In randomized clinical trials (RCTs), the accurate estimation of marginal treatment effects is crucial for determining the efficacy of interventions. Enhancing the statistical power of these analyses is a key objective for statisticians. The increasing availability of historical data from registries, prior trials, and health records presents an opportunity to improve trial efficiency. However, many methods for historical borrowing compromise strict type-I error rate control. Building on the work by Schuler et al. [2022] on prognostic score adjustment for linear models, this paper extends the methodology to the plug-in analysis proposed by Rosenblum et al. [2010] using generalized linear models (GLMs) to further enhance the efficiency of RCT analyses without introducing bias. Specifically, we train a prognostic model on historical control data and incorporate the resulting prognostic scores as covariates in the plug-in GLM analysis of the trial data. This approach leverages the predictive power of historical data to improve the precision of marginal treatment effect estimates. We demonstrate that this method achieves local semi-parametric efficiency under the assumption of an additive treatment effect on the link scale. We expand the GLM plug-in method to include negative binomial regression. Additionally, we provide a straightforward formula for conservatively estimating the asymptotic variance, facilitating power calculations that reflect these efficiency gains. Our simulation study supports the theory. Even without an additive treatment effect, we observe increased power or reduced standard error. While population shifts from historical to trial data may dilute benefits, they do not introduce bias.

翻译：在随机临床试验（RCT）中，准确估计边际处理效应对于确定干预措施的有效性至关重要。提高这些分析的统计功效是统计学家的一个核心目标。来自登记库、既往试验和健康记录的历史数据日益增多，为提高试验效率提供了机遇。然而，许多历史数据借用方法会损害严格的I类错误率控制。基于Schuler等人[2022]关于线性模型预后评分调整的研究，本文将该方法扩展到Rosenblum等人[2010]提出的插件分析中，使用广义线性模型（GLM）来进一步提升RCT分析的效率且不引入偏倚。具体而言，我们在历史对照数据上训练一个预后模型，并将所得的预后评分作为协变量纳入试验数据的插件GLM分析中。该方法利用历史数据的预测能力来提高边际处理效应估计的精度。我们证明，在链接尺度上存在加性处理效应的假设下，此方法能达到局部半参效率。我们将GLM插件方法扩展到包含负二项回归。此外，我们提供了一个用于保守估计渐近方差的简明公式，便于进行能反映这些效率增益的功效计算。我们的模拟研究支持了该理论。即使不存在加性处理效应，我们也观察到功效提升或标准误降低。虽然从历史数据到试验数据的总体偏移可能削弱效益，但不会引入偏倚。