Progressive multi-state survival outcomes are common in trials with recurrent or sequential events and require treatment effect estimands that remain interpretable without proportional intensity or Markov assumptions. The restricted mean time in favor of treatment (RMT-IF) extends the restricted mean survival time to ordered multi-state processes and provides such an interpretable estimand. However, existing RMT-IF methods are nonparametric, assume covariate-independent censoring for independent observations, and do not accommodate cluster-randomized trials (CRTs), limiting both efficiency and applicability. We develop a class of doubly robust estimators for RMT-IF under right censoring using an augmented inverse-probability weighting framework that combines stage-specific outcome regression with arm-specific censoring models, yielding consistency when either nuisance model is correctly specified. We further extend the framework to CRTs by formalizing both cluster-level and individual-level average RMT-IF estimands to address informative cluster size and by constructing corresponding doubly robust estimators that account for within-cluster correlation. For inference, we employ model-agnostic jackknife variance estimators in both individually randomized and cluster-randomized settings. Extensive simulation studies demonstrate finite-sample performance, and the methods are illustrated using two randomized trial examples.

翻译：渐进多状态生存结局在具有复发或顺序事件的试验中较为常见，需要能够在无需比例强度或马尔可夫假设下保持可解释性的治疗效果估计目标。限制性平均有利治疗时间将限制性平均生存时间推广至有序多状态过程，提供了此类可解释的估计目标。然而，现有RMT-IF方法均为非参数方法，对独立观测值假设协变量独立删失，且无法适用于整群随机化试验，从而限制了其效率与适用性。我们基于增强逆概率加权框架，通过结合阶段特异性结局回归与组别特异性删失模型，开发了一类针对右删失下RMT-IF的双重稳健估计器，当任一干扰模型被正确设定时均可保证一致性。我们进一步将该框架扩展至CRTs：通过形式化定义群组层面与个体层面的平均RMT-IF估计目标以处理信息性群组规模，并构建相应的、考虑群内相关性的双重稳健估计器。在推断方面，我们在个体随机化与整群随机化设置中均采用模型无关的刀切法方差估计器。大量模拟研究验证了有限样本性能，并通过两项随机化试验实例对方法进行了演示。