A framework for causal inference in the presence of extreme inverse probability weights: the role of overlap weights

In this paper, we consider recent progress in estimating the average treatment effect when extreme inverse probability weights are present and focus on methods that account for a possible violation of the positivity assumption. These methods aim at estimating the treatment effect on the subpopulation of patients for whom there is a clinical equipoise. We propose a systematic approach to determine their related causal estimands and develop new insights into the properties of the weights targeting such a subpopulation. Then, we examine the roles of overlap weights, matching weights, Shannon's entropy weights, and beta weights. This helps us characterize and compare their underlying estimators, analytically and via simulations, in terms of the accuracy, precision, and root mean squared error. Moreover, we study the asymptotic behaviors of their augmented estimators (that mimic doubly robust estimators), which lead to improved estimations when either the propensity or the regression models are correctly specified. Based on the analytical and simulation results, we conclude that overall overlap weights are preferable to matching weights, especially when there is moderate or extreme violations of the positivity assumption. Finally, we illustrate the methods using a real data example marked by extreme inverse probability weights.