Multiply robust estimators in longitudinal studies with missing data under control-based imputation

TL;DR

This paper introduces new multiply robust estimators for treatment effects in longitudinal studies with missing data, specifically under control-based imputation scenarios like jump-to-reference, demonstrating their theoretical properties and practical performance.

Contribution

The paper develops novel estimators based on a potential outcomes framework under J2R, achieving multiple robustness and $n^{1/2}$-consistency, with validation through simulations and clinical trial data.

Findings

Estimators are consistent and robust under various model misspecifications.

Simulation studies show improved finite-sample performance.

Application to clinical trial data demonstrates practical utility.

Abstract

Longitudinal studies are often subject to missing data. The ICH E9(R1) addendum addresses the importance of defining a treatment effect estimand with the consideration of intercurrent events. Jump-to-reference (J2R) is one classically envisioned control-based scenario for the treatment effect evaluation using the hypothetical strategy, where the participants in the treatment group after intercurrent events are assumed to have the same disease progress as those with identical covariates in the control group. We establish new estimators to assess the average treatment effect based on a proposed potential outcomes framework under J2R. Various identification formulas are constructed under the assumptions addressed by J2R, motivating estimators that rely on different parts of the observed data distribution. Moreover, we obtain a novel estimator inspired by the efficient influence function, with multiple robustness in the sense that it achieves $n^{1/2}$-consistency if any pairs of multiple nuisance functions are correctly specified, or if the nuisance functions converge at a rate not slower than $n^{-1/4}$ when using flexible modeling approaches. The finite-sample performance of the proposed estimators is validated in simulation studies and an antidepressant clinical trial.