Longitudinal Generalizations of the Average Treatment Effect on the Treated for Multi-valued and Continuous Treatments

TL;DR

This paper introduces Generalized ATTs (GATTs), extending the concept of ATT to complex longitudinal, multi-valued, and continuous treatments, with a focus on efficient semi-parametric inference and practical estimation methods.

Contribution

It proposes a new family of causal parameters, GATTs, along with identification results, efficient influence functions, and a novel ratio estimation approach using Riesz representers.

Findings

Simulation studies show improved stability of density ratio estimation.

The method effectively evaluates treatment effects on opioid use disorder.

The approach is demonstrated on Medicare patient data.

Abstract

The Average Treatment Effect on the Treated (ATT) is a common causal parameter defined as the average effect of a binary treatment among the subset of the population receiving treatment. We propose a novel family of parameters, Generalized ATTs (GATTs), that generalize the concept of the ATT to longitudinal data structures, multi-valued or continuous treatments, and conditioning on arbitrary treatment subsets. We provide a formal causal identification result that expresses the GATT in terms of sequential regressions, and derive the efficient influence function of the parameter, which defines its semi-parametric efficiency bound. Efficient semi-parametric inference of the GATT requires estimating the ratios of functions of conditional probabilities (or densities); we propose directly estimating these ratios via empirical loss minimization, drawing on the theory of Riesz representers. Simulations suggest that estimation of the density ratios using Riesz representation have better stability in finite samples. Lastly, we illustrate the use of our methods to evaluate the effect of chronic pain management strategies on the development of opioid use disorder among Medicare patients with chronic pain.