Effective and rapid decision-making from randomized controlled trials (RCTs) requires unbiased and precise treatment effect inferences. Two strategies to address this requirement are to adjust for covariates that are highly correlated with the outcome, and to leverage historical control information via Bayes' theorem. We propose a new Bayesian prognostic covariate adjustment methodology, referred to as Bayesian PROCOVA, that combines these two strategies. Covariate adjustment in Bayesian PROCOVA is based on generative artificial intelligence (AI) algorithms that construct a digital twin generator (DTG) for RCT participants. The DTG is trained on historical control data and yields a digital twin (DT) probability distribution for each RCT participant's outcome under the control treatment. The expectation of the DT distribution, referred to as the prognostic score, defines the covariate for adjustment. Historical control information is leveraged via an additive mixture prior with two components: an informative prior probability distribution specified based on historical control data, and a weakly informative prior distribution. The mixture weight determines the extent to which posterior inferences are drawn from the informative component, versus the weakly informative component. This weight has a prior distribution as well, and so the entire additive mixture prior is completely pre-specifiable without involving any RCT information. We establish an efficient Gibbs algorithm for sampling from the posterior distribution, and derive closed-form expressions for the posterior mean and variance of the treatment effect parameter conditional on the weight, in Bayesian PROCOVA. We evaluate efficiency gains of Bayesian PROCOVA via its bias control and variance reduction compared to frequentist PROCOVA in simulation studies that encompass different discrepancies. These gains translate to smaller RCTs.

翻译：从随机对照试验（RCT）中实现有效且快速的决策，需要对处理效应进行无偏且精确的推断。两种应对策略包括：调整与结局高度相关的协变量，以及通过贝叶斯定理利用历史对照信息。我们提出了一种新的贝叶斯预后协变量调整方法，称为Bayesian PROCOVA，该方法融合了以上两种策略。贝叶斯PROCOVA中的协变量调整基于生成式人工智能（AI）算法，该算法为RCT参与者构建数字孪生生成器（DTG）。DTG基于历史对照数据进行训练，并为每位RCT参与者在对照治疗下的结局生成一个数字孪生（DT）概率分布。DT分布的期望（称为预后评分）定义了调整所用的协变量。历史对照信息通过一个加性混合先验加以利用，该先验包含两个分量：基于历史对照数据指定的信息性先验概率分布，以及弱信息性先验分布。混合权重决定了后验推断来自信息性分量还是弱信息性分量的程度。该权重本身也具有先验分布，因此整个加性混合先验可完全预设，无需涉及任何RCT信息。我们建立了一种高效的吉布斯算法用于从后验分布中采样，并推导了贝叶斯PROCOVA中条件于权重的处理效应参数后验均值和方差的闭式表达式。通过模拟研究（涵盖不同差异情形）比较频率学派PROCOVA，我们评估了贝叶斯PROCOVA在偏差控制和方差缩减方面的效率提升。这些提升可转化为更小规模的RCT。