Surrogate markers offer the potential to reduce the burden of data collection by replacing costly or invasive primary outcomes with more accessible measurements, provided that they can faithfully indicate the effectiveness of a treatment. However, appropriate evaluation of a surrogate is particularly complex in longitudinal studies, where both outcomes and surrogates can evolve dynamically over time and interest lies not only in the treatment effect at one time, but rather treatment effects that may vary along the entire trajectory. In this paper, we develop a statistical framework for surrogate evaluation when both the surrogate and primary outcome are measured over time. Specifically, within the potential outcomes framework, we propose a formal causal definition of the proportion of the treatment effect on the longitudinal primary outcome that is explained by the treatment effect on the longitudinal surrogate. For estimation, we leverage state-space models, together with the Kalman filter and smoother, enabling efficient estimation of treatment effects under realistic conditions of temporal evolution and patient-level variability. We introduce a nonparametric bootstrap strategy for state-space models, a temporal homogeneity test, and demonstrate the finite-sample performance of our proposed methods via a simulation study and application to a diabetes clinical trial.

翻译：替代标志物通过用更易获取的测量替代昂贵或侵入性的主要结局，有望减轻数据收集负担，前提是它们能可靠地指示治疗效果。然而，在纵向研究中，对替代标志物的恰当评估尤为复杂——结局与替代标志物均随时间动态演变，且关注点不仅限于某一时刻的治疗效应，更在于可能沿整个轨迹变化的治疗效应。本文针对替代标志物与主要结局均随时间测量的场景，构建了统计评估框架。具体而言，在潜在结局框架内，我们提出了治疗效应对纵向主要结局的效应中被纵向替代标志物效应所解释比例的正式因果定义。在估计方面，我们利用状态空间模型结合卡尔曼滤波与平滑器，能在考虑时间演变与患者层面变异性的现实条件下实现治疗效应的高效估计。我们还引入了状态空间模型的非参数自助法、时间同质性检验，并通过模拟研究及应用于一项糖尿病临床试验，展示了所提出方法的有限样本性能。