AI 中文总结
该研究针对纵向多阶段时变处理的估计问题，提出半参数效率框架与纵向自适应设计及ADL-LTMLE估计器，可提升估计效率且性能接近最优设计。
AI 中文摘要
自适应设计正越来越多地用于临床试验和数字实验，通过随着数据积累更新处理随机化概率来提高估计效率。虽然现有多数工作聚焦于单阶段处理的场景，但针对具有多阶段、时变处理的纵向研究的自适应设计仍相对未被充分探索。在本研究中，我们开发了一个通用的半参数效率框架，用于设计纵向自适应实验，以优化广泛关注的目标估计量类别的估计效率。我们提出了一个面向效率的设计准则，以适配单估计量目标以及多个估计量的联合优化。我们证明，早期阶段的最优随机化依赖于后期阶段的分配，从而产生了推导 oracle 设计的反向递归策略，并提出了一种纵向自适应设计，利用积累的数据依次学习并瞄准该 oracle 设计。我们进一步开发了一种基于自适应设计似然的纵向目标最大似然估计器（ADL-LTMLE），用于对来自自适应实验的相关数据进行统计估计量的渐近正态且半参数有效的估计，且不依赖参数模型假设。将该框架应用于比较在给定阶段启动治疗与延迟至后续阶段启动治疗的治疗启动时间效应时，我们发现，针对特定阶段效应优化的设计会大幅损害其他阶段定义的效应的估计效率，凸显了我们框架所解决的设计权衡问题。模拟研究表明，所提出的设计和估计方法相较于非自适应设计实现了显著的方差降低，性能接近 oracle 设计。
英文摘要
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.
