Prognostic covariate adjustment (PROCOVA) is a two-sample two-stage estimation method used in randomized controlled trials. In the first stage, a prognostic score, defined as the conditional expectation of an outcome given covariates under the control treatment, is estimated using historical data. In the second stage, analysis of covariance 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 estimated in this procedure, the variance estimator, which treats the prognostic score as known, has been used. Furthermore, the difference in the asymptotic variance between cases where the prognostic score is known versus where it is estimated has not been previously clarified. In this study, we derived these two asymptotic variances and showed that they are equal. We also constructed two variance estimator: one that treats the prognostic score as known, and another that accounts for its estimation, and compared their performance through simulation studies and data applications. For PROCOVA, since both variance estimators are asymptotically valid, it is generally recommended to use a variance estimator that treats the prognostic score as known, as it is simpler to derive and implement. However, when historical data is small, a variance estimator that explicitly accounts for prognostic score estimation is recommended if conservative inference is preferred.

翻译：预后协变量调整（PROCOVA）是一种用于随机对照试验的两样本两阶段估计方法。在第一阶段，利用历史数据估计预后评分——定义为对照治疗条件下给定协变量时结果变量的条件期望。在第二阶段，以估计的预后评分与治疗分配作为解释变量进行协方差分析，并估计平均治疗效果。尽管该流程中已对预后评分进行估计，但当前仍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情形下渐近方差的差异此前尚未被阐明。本研究推导了这两种渐近方差并证明其相等性。我们同时构建了两种方差估计量：一种将预后评分视为已知，另一种则明确考虑其估计过程，并通过模拟研究与实际数据应用比较两者性能。对于PROCOVA而言，由于两种方差估计量均具有渐近有效性，通常推荐使用更易推导与实现的“预后评分已知”型方差估计量。但当历史数据量较小时，若需保守推断，建议采用明确考虑预后评分估计过程的方差估计量。