A tutorial dedicated to the correct estimation of the variance of the treatment effect estimated using propensity score weighting
Weighting on the propensity score is widely used to balance covariates in observational studies and randomized trials, to account for both systematic and random imbalances. This approach is based on two steps: (i) estimating individual propensity scores (PS), and (ii) estimating the treatment effect by applying PS weights. Using a variance estimator that accounts for these two steps is crucial for correct inference. Indeed, a variance estimator that ignores the first step leads to an overestimation of the variance when the estimand is the average treatment effect (ATE), and to an under- or overestimation of the variance when targeting the average treatment effect on the treated (ATT).
We present a comprehensive tutorial for obtaining unbiased variance estimates, by proposing and applying a unifying formula (and corresponding R code) for different propensity models (logistic, probit, cloglog) and weighting types (ATE weights, ATT weights, matching weights, and overlap weights). A simulation study also illustrates the performance of the estimators under different scenarios.
Link to the publication (open access): https://doi.org/10.1002/sim.10078