Modified treatment policies that depend on the natural history of treatment

2026-05-22

AI Summary

Existing longitudinal modified treatment policy (LMTP) approaches rely solely on the current natural treatment value, making them ill-suited to capture history-dependent intervention effects such as treatment delays. This work extends LMTP for the first time to settings where interventions depend on the entire treatment history, establishing a generalized framework for causal effect estimation. Building on an augmented longitudinal data structure, the proposed method integrates longitudinal g-computation with efficient influence functions and doubly robust targeted machine learning to yield a √n-consistent estimator. The approach is successfully applied to estimate the causal effect of delaying treatment by one month on the incidence of opioid use disorder at 12 months among high-risk pain patients, enabling valid inference for complex time-varying interventions.

Abstract

Longitudinal modified treatment policies (LMTP) are a class of interventions that allow the definition, identification, and estimation of causal effects in general settings, such as with continuous or multivariate exposures, treatment regimens that require grace periods. Targeted machine learning estimators (i.e., double/debiased) have been formulated for LMTPs that assign the exposure at time $t$ as a function of the natural value of treatment at time $t$. However, important applications such as estimating the effect of a delay in the start of a treatment require formulating LMTPs that depend not only on the natural value of treatment at time $t$ but also on the \textit{history} of the natural value of treatment prior to time $t$. This paper develops targeted learning estimators for this general case. We discuss the definition of the effects, and propose estimators that use an augmented-data version of the sequential regression form of the longitudinal g-computation formula. Our estimators are based on the efficient influence function and provide $\sqrt{n}$ inference under standard doubly robust rate assumptions on the convergence of the outcome and treatment regressions. We apply the new estimators to assess the effect of delaying a risky pain treatment by one month on 12-month incidence of opioid use disorder.

Problem

• longitudinal modified treatment policies
• causal inference
• treatment delay
• natural treatment history
• targeted learning

Innovation

• longitudinal modified treatment policies
• targeted learning
• efficient influence function
• g-computation
• causal inference