Longitudinal Adaptive Experimental Design for Learning Multiple Target Estimands with Semiparametric Efficient Inference

2026-07-31

AI Summary

This study addresses the limitations of existing adaptive experimental designs, which are typically confined to single-stage interventions and thus ill-suited for longitudinal studies involving multi-stage, time-varying treatments and the joint estimation of multiple target parameters. The authors propose a longitudinal adaptive experimental design framework that derives optimal randomization allocations through a backward recursive strategy and progressively approximates this design using accumulating data. They introduce a novel design criterion that balances both individual and joint estimation efficiency, revealing that optimal allocation at early stages depends critically on future decisions. Furthermore, they develop a semiparametric, assumption-lean efficient estimation method (ADL-LTMLE). Simulations demonstrate that the proposed approach substantially reduces estimation variance, achieves performance close to the theoretical optimum, and elucidates the efficiency trade-offs among effect estimates across different stages.

Abstract

Adaptive designs are increasingly used in clinical trials and digital experiments to improve estimation efficiency by updating treatment randomization probabilities as data accumulate. While most existing work focuses on settings with a single-stage treatment, adaptive designs for longitudinal studies with multi-stage, time-varying treatments remain relatively underexplored. In this work, we develop a general semiparametric efficiency framework for designing longitudinal adaptive experiments to optimize the estimation efficiency of a broad class of target estimands of interest. An efficiency-oriented design criterion is proposed to accommodate both single-estimand targets and joint optimization across multiple estimands. We demonstrate that optimal randomization at earlier stages depends on later-stage allocations, yielding a backward-recursive strategy for deriving the oracle design, and propose a longitudinal adaptive design to sequentially learn and target the oracle design using accumulating data. We further develop an adaptive-design-likelihood-based longitudinal targeted maximum likelihood estimator (ADL-LTMLE) for asymptotically normal and semiparametric efficient estimation of statistical estimands from dependent data collected from adaptive experiments, without relying on parametric model assumptions. Applying the framework to time-to-treatment-initiation effects that compare initiating treatment at a given stage with delaying initiation until a subsequent stage, we show that designs optimized for a particular stage-specific effect can substantially compromise estimation efficiency for effects defined at other stages, highlighting the design trade-offs addressed by our framework. Simulation studies show the proposed design and estimation approaches achieve substantial variance reductions relative to non-adaptive designs, with performance close to that of the oracle design.

Problem

• longitudinal adaptive design
• multiple target estimands
• semiparametric efficiency
• time-varying treatments
• estimation efficiency

Innovation

• longitudinal adaptive design
• semiparametric efficiency
• multiple estimands
• targeted maximum likelihood estimation
• backward-recursive optimization