Demystifying stabilization in inverse probability of treatment weighting

Inverse probability of treatment weighting (IPTW) is a common approach to infer causal treatment effects when covariates are imbalanced at baseline or over time among treatment groups. One limitation of the IPTW is that a few observations with large weights can disproportionately influence inference, leading to dramatically increased variability in estimation. Stabilizing weights were developed to mitigate such a variability caused by excessively large weights. Since then, stabilizing weights have been widely regarded as good practice for IPTW, despite some misunderstandings and misinterpretations of their functionality. For example, a common misconception is that the original IPTW artificially inflates a study's statistical power because the weighted sample size appears to double that of the original. This article clarifies the role of stabilization in IPTW analysis, focusing on linear, logistic, and Cox's Proportional Hazard analyses in baseline binary treatment settings, which are commonly encountered in the regulatory space. Through theoretical derivations and simulation studies, we show that stabilized IPTW models yield identical point estimates to the original IPTW models in saturated linear and logistic regressions but yield slightly different estimates in Cox regressions. Stabilizing IPTW improves variance estimation over the original IPTW only when within-subject correlation due to weighting is ignored (as in model-based variance estimation, which is an incorrect approach), while none to minimal differences are observed when using robust variance estimation. Regardless of stabilization, a robust, sandwich-type variance estimator or resampling-based methods are the more appropriate approach for accurate variance estimation.