Primary Submission Category: Matching, Weighting
Doubly Robust Estimation of the Average Probabilistic Index
Authors: Sarah Boese, Rui Wang, Tom Chen,
Presenting Author: Sarah Boese*
There are many trial settings when researchers want to report a marginal summary of treatment effect but targeting the Average Treatment Effect (ATE) is inappropriate. When outcomes are semi-continuous ordinal or composed of multiple endpoints with ordered levels of severity, like hierarchical composite endpoints, then rank-based comparisons are often tractable when treatment effect differences are not. Targeting the average probabilistic index (API), or the probability that a treatment unit does better than a control unit, is the most appropriate measure of treatment effectiveness in these scenarios. A locally semi-parametric efficient estimator for the probabilistic index has been established under a restricted moment model framework when outcomes for all treatment units are observed. In practice, outcomes are rarely fully observed. We develop a novel class of doubly robust estimators for the marginal probabilistic index under the missing at random framework and identify the semi-parametric efficient estimator from that class. We compare three estimators from our class: an inverse probability weighted estimator, a doubly robust estimator which assumes working independence and a locally semi-parametric efficient estimator under the semi-parametric transform model. We use machine learning tools like SuperLearner to estimate propensity score nuisance functional needed to fit our models.