Thomadakis Christos, Meligkotsidou Loukia, Pantazis Nikos, Touloumi Giota
Department of Hygiene, Epidemiology and Medical Statistics, Medical School, National and Kapodistrian University of Athens, Mikras Asias 75, Athens, 115 27, Greece.
Department of Mathematics, National and Kapodistrian University of Athens, Panepistemiopolis, Athens, 157 84, Greece.
Biostatistics. 2024 Dec 31;26(1). doi: 10.1093/biostatistics/kxae041.
Joint modeling of longitudinal and time-to-event data, particularly through shared parameter models (SPMs), is a common approach for handling longitudinal marker data with an informative terminal event. A critical but often neglected assumption in this context is that the visiting/observation process is noninformative, depending solely on past marker values and visit times. When this assumption fails, the visiting process becomes informative, resulting potentially to biased SPM estimates. Existing methods generally rely on a conditional independence assumption, positing that the marker model, visiting process, and time-to-event model are independent given shared or correlated random effects. Moreover, they are typically built on an intensity-based visiting process using calendar time. This study introduces a unified approach for jointly modeling a normally distributed marker, the visiting process, and time-to-event data in the form of competing risks. Our model conditions on the history of observed marker values, prior visit times, the marker's random effects, and possibly a frailty term independent of the random effects. While our approach aligns with the shared-parameter framework, it does not presume conditional independence between the processes. Additionally, the visiting process can be defined on either a gap time scale, via proportional hazard models, or a calendar time scale, via proportional intensity models. Through extensive simulation studies, we assess the performance of our proposed methodology. We demonstrate that disregarding an informative visiting process can yield significantly biased marker estimates. However, misspecification of the visiting process can also lead to biased estimates. The gap time formulation exhibits greater robustness compared to the intensity-based model when the visiting process is misspecified. In general, enriching the visiting process with prior visit history enhances performance. We further apply our methodology to real longitudinal data from HIV, where visit frequency varies substantially among individuals.
纵向数据和事件发生时间数据的联合建模，特别是通过共享参数模型（SPM），是处理带有信息性终端事件的纵向标记数据的常用方法。在这种情况下，一个关键但常被忽视的假设是访问/观察过程是非信息性的，仅取决于过去的标记值和访问时间。当这个假设不成立时，访问过程就变得具有信息性，可能导致SPM估计有偏差。现有方法通常依赖于条件独立性假设，即假设在给定共享或相关随机效应的情况下，标记模型、访问过程和事件发生时间模型是独立的。此外，它们通常基于使用日历时间的基于强度的访问过程构建。本研究引入了一种统一的方法，以竞争风险的形式对正态分布的标记、访问过程和事件发生时间数据进行联合建模。我们的模型以观察到的标记值历史、先前的访问时间、标记的随机效应以及可能与随机效应独立的脆弱项为条件。虽然我们的方法与共享参数框架一致，但它并不假定过程之间存在条件独立性。此外，访问过程可以通过比例风险模型在间隔时间尺度上定义，或者通过比例强度模型在日历时间尺度上定义。通过广泛的模拟研究，我们评估了我们提出的方法的性能。我们证明，忽略一个具有信息性的访问过程会产生显著有偏差的标记估计。然而，访问过程的错误设定也可能导致有偏差的估计。当访问过程被错误设定时，间隔时间公式比基于强度的模型表现出更大的稳健性。一般来说，用先前的访问历史丰富访问过程可以提高性能。我们进一步将我们的方法应用于来自艾滋病毒的真实纵向数据，其中个体之间的访问频率差异很大。
