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：在随机对照试验中，准确估计边际处理效应对于评估干预措施的有效性至关重要。提高此类分析的统计功效是统计学家的核心目标。来自注册库、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，许多历史借用法会损害严格的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，本文将方法扩展至Rosenblum等人[2010]提出的插件分析，采用广义线性模型进一步在无偏倚的前提下提升RCT分析效率。具体而言，我们在历史对照组数据上训练预后模型，并将所得预后评分作为协变量纳入试验数据的GLM插件分析中。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确度。我们证明，在连接尺度上存在可加处理效应的假设下，此方法能达到局部半参效率。我们将GLM插件法扩展至负二项回归，并提供了保守估计渐近方差的简明公式，便于进行反映效率提升的统计功效计算。仿真研究验证了理论结果：即使不存在可加处理效应，我们仍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。