Assumption-lean covariate adjustment under covariate adaptive randomization when $p = o (n)$
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协变量自适应随机化下 p=o(n) 的弱模型假设协变量调整
- 研究问题
- 在超总体模型与协变量自适应随机化下，协变量维度满足 p=o(n) 时，如何避免普通最小二乘调整的偏差并改善处理效应估计？
- 方法与思路
- 作者构造基于二阶 U 统计量的调整估计量，将随机化文献中的耦合技术推广至 U 统计量，并以留出多个观测分析逆样本 Gram 矩阵。
- 材料陈述的贡献
- 摘要称新估计量在所研究条件下近乎无偏地估计平均处理效应并保证效率增益，且合成与半合成实验显示较好的有限样本表现。
- 阅读关注点
- 应核对允许的随机化方案、协变量与矩阵的正则条件、近乎无偏的精确定义，以及效率保证和维度增长限制的适用范围。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收未经核实；弱结果模型假设并非完全无假设，摘要未列出完整条件或实验数值。
原文摘要
Adjusting for (baseline) covariates with working regression models becomes standard practice in the analysis of randomized clinical trials (RCT). When the dimension $p$ of the covariates is large relative to the sample size $n$, specifically $p = o (n)$, adjusting for covariates even in a linear working model by ordinary least squares can yield overly large bias, defeating the purpose of improving efficiency. This issue arises when no structural assumptions are imposed on the outcome model, a scenario that we refer to as the assumption-lean setting. Several new estimators have been proposed to address this issue. However, they focus mainly on simple randomization under the finite-population model, not covering covariate adaptive randomization (CAR) schemes under the superpopulation model. Due to improved covariate balance between treatment groups, CAR is more widely adopted in RCT; and the superpopulation model fits better when subjects are enrolled sequentially or when generalizing to a larger population is of interest. Thus, there is an urgent need to develop procedures in these settings, as the current regulatory guidance provides little concrete direction. In this paper, we fill this gap by demonstrating that an adjusted estimator based on second-order $U$-statistics can almost unbiasedly estimate the average treatment effect and enjoy a guaranteed efficiency gain if $p = o (n)$. In our analysis, we generalize the coupling technique commonly used in the CAR literature to $U$-statistics and also obtain several useful results for analyzing inverse sample Gram matrices by a delicate leave-$m$-out analysis, which may be of independent interest. Both synthetic and semi-synthetic experiments are conducted to demonstrate the superior finite-sample performance of our new estimator compared to popular benchmarks.