Efficient Statistical Estimation for Sequential Adaptive Experiments with Implications for Adaptive Designs
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序贯自适应实验的有效统计估计及其对自适应设计的启示
- 研究问题
- 当实验随机分配随累积数据调整并产生观测依赖时，如何有效估计因果参数，并据此设计降低估计方差的实验？
- 方法与思路
- 作者在自适应设计的 TMLE 框架上提出基于设计似然的 ADL-TMLE，以平均处理效应为例，并据此构造方差导向设计。
- 材料陈述的贡献
- 摘要称在放宽的正值性和设计稳定条件下建立渐近正态性及半参数效率，模拟显示方差改善，并扩展至纵向结构。
- 阅读关注点
- 应核对正值性和设计稳定条件的精确定义、效率界的参照模型，以及新设计的方差目标如何估计并在序贯实验中实现。
- 阅读边界
- 这是 arXiv 预印本，同行评审与接收未核实；摘要未给出放宽条件和模拟数值，不能外推其方差优势至所有自适应实验。
原文摘要
Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design features in response to data accumulated sequentially during the experiment. These adaptations are useful to achieve diverse objectives, including reducing uncertainty in the estimation of causal estimands or increasing participants' chances of receiving better treatments during the experiment. At the end of the experiment, it is often desirable to answer causal questions from the observed data. However, the adaptive nature of such experiments and the resulting dependence among observations pose significant challenges to providing valid statistical inference and efficient estimation of causal estimands. Building upon the Targeted Maximum Likelihood Estimator (TMLE) framework tailored for adaptive designs (van der Laan, 2008), we introduce a new Adaptive-Design-Likelihood-based TMLE (ADL-TMLE) to estimate a wide class of causal estimands from adaptive experiment data, including the average treatment effect as our primary example. We establish asymptotic normality and semiparametric efficiency of ADL-TMLE under relaxed positivity and design stabilization assumptions for adaptive experiments. Motivated by these results, we further propose a novel adaptive design aimed at minimizing the variance of the estimator based on data generated under that design. Simulations show that ADL-TMLE demonstrates superior variance-reduction performance across different types of adaptive experiments, and that the proposed adaptive design attains lower variance than the standard efficiency-oriented adaptive design. Finally, we generalize our framework to broader settings, including those with longitudinal structures.