Encoding and inference on separable effects for sustained treatments

TL;DR

This paper develops a new theoretical framework for estimating the effects of sustained, time-varying treatments, with practical estimators, applied to blood pressure treatment data to assess kidney injury risk.

Contribution

It extends the theory of separable effects to sustained treatment strategies using an unconventional encoding, enabling better identification and estimation methods.

Findings

Derived concise identifying assumptions with practical properties.

Developed doubly robust semiparametrically efficient estimators.

Applied to SPRINT data to estimate treatment effects on kidney injury.

Abstract

Sustained treatment strategies are common in many domains, particularly in medicine, where many treatment are delivered repeatedly over time. The effects of adherence to a treatment strategy throughout follow-up are often more relevant to decision-makers than effects of treatment assignment or initiation. Here we consider the separable effect of sustained use of a time-varying treatment. Despite the potential usefulness of this estimand, the theory of separable effects has yet to be extended to settings with sustained treatment strategies. To derive our results, we use an unconventional encoding of time-varying treatment strategies. This allows us to obtain concise formulations of identifying assumptions with better practical properties; for example, they admit frugal graphical representations and formulations of identifying functionals. These functionals are used to motivate doubly robust semiparametrically efficient estimators. The results are applied to the Systolic Blood Pressure Intervention Trial (SPRINT), where we estimate a separable effect of modified blood pressure treatments on the risk of acute kidney injury.