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：随机对照试验（RCT）中高效准确的决策需要无偏且精确的治疗效应推断。满足该需求的两项策略是：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。我们提出一种新的贝叶斯预后协变量调整方法（简称贝叶斯PROCOVA），该方法融合了上述两种策略。贝叶斯PROCOVA中的协变量调整基于生成式人工智能算法，该算法为RCT参与者构建数字孪生生成器。DTG使用历史对照数据进行训练，为每位RCT参与者在对照治疗下的结局生成数字孪生概率分布。该DT分布的期望值（称为预后评分）定义了待调整的协变量。历史对照信息通过具有两个分量的加性混合先验加以利用：基于历史对照数据指定的信息性先验概率分布，以及弱信息先验分布。混合权重决定了后验推断在何种程度上来自信息性分量与弱信息分量。该权重本身也服从先验分布，因此整个加性混合先验可完全预先指定，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后验分布采样，并在贝叶斯PROCOVA中推导了治疗效应参数在权重条件下后验均值与方差的闭式表达式。通过模拟研究（涵盖不同偏差场景）评估贝叶斯PROCOVA相较于频率学派PROCOVA的效率增益，重点考察其偏差控制与方差缩减特性。这些增益可直接转化为更小规模的RCT。