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Alan M. Zaslavsky develops statistical methods for measuring health-care quality and disparities. His research includes missing data, hierarchical Bayesian models and Bayesian inference, bringing statistical adjustment to comparisons between health-care providers and populations.^[ref]

With Fan Li and Kari Lock Morgan, he developed a framework for balancing covariates through propensity score weighting. Their overlap weights emphasize people with a substantial chance of receiving either treatment, defining an overlap-weighted average treatment effect for that comparison population.^[ref]

For binary treatment and propensity score $e(X)=P(A=1\mid X)$, the observed-unit overlap weights areEach unit receives the probability of assignment to the opposite group. These weights are bounded between zero and one.^[ref]

The common target-population tilting function is instead $h(X)=e(X)\{1-e(X)\}$. If the original covariate density is $f(X)$, then the unnormalized weighted densities in the two arms are equal:Thus $h$ describes the target population, while $w_1,w_0$ are the arm-specific observation weights. Multiplying every observed unit by $h(X)$ would not give this balance identity.

Under conditional exchangeability, consistency in causal inference and nonzero total overlap, the weighted contrast identifies the overlap-weighted average treatment effectUnits with deterministic treatment assignment have $h=0$ and contribute nothing to this target. The estimand therefore generally differs from the full-population average treatment effect.

The overlap-weighted average treatment effect averages the conditional average treatment effect with weight proportional to $e(X)\{1-e(X)\}$, where $e(X)$ is the propensity score. It emphasizes covariate strata in which both treatments are plausible.

For fixed $\beta$, conditional least squares is minimized byTherefore the remaining objective iswhose normal equation givesLetbe the conditional average treatment effect. Since $A$ is binary, conditional exchangeability impliesand $\mathrm{Var}(A\mid X)=e(X)\{1-e(X)\}$. HenceThus ${\beta }_3$ is the overlap-weighted average treatment effect. It weights covariate strata by the overlap weight and generally differs from the ordinary ATE ${\beta }_1=\mathbb{E}[\tau (X)]$ when treatment effects are heterogeneous and overlap varies with $X$.