D'Alessandro Antonio, Kim Jiyu, Adhikari Samrachana, Goff Donald, Bargagli-Stoffi Falco J, Santacatterina Michele
Division of Biostatistics, New York University, New York, USA.
Department of Psychiatry, New York University, New York, USA.
Stat Med. 2026 Feb;45(3-5):e70436. doi: 10.1002/sim.70436.
Randomized controlled trials (RCTs) often include subgroup analyses to assess whether treatment effects vary across prespecified patient populations. However, these analyses frequently suffer from small sample sizes, which limit the power to detect heterogeneous effects. Power can be improved by leveraging predictors of the outcome-that is, through covariate adjustment-as well as by borrowing external data from similar RCTs or observational studies. The benefits of covariate adjustment may be limited when the trial sample is small. Borrowing external data can increase the effective sample size and improve power, but it introduces two key challenges: (i) integrating data across sources can lead to model misspecification, and (ii) practical violations of the positivity assumption-where the probability of receiving the target treatment is near zero for some covariate profiles in the external data-can lead to extreme inverse-probability weights and unstable inferences, ultimately negating potential power gains. To account for these shortcomings, we present an approach to improving power in preplanned subgroup analyses of small RCTs that leverages both baseline predictors and external data. We propose de-biased estimators that accommodate parametric, machine learning (ML), and nonparametric Bayesian methods. To address practical positivity violations (PPVs), we introduce three estimators: A covariate-balancing approach, an automated de-biased machine learning (DML) estimator, and a calibrated-DML estimator. We show improved power in various simulations and offer practical recommendations for the application of the proposed methods. Finally, we apply them to evaluate the effectiveness of citalopram for negative symptoms in first-episode schizophrenia (FES) patients across subgroups defined by duration of untreated psychosis (DUP), using data from two small RCTs.
随机对照试验（RCT）通常包括亚组分析，以评估治疗效果在预先指定的患者群体中是否存在差异。然而，这些分析常常受到样本量小的困扰，这限制了检测异质性效应的效能。可以通过利用结局的预测因素（即通过协变量调整）以及从类似的随机对照试验或观察性研究中借用外部数据来提高效能。当试验样本量较小时，协变量调整的益处可能有限。借用外部数据可以增加有效样本量并提高效能，但会带来两个关键挑战：（i）跨数据源整合数据可能导致模型设定错误，以及（ii）实际违反阳性假设（即外部数据中某些协变量特征接受目标治疗的概率接近零）可能导致极端的逆概率权重和不稳定的推断，最终抵消潜在的效能提升。为了解决这些缺点，我们提出了一种在小型随机对照试验的预先计划亚组分析中提高效能的方法，该方法同时利用基线预测因素和外部数据。我们提出了去偏估计量，它适用于参数、机器学习（ML）和非参数贝叶斯方法。为了解决实际的阳性假设违反（PPV）问题，我们引入了三种估计量：一种协变量平衡方法、一种自动去偏机器学习（DML）估计量和一种校准DML估计量。我们在各种模拟中展示了提高的效能，并为所提出方法的应用提供了实际建议。最后，我们使用来自两项小型随机对照试验的数据，应用这些方法来评估西酞普兰对首发精神分裂症（FES）患者中由未治疗精神病持续时间（DUP）定义的亚组的阴性症状的有效性。
