纵向与时间-事件数据联合模型中的函数形式：含应用与解释的实用指南
Functional forms in joint models for longitudinal and time-to-event data: A practical guide with application and interpretation
浏览论文内容
中文总结 AI 辅助
本文针对纵向与时间-事件数据联合模型的函数形式展开研究，通过结构化概述不同关联结构，结合MIRAGE胶质母细胞瘤试验数据，阐明函数形式选择对生物标志物-风险关系解释的关键作用，强调需匹配科学问题以保证模型有效性。
中文摘要 AI 辅助
背景：纵向与时间-事件数据的联合模型广泛应用于临床研究。然而，将生物标志物轨迹与事件风险关联的函数形式选择常被视为技术细节，尽管其对模型假设和解释至关重要，默认设定可能无法捕捉生物标志物轨迹的临床相关特征。方法：本文对联合模型中连接纵向与生存过程的函数形式进行结构化概述，比较关联结构，包括瞬时效应（当前值、斜率及加速度）、基于累积与变化的公式、共享随机效应，以及基于变异性的关联。利用MIRAGE胶质母细胞瘤试验的纵向白细胞测量值与总生存期数据，说明不同函数形式如何捕捉生物标志物轨迹的不同特征，并定义不同的生物标志物-风险关系。结果：瞬时形式捕捉生物标志物的当前水平或短期动态，而累积与变化形式反映长期暴露或趋势，基于变异性的结构则量化生物标志物轨迹的不稳定性作为替代预后信号。关联参数取决于函数形式、生物标志物尺度和时间尺度，因此效应量无法直接比较。在MIRAGE应用中，不同函数形式产生不同的效应解释，部分情况下对生物标志物-风险关系的结论也不同。结论：函数形式的选择是联合模型中的关键建模决策，决定生物标志物-风险关联的解释，使函数形式与科学问题相匹配，对有效解释和透明报告至关重要。
英文摘要
Background: Joint models for longitudinal and time-to-event data are widely used in clinical research. However, the choice of functional form linking the biomarker trajectory to event risk is often treated as a technical detail, despite its importance for model assumptions and interpretation. Default specifications may fail to capture clinically relevant features of biomarker trajectories. Methods: We provide a structured overview of functional forms linking longitudinal and survival processes in joint models. We compare association structures including instantaneous effects (current value, slope, and acceleration), cumulative and change-based formulations, shared random effects, and variability-based associations. Using longitudinal white blood cell measurements and overall survival data from the MIRAGE glioblastoma trial, we illustrate how different functional forms capture distinct features of biomarker trajectories and define different biomarker-risk relationships. Results: Instantaneous forms capture the biomarker's current level or short-term dynamics, whereas cumulative and change-based forms reflect longer-term exposure or trends. Variability-based structures quantify instability in the biomarker trajectory as an alternative prognostic signal. Association parameters depend on the functional form, biomarker scale, and time scale, and effect sizes are therefore not directly comparable. In the MIRAGE application, alternative functional forms produced different effect interpretations and, in some cases, different conclusions regarding the biomarker-risk relationship. Conclusions: The choice of functional form is a key modelling decision in joint models and determines the interpretation of the biomarker-risk association. Aligning the functional form with the scientific question is essential for valid interpretation and transparent reporting.
