提出可为个体定制时滞效应的统计模型，解决传统方法忽视个体差异的问题。
DTVEM-RE: A Hierarchical Random-Effects Extension of the Differential Time-Varying Effect Model for Person-Specific Multi-Lag Estimation in Intensive Longitudinal Data
- 构建分层随机效应模型，让每个人拥有独立时滞系数。
- 模拟与真实数据验证：个体间时滞差异可达一个数量级，预测性能优于四种对比方法。
- 支持不等间距数据，两种实现版本结果高度一致，适合个性化临床研究。
Jacobson 等人（2019）提出的差分时变效应模型（DTVEM）是密集纵向数据中识别最佳时滞的常用工具，但其假设所有人共享相同时滞结构，这与现代临床研究强调个体差异的主旨相悖。本文提出 DTVEM-RE，一种分层随机效应扩展，允许每个个体具有独立的时滞系数。包含两个确认步骤：在 Stan 中使用离散时间分层贝叶斯向量自回归模型，实现跨个体信息融合并提供校准的不确定性估计；在 ctsem 中使用连续时间个体化奥恩斯坦-乌伦贝克模型，直接处理不规则采样数据。四个结果表明：模拟显示贝叶斯版本对群体间方差 τₐ 的估计偏差低于 0.01，置信区间覆盖率为 90%–93%；在 Fisher 等人（2017）的 EMA 数据集（N=40）上，三个情绪指标的个体滞后-1 效应相差一个数量级，贝叶斯与 GAMM 估计高度一致（r=0.87–0.92），DTVEM-RE 在四种离散时间方法中预测表现最优；多时滞版本显示全部九个 τₖ 值的可信区间均不含零，且个体间差异最大的时滞随变量而异，这是仅限滞后-1 的 mlVAR 无法捕捉的特征；两版本在个体滞后-1 估计上几乎完全一致（r ≥ 0.995），差异仅由收缩效应导致。DTVEM-RE 是目前首个实现个体化时滞检测的 DTVEM 框架，标准 DTVEM 可作为其特例。
原文摘要 · Abstract (English)
The Differential Time-Varying Effect Model (DTVEM) of Jacobson et al. (2019) is a popular tool for finding the best time lag in intensive longitudinal data, but it assumes everyone shares the same lag structure. The original authors named fixing this as future work, and it clashes with the premise of modern clinical research, which is that people differ. We present DTVEM-RE, an extension that lets each person have their own lag coefficients, with two versions of the confirmatory step: a discrete-time hierarchical Bayesian VAR in Stan, which pools across people and gives calibrated uncertainty, and a continuous-time per-person Ornstein-Uhlenbeck model in ctsem, which handles unevenly spaced beeps directly. We report four results. A simulation shows the Bayesian version recovers the between-person spread tau_a with bias below 0.01 and coverage of 90 to 93 percent. On the Fisher et al. (2017) EMA dataset (N=40), person-specific lag-1 effects vary by an order of magnitude across three mood items, the Bayesian and GAMM estimates agree closely (r=0.87 to 0.92), and DTVEM-RE gives the best one-step-ahead prediction among four discrete-time methods. A multi-lag version shows all nine tau_k values have credible intervals excluding zero, and the lag where people differ most changes across items, something lag-1-only methods like mlVAR cannot detect. Finally, the two versions agree almost exactly on person-specific lag-1 estimates (r >= 0.995), differing only as shrinkage predicts. DTVEM-RE is, to our knowledge, the first person-specific implementation of DTVEM-style lag detection, and it contains standard DTVEM as a special case.
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