Nonparametric Estimation of Conditional Incremental Effects

Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Previous work has focused primarily on estimating the conditional average treatment effect (CATE), which considers the difference between counterfactual mean outcomes under interventions when all subjects receive treatment and all subjects receive control. However, these interventions may be unrealistic in certain policy scenarios. Furthermore, identification of the CATE requires that all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. In this paper, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions under which the odds of treatment are multiplied by some user-specified factor. These effects do not require positivity for identification and can be better suited for modeling real-world policies in which people cannot be forced to treatment. We develop a projection estimator, the "Projection-Learner", and a flexible nonparametric estimator, the "I-DR-Learner", which can each estimate all the conditional effects we propose. We derive model-agnostic error guarantees for both estimators, and show that both satisfy a form of double robustness, whereby the Projection-Learner attains parametric efficiency and the I-DR-Learner attains oracle efficiency under weak convergence conditions on the nuisance function estimators. We then propose a summary of treatment effect heterogeneity, the variance of a conditional derivative, and derive a nonparametric estimator for the effect that also satisfies a form of double robustness. Finally, we demonstrate our estimators with an analysis of the the effect of ICU admission on mortality using a dataset from the (SPOT)light prospective cohort study.