Division of Public Health Sciences, Department of Surgery, Washington University School of Medicine in St Louis, 660 S. Euclid Ave., St. Louis, MO, 63110, USA.
Division of Biostatistics, Washington University School of Medicine in St Louis, 660 S. Euclid Ave., St. Louis, MO, 63110, USA.
BMC Med Res Methodol. 2022 Jul 22;22(1):201. doi: 10.1186/s12874-022-01686-7.
In recent years there is increasing interest in modeling the effect of early longitudinal biomarker data on future time-to-event or other outcomes. Sometimes investigators are also interested in knowing whether the variability of biomarkers is independently predictive of clinical outcomes. This question in most applications is addressed via a two-stage approach where summary statistics such as variance are calculated in the first stage and then used in models as covariates to predict clinical outcome in the second stage. The objective of this study is to compare the relative performance of various methods in estimating the effect of biomarker variability.
A joint model and 4 different two-stage approaches (naïve, landmark analysis, time-dependent Cox model, and regression calibration) were illustrated using data from a large multi-center randomized phase III trial, the Ocular Hypertension Treatment Study (OHTS), regarding the association between the variability of intraocular pressure (IOP) and the development of primary open-angle glaucoma (POAG). The model performance was also evaluated in terms of bias using simulated data from the joint model of longitudinal IOP and time to POAG. The parameters for simulation were chosen after OHTS data, and the association between longitudinal and survival data was introduced via underlying, unobserved, and error-free parameters including subject-specific variance.
In the OHTS data, joint modeling and two-stage methods reached consistent conclusion that IOP variability showed no significant association with the risk of POAG. In the simulated data with no association between IOP variability and time-to-POAG, all the two-stage methods (except the naïve approach) provided a reliable estimation. When a moderate effect of IOP variability on POAG was imposed, all the two-stage methods underestimated the true association as compared with the joint modeling while the model-based two-stage method (regression calibration) resulted in the least bias.
Regression calibration and joint modelling are the preferred methods in assessing the effect of biomarker variability. Two-stage methods with sample-based measures should be used with caution unless there exists a relatively long series of longitudinal measurements and/or strong effect size (NCT00000125).
近年来，人们对建模早期纵向生物标志物数据对未来时间事件或其他结果的影响越来越感兴趣。有时，研究人员还想知道生物标志物的变异性是否独立地预测临床结果。在大多数应用中，这个问题是通过两阶段方法来解决的，即在第一阶段计算汇总统计信息（如方差），然后在第二阶段将其用作协变量来预测临床结果。本研究的目的是比较各种方法估计生物标志物变异性影响的相对性能。
使用来自大型多中心随机 III 期试验（Ocular Hypertension Treatment Study，OHTS）的数据，说明了联合模型和 4 种不同的两阶段方法（naïve、landmark 分析、time-dependent Cox 模型和回归校准），这些方法涉及到眼压（IOP）变异性与原发性开角型青光眼（POAG）发展之间的关系。还通过来自纵向 IOP 和 POAG 时间的联合模型的模拟数据，从偏差的角度评估了模型性能。模拟的参数是根据 OHTS 数据选择的，纵向和生存数据之间的关联是通过包括个体特定方差在内的潜在、未观察到和无误差参数引入的。
在 OHTS 数据中，联合建模和两阶段方法得出了一致的结论，即 IOP 变异性与 POAG 的风险之间没有显著关联。在没有 IOP 变异性与 POAG 时间之间关联的模拟数据中，所有两阶段方法（naive 方法除外）都提供了可靠的估计。当 IOP 变异性对 POAG 的影响适中时，与联合建模相比，所有两阶段方法都低估了真实关联，而基于模型的两阶段方法（回归校准）则导致了最小的偏差。
回归校准和联合建模是评估生物标志物变异性影响的首选方法。除非存在相对较长的纵向测量系列和/或较强的效应大小（NCT00000125），否则应谨慎使用基于样本的两阶段方法。
