Propensity scores

As treatment is not assigned randomly in observational studies, patients receiving a particular exposure (or treatment) may differ systematically from patients receiving other exposures or no exposure at all. Consequentially, when investigating the effects of an exposure, the effect of the systematic differences (confounders) needs to be taken into account, preferably be adjusted away in the statistical analysis. Traditionally, this has been made by stratifying on the confounders or including them in a regression model. More recently, adjustment using propensity scores has become increasingly popular (1).

A propensity score is a subject’s estimated probability of receiving a particular exposure or treatment, given their observed baseline characteristics. The propensity score thus condenses several measured baseline covariates into a single score. The purpose of this score is to balance the groups receiving different exposures or treatments. Given the score, the covariates included in the development of the score should have the same distribution in treated and untreated patients. The confounding adjustment can then be performed by matching, weighting, or stratifying on the propensity scores or by including them as covariate.


To develop a propensity score that gives a treatment effect estimator with small variance a few recommendations have been made: confounders (associated with both exposure and outcome) and prognostically important variables (associated with outcome) should be included in the development, variables only associated with exposure should not (2).

However, propensity scores are often developed using data-driven techniques, such as stepwise regression. The additional uncertainty of whether the selected variables included in the propensity score development allow valid inferences complicates the analysis. Conventional statistical tests and confidence intervals may be invalid. However, suggestions on how to calculate valid statistical tests and confidence intervals have been published (3).

References

1. Austin PC. Advances in propensity score analysis. Statistical Methods in Medical Research 2020;29:641-643. doi:~[10.1177/0962280219899](https://doi.org/10.1177/0962280219899248)~

2. Rubin DB. The Use of Matched Sampling and Regression Adjustment to Remove Bias in Observational Studies. Biometrics 1973;29:185-203, doi:~[10.2307/2529685](https://doi.org/10.2307/2529685)~

3. Dukes O, Vansteelandt S. How to obtain valid tests and confidence intervals after propensity score variable selection? Statistical Methods in Medical Research 2020;29:677-694. doi:~[10.1177/0962280219862005](

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