Primary Submission Category: Positivity violations
Fair comparisons of causal parameters with many treatments and positivity violations
Authors: Alec McClean, Yiting Li, Sunjae Bae, Mara McAdams-DeMarco, Ivan Diaz,
Presenting Author: Wenbo Wu*
Comparing outcomes across treatments is essential in causal inference. Researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means (TSMs) are commonly used, but identification requires a positivity assumption—that all subjects have non-zero probability of receiving each treatment—which is often implausible, especially with many treatment values. Parameters based on dynamic stochastic interventions offer robustness to positivity violations, but comparisons between the parameters may be unfair, because they can depend on outcomes under non-target treatments. To clarify when a fair comparison between two parameters targeting different treatments is possible, we propose a fairness criterion: if the conditional TSM for one treatment is greater than that for another, then the corresponding causal parameter is greater. We derive two intuitive properties equivalent to this criterion and show that only a mild positivity assumption is needed to identify fair parameters. We provide parameters that satisfy this criterion and are identifiable under the milder positivity assumption. Their non-smoothness makes standard efficiency theory inapplicable, so we propose smooth approximations of them. We then develop doubly robust-style estimators that attain parametric convergence rates under nonparametric conditions. We illustrate our methods with an analysis of dialysis providers in New York State.