Covariate adjustment can enhance precision and power in clinical trials, yet its application to the win odds remains unclear. The win odds is an extension of the win ratio that counts ties as half a win for the treatment and the control group, respectively. In their original form, both the win ratio and the win odds rely on comparing each individual from the treatment group to each individual from the control group in a pairwise manner, and count the number of wins, losses, and ties from these pairwise comparisons. A priori, it is not clear how covariate adjustment can be implemented for the win odds. To address this, we establish a connection between the win odds and the marginal probabilistic index, a measure for which covariate adjustment theory is well-developed. Using this connection, we show how covariate adjustment for the win odds is possible, leading to potentially more precise estimators and larger power as compared to the unadjusted win odds. We present the underlying theory for covariate adjustment for the win odds in an accessible way and apply the method on synthetic data based on the CANTOS trial (ClinicalTrials.gov identifier: NCT01327846) characteristics, on a subset of the HF-ACTION trial data (ClinicalTrials.gov identifier: NCT00047437), and on simulated data to study the operating characteristics of the method. We observe that there is indeed a potential gain in power when the win odds is adjusted for baseline covariates if the baseline covariates are prognostic for the outcome. This comes at the cost of a slight inflation of the type I error rate for small sample sizes.

翻译：协变量调整可提升临床试验的精准度与统计效力，但其在胜算比中的应用仍不明确。胜算比是胜率的扩展形式，将平局分别计为治疗组和对照组各半次胜利。在原始形式中，胜率与胜算比均通过将治疗组每位受试者与对照组每位受试者进行配对比较，并统计配对比较中的获胜、失败与平局次数。理论上，尚不清楚如何对胜算比实施协变量调整。为解决此问题，我们建立了胜算比与边际概率指数之间的关联——后者是一种协变量调整理论已充分发展的度量指标。利用这一关联，我们展示了如何实现胜算比的协变量调整，从而相较于未调整的胜算比，获得潜在更高精度的估计量及更大统计效力。我们以直观方式阐述了胜算比协变量调整的底层理论，并基于CANTOS试验（ClinicalTrials.gov标识符：NCT01327846）特征合成的数据、HF-ACTION试验（ClinicalTrials.gov标识符：NCT00047437）数据子集以及模拟数据应用了该方法，以研究其操作性能。我们观察到，当基线协变量对结局具有预后意义时，对胜算比进行基线协变量调整确实能提升统计效力，但代价是小样本情况下I类错误率略有膨胀。