Randomized controlled trials (RCTs) with binary primary endpoints introduce novel challenges for inferring the causal effects of treatments. The most significant challenge is non-collapsibility, in which the conditional odds ratio estimand under covariate adjustment differs from the unconditional estimand in the logistic regression analysis of RCT data. This issue gives rise to apparent paradoxes, such as the variance of the estimator for the conditional odds ratio from a covariate-adjusted model being greater than the variance of the estimator from the unadjusted model. We address this challenge in the context of adjustment based on predictions of control outcomes from generative artificial intelligence (AI) algorithms, which are referred to as prognostic scores. We demonstrate that prognostic score adjustment in logistic regression increases the power of the Wald test for the conditional odds ratio under a fixed sample size, or alternatively reduces the necessary sample size to achieve a desired power, compared to the unadjusted analysis. We derive formulae for prospective calculations of the power gain and sample size reduction that can result from adjustment for the prognostic score. Furthermore, we utilize g-computation to expand the scope of prognostic score adjustment to inferences on the marginal risk difference, relative risk, and odds ratio estimands. We demonstrate the validity of our formulae via extensive simulation studies that encompass different types of logistic regression model specifications. Our simulation studies also indicate how prognostic score adjustment can reduce the variance of g-computation estimators for the marginal estimands while maintaining frequentist properties such as asymptotic unbiasedness and Type I error rate control. Our methodology can ultimately enable more definitive and conclusive analyses for RCTs with binary primary endpoints.

翻译：二元主要结局的随机对照试验（RCTs）在推断治疗因果效应时引入了新挑战。其中最主要的是非可压缩性，即RCT数据逻辑回归分析中经协变量调整的条件比值比估计值与未经调整的边际估计值存在差异。该问题导致明显悖论，例如协变量调整模型中条件比值比估计量的方差反而大于未调整模型。我们针对基于生成式人工智能算法预测对照结局的调整方式（即预后评分）解决此挑战。研究表明，与未调整分析相比，逻辑回归中纳入预后评分调整可在固定样本量下提高条件比值比的Wald检验效能，或降低达到预期效能所需的样本量。我们推导了因预后评分调整可获得的效能提升和样本量缩减的前瞻性计算公式。进一步采用G计算方法将预后评分调整的应用范围扩展至边际风险差、相对风险和比值比估计量的推断。通过涵盖多种逻辑回归模型设定的广泛模拟研究，验证了公式的有效性。模拟结果同时表明，预后评分调整可在保持渐近无偏性和I类错误率控制等频率学派性质的同时，降低边际估计量G计算估计量的方差。最终，该方法有望为二元主要结局RCTs提供更具确定性和结论性的分析。