In various biomedical studies, the focus of analysis centers on the magnitudes of data, particularly when algebraic signs are irrelevant or lost. To analyze the magnitude outcomes in repeated measures studies, using models with random effects is essential. This is because random effects can account for individual heterogeneity, enhancing parameter estimation precision. However, there are currently no established regression methods that incorporate random effects and are specifically designed for magnitude outcomes. This article bridges this gap by introducing Bayesian regression modeling approaches for analyzing magnitude data, with a key focus on the incorporation of random effects. Additionally, the proposed method is extended to address multiple causes of informative dropout, commonly encountered in repeated measures studies. To tackle the missing data challenge arising from dropout, a joint modeling strategy is developed, building upon the previously introduced regression techniques. Two numerical simulation studies are conducted to assess the validity of our method. The chosen simulation scenarios aim to resemble the conditions of our motivating study. The results demonstrate that the proposed method for magnitude data exhibits good performance in terms of both estimation accuracy and precision, and the joint models effectively mitigate bias due to missing data. Finally, we apply proposed models to analyze the magnitude data from the motivating study, investigating if sex impacts the magnitude change in diaphragm thickness over time for ICU patients.

翻译：在各类生物医学研究中，当数据的代数符号无关或缺失时，分析重点常集中于数据的幅度。为分析重复测量研究中的幅度结果，使用含随机效应的模型至关重要，因为随机效应能够解释个体异质性，从而提高参数估计的精度。然而，目前尚无成熟的回归方法能够专门针对幅度结果并纳入随机效应。本文通过引入贝叶斯回归建模方法来分析幅度数据，填补了这一空白，其中重点整合了随机效应。此外，所提方法进一步扩展至处理重复测量研究中常见的多原因信息性退出问题。为应对退出导致的缺失数据挑战，我们在先前引入的回归技术基础上，开发了一种联合建模策略。通过两项数值模拟研究评估了所提方法的有效性，所选模拟场景旨在模拟我们动机研究的实际条件。结果表明，所提幅度数据分析方法在估计准确性与精度方面均表现良好，且联合模型能有效缓解因缺失数据引起的偏差。最后，我们将所提模型应用于动机研究中的幅度数据分析，探究性别是否影响ICU患者膈肌厚度随时间变化的幅度。