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In causal inference, a variety of causal effect estimands have been studied,including the sample, uncensored, target, conditional, optimal subpopulation,and optimal weighted average treatment effects. Ad-hoc methods have beendeveloped for each estimand based on inverse probability weighting (IPW) and onoutcome regression modeling, but these may be sensitive to modelmisspecification, practical violations of positivity, or both. The contributionof this paper is twofold. First, we formulate the generalized average treatmenteffect (GATE) to unify these causal estimands as well as their IPW estimates.Second, we develop a method based on Kernel Optimal Matching (KOM) to optimallyestimate GATE and to find the GATE most easily estimable by KOM, which we termthe Kernel Optimal Weighted Average Treatment Effect. KOM provides uniformcontrol on the conditional mean squared error of a weighted estimator over aclass of models while simultaneously controlling for precision. We study itstheoretical properties and evaluate its comparative performance in a simulationstudy. We illustrate the use of KOM for GATE estimation in two case studies:comparing spine surgical interventions and studying the effect of peer supporton people living with HIV.

Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal Matching