A method for covariate adjustment in randomized controlled trials is prognostic covariate adjustment (PROCOVA). PROCOVA is a two-sample two-stage estimation method. In the first stage, the prognostic score, which is the conditional expectation of an outcome given covariates under control treatment, is estimated using historical data. In the second stage, ANCOVA with the estimated prognostic score and treatment assignment as explanatory variables is performed, and the average treatment effect is estimated. Although the prognostic score is actually estimated in this procedure, the variance estimator, which treats the prognostic score as known, has been used. Furthermore, the difference in asymptotic variance between cases where the prognostic score is known and cases where it is estimated has not been clarified. In this study, we derived these two asymptotic variances and showed that they are equal. We also constructed the variance estimator, which treats the prognostic score as known, and the variance estimator, which accounts for the prognostic score estimation, and compared their performance through simulation studies and data application. Both variance estimators are asymptotically valid. When historical data is small, the variance estimator which explicitly accounts for the prognostic score estimation is recommended if one prefers conservative inference.

翻译：随机对照试验中协变量调整的一种方法是预后协变量调整（PROCOVA）。该方法是一种两样本两阶段估计法。第一阶段利用历史数据估计预后评分，即控制治疗条件下给定协变量的结果条件期望；第二阶段以估计的预后评分和治疗分配为解释变量进行协方差分析，并估计平均治疗效果。尽管该流程实际对预后评分进行了估计，但一直采用将预后评分视为已知的方差估计量。此外，预后评分已知与估计两种情况下的渐近方差差异尚未明确。本研究推导了这两种渐近方差，并证明二者相等。我们还构建了将预后评分视为已知的方差估计量，以及考虑预后评分估计过程的方差估计量，并通过模拟研究和数据应用比较其性能。两种方差估计量均具有渐近有效性。当历史数据量较小时，若偏好保守推断，建议使用明确考虑预后评分估计过程的方差估计量。