Evaluating quality-of-life (QoL) outcomes in populations with high mortality risk is complicated by truncation by death, since QoL is undefined for individuals who do not survive to the planned measurement time. We propose a framework that jointly models the distribution of QoL and survival without extrapolating QoL beyond death. Inspired by multistate formulations, we extend the joint characterization of binary health states and mortality to continuous QoL outcomes. Because treatment effects cannot be meaningfully summarized in a single one-dimensional estimand without strong assumptions, our approach simultaneously considers both survival and the joint distribution of QoL and survival with the latter conveniently displayed in a simplex. We develop assumption-lean, semiparametric estimators based on efficient influence functions, yielding flexible, root-n consistent estimators that accommodate machine-learning methods while making transparent the conditions these must satisfy. The proposed method is illustrated through simulation studies and two real-data applications.

翻译：在死亡风险较高的人群中评估生活质量（QoL）结果时，常因“死亡截断”问题而变得复杂——对于未能存活至预设测量时间的个体，其QoL实际上处于未定义状态。本文提出一种联合建模QoL与生存分布的框架，避免对死亡后的QoL进行外推。受多状态模型框架启发，我们将二元健康状态与死亡率的联合表征推广至连续型QoL结局。由于在缺乏强假设的情况下，治疗效果无法通过单一的一维估计量进行有效概括，本方法同时考虑生存结局以及QoL与生存的联合分布，后者可通过单纯形直观呈现。基于高效影响函数，我们开发了假设约束宽松的半参数估计量，得到具有灵活性且满足根号n一致性的估计器，该估计器可兼容机器学习方法，同时明确揭示了这些方法所需满足的条件。通过模拟研究和两项实际数据应用，验证了所提方法的有效性。