Randomized controlled trials (RCTs) are often underpowered to detect treatment heterogeneity in subgroups defined by cross-classifications of multiple covariates, due to sparse sample sizes in some strata. External RCT data can help, but typically provide treatment effect estimates at a coarser level (e.g., by sex or race) rather than for the finer subgroups of interest (e.g., race-by-sex). We propose a novel James-Stein (JS)-type estimator that borrows strength from such coarsened external estimates to improve estimation of finer subgroup-specific conditional average treatment effects (CATEs) in an internal study, while accommodating potential incompatibility in marginal CATEs across populations. Based on asymptotic theory, we derive a practical analytic variance estimator for the JS estimator that exhibits acceptable empirical performance. Under mild conditions, we show that the proposed estimator uniformly dominates the ordinary least squares (OLS) estimator based on internal data regarding a weighted quadratic loss. Simulation studies demonstrate favorable performance compared with existing shrinkage methods, including empirical Bayes and generalized ridge estimators. We illustrate our method by estimating race-by-sex subgroup CATEs in a tirzepatide weight-loss trial (SURMOUNT-1), borrowing sex-specific and race-specific estimates from two previous semaglutide trials (STEP 1 and STEP 2). The proposed method detects a significantly larger treatment effect on percentage weight loss in the female-White subgroup than in the female-Asian subgroup, a difference not detected using internal data alone.

翻译：随机对照试验（RCT）常因某些分层样本量稀疏而难以检测由多个协变量交叉分类定义的子组中的处理异质性。外部RCT数据可提供帮助，但通常仅能提供粗粒度层面的处理效应估计（如按性别或种族），而非所需细粒度子组（如种族与性别的交叉组合）的估计。我们提出一种新型詹姆斯-斯坦（JS）型估计量，通过借用此类粗粒度外部估计信息，在内部研究中改进对细粒度子组特异性条件平均处理效应（CATEs）的估计，同时兼容不同人群间边际CATE可能存在的不可比性。基于渐近理论，我们推导出该JS估计量的实用解析方差估计量，且该估计量展现出可接受的实证表现。在温和条件下，我们证明所提估计量在加权二次损失下一致优于仅基于内部数据的普通最小二乘（OLS）估计量。模拟研究表明，与现有收缩方法（包括经验贝叶斯和广义岭估计量）相比，该估计量具有更优性能。我们通过替西帕肽减肥试验（SURMOUNT-1）估计种族与性别交叉子组的CATEs，并借用先前两项司美格鲁肽试验（STEP 1和STEP 2）中性别特异性和种族特异性估计值，对方法进行实证。所提方法检测到女性-白种人子组的体重减轻百分比处理效应显著大于女性-亚裔子组，而仅使用内部数据无法检测此差异。