Xiong Chengjie, Agboola Folasade, Luo Jingqin
Division of Biostatistics, Washington University School of Medicine, St. Louis, MO, USA.
Knight Alzheimer Disease Research Center, Washington University School of Medicine, St. Louis, MO, USA.
Res Sq. 2025 Jun 12:rs.3.rs-6681661. doi: 10.21203/rs.3.rs-6681661/v1.
Biomarkers are routinely measured from human biospecimens and imaging scans in Alzheimer disease (AD) research. Age is a well-known risk factor for AD. Detecting the age at which the longitudinal change in biomarkers starts to accelerate, i.e., a change-point in age, is important to design preventive interventions.
We analyzed longitudinal biomarker data by a random intercept and random slope model where the slope (longitudinal rate of change) was modeled as a piecewise linear and continuous function of baseline age. We proposed to estimate the intersection of the two linear functions, i.e., the change-point in age by multiple methods: maximum (profile) likelihood, minimum squared pseudo bias, minimum variance, minimum mean square error (MSE), and a two-stage method. We simulated large numbers of data sets to evaluate the performance of these estimators and implemented them to analyze the longitudinal white matter hypointensity from brain magnetic resonance imaging scans in an AD cohort study of 616 participants to estimate the age when the longitudinal rate of change starts to accelerate.
Our simulations indicated that performance was universally poor for all point estimators and CI estimates when the true change-point was near the boundary or when sample size was small (N=100). Yet, the proposed change-point estimators became approximately unbiased and showed relatively small MSE when sample size increased (N>200) and the true change-point was away from boundary. The 95% CIs from these methods also provided good nominal coverage with large sample sizes if the change-point was away from boundary. When applied to the AD biomarker study, we found that almost all methods yielded similar estimates to the change-point from 59.19 years to 65.78 years, but the profile likelihood approach led to a much later estimate.
Our proposed estimators for the change-point performed reasonably well, especially when it is away from the boundary and the sample sizes are large. Our methods revealed a largely consistent age when the longitudinal change in white matter hypointensity started to accelerate. Further research is needed to tackle more complex challenges, i.e., multiple change-points that may depend on other AD risk factors.
在阿尔茨海默病（AD）研究中，生物标志物通常是从人体生物样本和影像扫描中测量得到的。年龄是AD一个众所周知的风险因素。检测生物标志物纵向变化开始加速的年龄，即年龄变化点，对于设计预防干预措施很重要。
我们通过随机截距和随机斜率模型分析纵向生物标志物数据，其中斜率（纵向变化率）被建模为基线年龄的分段线性连续函数。我们提出通过多种方法估计两个线性函数的交点，即年龄变化点：最大（轮廓）似然法、最小平方伪偏差法、最小方差法、最小均方误差（MSE）法和两阶段法。我们模拟了大量数据集以评估这些估计器的性能，并将它们应用于分析616名参与者的AD队列研究中脑磁共振成像扫描的纵向白质低信号强度，以估计纵向变化率开始加速的年龄。
我们的模拟表明，当真实变化点接近边界或样本量较小时（N = 100），所有点估计器和置信区间（CI）估计的性能普遍较差。然而，当样本量增加（N>200）且真实变化点远离边界时，所提出的变化点估计器变得近似无偏且显示出相对较小的MSE。如果变化点远离边界，这些方法的95%置信区间在大样本量时也提供了良好的名义覆盖率。当应用于AD生物标志物研究时，我们发现几乎所有方法得出的变化点估计值相似，从59.19岁到65.78岁，但轮廓似然法得出的估计值要晚得多。
我们提出的变化点估计器表现相当不错，特别是当它远离边界且样本量较大时。我们的方法揭示了白质低信号强度纵向变化开始加速时在很大程度上一致的年龄。需要进一步研究来应对更复杂的挑战，即可能依赖于其他AD风险因素的多个变化点。
