Propensity score weighting under limited overlap and model misspecification

Abstract

Propensity score weighting methods are often used in non-randomized studies to adjust for confounding and assess treatment effects. The most popular among them, the inverse probability weighting, assigns weights that are proportional to the inverse of the conditional probability of a specific treatment assignment, given observed covariates. A key requirement for inverse probability weighting estimation is the positivity assumption, i.e. the propensity score must be bounded away from 0 and 1. In practice, violations of the positivity assumption often manifest by the presence of limited overlap in the propensity score distributions between treatment groups. When these practical violations occur, a small number of highly influential inverse probability weights may lead to unstable inverse probability weighting estimators, with biased estimates and large variances. To mitigate these issues, a number of alternative methods have been proposed, including inverse probability weighting trimming, overlap weights, matching weights, and entropy weights. Because overlap weights, matching weights, and entropy weights target the population for whom there is equipoise (and with adequate overlap) and their estimands depend on the true propensity score, a common criticism is that these estimators may be more sensitive to misspecifications of the propensity score model. In this paper, we conduct extensive simulation studies to compare the performances of inverse probability weighting and inverse probability weighting trimming against those of overlap weights, matching weights, and entropy weights under limited overlap and misspecified propensity score models. Across the wide range of scenarios we considered, overlap weights, matching weights, and entropy weights consistently outperform inverse probability weighting in terms of bias, root mean squared error, and coverage probability.

Causal Inference with Multilevel Data: A Comparison of Different Propensity Score Weighting Approaches

“…However, these estimates can be severely biased as estimates for the ATE because they upweigh observations in the center of the area of overlap. Alternatively, one could argue that the overlap estimator is targeting an estimand that is different from the ATE and that focuses on a population for whom there is equipoise (Zhou et al, 2020). Thus, the application of overlap weights may be particularly attractive when the assessment of treatment effects is most relevant for observations in the area of overlap.…”

Applying Propensity Score Methods in Clinical Research in Neurology

“…The investigator must choose the set of weights (ATE vs. ATT) that is appropriate to address the specific study question. While ATE and ATT weights are the most commonly-used propensity score-based weights, matching weights, overlap weights, and entropy weights are alternatives (34).…”

Informing power and sample size calculations when using inverse probability of treatment weighting using the propensity score

“…Recently, alternative sets of weights have been proposed. These include overlap weights (OW), matching weights (MW), and entropy weights (EW) 10,16 . These are defined as: , , and respectively.…”

“…These are defined as: , , and respectively. Use of these alternative weights targets inference at the subpopulation for whom there is the greatest clinical equipoise about treatment 10 . These weights have been shown to have desirable statistical properties 10 .…”

“…However, estimation of the variance of the treatment effect must account for the within‐subject homogeneity in outcomes that is induced by weighting 8,9 . Zhou and colleagues described a variance inflation factor (VIF) that describes the inflation in the sample size that has occurred due to the incorporation of weights 10 . The concept of the VIF, or equivalently the design effect (DE), arises from sample survey design and cluster randomized trials 11‐13 .…”