Propensity-score methods
What question does this help answer?
“How can an observational treatment comparison be made more comparable with respect to measured baseline confounders?”
When to use it
Use propensity-score methods in observational comparative-effectiveness or causal analyses when treatment assignment is not randomized and a well-defined set of baseline confounders is available.
When not to use it
Propensity scores do not solve unmeasured confounding, poor overlap, immortal time bias, measurement error, or a badly defined causal question. They are not a substitute for careful study design.
How it works in plain language
A model estimates each participant’s probability of receiving treatment based on baseline characteristics. That score can support matching, weighting, stratification, or other balancing approaches. The goal is covariate balance, not a high predictive accuracy for treatment assignment.
Why Mallard may recommend it
Mallard may recommend a propensity approach when the research question compares nonrandomized treatment groups and confounding by baseline clinical characteristics is a major concern.
Key assumptions
- All important confounders needed for exchangeability are measured sufficiently.
- Positivity/overlap exists across treatment groups.
- Treatment, outcome, and covariate timing are correctly defined.
- The propensity model or weighting strategy achieves adequate balance.
- Standard errors reflect the chosen design and estimation procedure.
What overlap looks like
Weighting: which population, and doubly robust estimation
Weighting by the propensity score can target different populations, and the choice is part of the question. Inverse probability of treatment weighting gives each patient a weight of one over the probability of the treatment they actually received, and estimates the average effect had everyone been treated rather than no one. Patients with a probability near 0 or 1 receive very large weights, so a few of them can dominate the estimate: inspect the weights, and treat trimming or truncation as a change to the question rather than a technical fix. Overlap weights give treated patients a weight of one minus the score and untreated patients a weight equal to the score. They cannot be extreme, and when the score comes from a logistic model they balance the means of the covariates in that model exactly, but they estimate the effect among patients for whom either treatment was plausible, which is a different population from the whole cohort. Augmented inverse probability weighting combines the weights with an outcome model and is called doubly robust: the estimate is consistent if either the propensity model or the outcome model is correctly specified. It is not robust to unmeasured confounding or to poor overlap. For every weighting method, the default standard error of a weighted regression is wrong; a robust variance that treats the weights as known is usually conservative, and stacked estimating equations or a bootstrap of the whole procedure account for the weights having been estimated.
What to watch out for
Do not select propensity covariates solely because they predict treatment statistically. Use causal and subject-matter reasoning. Always assess post-adjustment balance and overlap.
Clinical example
Compare outcomes among patients initiating two antihypertensive drug classes using inverse probability of treatment weighting based on measured baseline characteristics.
- An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies (opens in a new tab) · Multivariate Behav Res · doi 10.1080/00273171.2011.568786
- Principles of confounder selection (opens in a new tab) · Eur J Epidemiol · doi 10.1007/s10654-019-00494-6
- Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies (opens in a new tab) · Stat Med · doi 10.1002/sim.6607
- Overlap Weighting: A Propensity Score Method That Mimics Attributes of a Randomized Clinical Trial (opens in a new tab) · JAMA · doi 10.1001/jama.2020.7819
- Doubly robust estimation of causal effects (opens in a new tab) · Am J Epidemiol · doi 10.1093/aje/kwq439