Modified treatment policies that depend on the sequence of natural treatment values
Abstract
Longitudinal modified treatment policies (LMTPs) are a class of interventions that allow the definition, identification, and estimation of causal effects in general settings, including continuous or multivariate exposures and treatment regimens that require grace periods. Targeted machine learning estimators (i.e., double/debiased) have been formulated for LMTPs that assign exposure at time $t$ as a function of the natural treatment value at time $t$. However, applications such as delaying treatment initiation or withholding a potentially harmful treatment require LMTPs that also depend on the sequence of prior natural treatment values. This paper develops identification and targeted learning methods for estimating mean counterfactual outcomes under prespecified LMTPs that may depend on this sequence. We define 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 estimators to higher-risk pain treatment to assess the effect of withholding treatment during the first month it would naturally be indicated on the 12-month incidence of opioid use disorder.