatment/exposure group, given your baseline characteristics.

A propensity score is the ‘probability of treatment assignment conditional on observed baseline characteristics’. It was defined by was Rosenbaum and Rubin (1983). It is a ‘balancing score: conditional on the propensity score, the distribution of measured baseline covariates is similar between treated and untreated subjects’. [Austin 2011]

Propensity scores are often estimated using a logistic regression model with:

  • Outcome = Treatment (e.g. insulin therapy)

  • Predictors = Observed baseline characteristics (e.g. blood pressure, BMI, lipid profile)

  • Propensity score = Predicted probability of treatment from the fitted model [Valojerdi et al. 2018]

Image from Shaw Talebi on Towards Data Science:

Propensity score

Use of a propensity score enables incorporation of ‘a larger number of background covariates because it uses the covariates to estimate a single number’. [Valojerdi et al. 2018]

Four different propensity scores methods are used for removing the effects of confounding:

  • Stratification on the propensity score

  • Propensity score matching

  • Inverse probability of treatment weighting (IPTW) using the propensity score

  • Covariate adjustment using the propensity score [Austin 2011]

Assumptions of propensity score analysis/methods:

  • All covariates related to outcome and treatment (exposure) are measured and included

  • SUTVA - treatment effect for one individual is not affected by the treatment status of another

  • The assumptions of logistic regression [Valojerdi et al. 2018]