标题： 双阶段三角函数回归建模昼夜节律 显示英文标题

标题： Two-Stage Trigonometric Regression for Modeling Circadian Rhythms

摘要： 基因表达水平、激素分泌和体内温度各自在约24小时的周期内振荡，或表现出昼夜节律。 许多昼夜节律生物学研究探讨了这些节律在不同群体中的变化，揭示了异常节律与癌症、代谢综合征和睡眠障碍等疾病之间的关联。 分析昼夜节律生物学数据的一个挑战是，不同个体中某一现象的振荡峰值和谷值时间各不相同。 如果在昼夜节律研究中普遍使用的三角回归中未考虑这些个体层面的差异，则种群层面振幅参数的估计可能会受到衰减偏差的影响。 这种衰减偏差可能导致研究结论不准确。 为解决衰减偏差，我们提出了一种改进的两阶段（RTS）方法，用于在从参与研究的每个个体获得的纵向数据基础上进行三角回归。 在第一阶段，估计个体层面模型的参数。 在第二阶段，对这些个体层面的估计进行转换，并汇总以生成用于推断的种群层面参数估计。 模拟研究表明，与忽略峰值和谷值时间个体差异的标准两阶段（STS）方法相比，我们的RTS方法能够减轻参数估计中的偏差，获得更大的统计功效，并保持适当的I型错误控制。 在振荡振幅相对于数据中的随机变异较弱且样本量较小时，参数估计和统计功效会出现唯一例外情况。 用皮质醇水平数据和心率数据进行说明显示，与STS方法相比，我们的RTS方法在多个假设检验中获得了更大的种群层面振幅参数估计值和更小的$p$-值。 显示英文摘要

摘要： Gene expression levels, hormone secretion, and internal body temperature each oscillate over an approximately 24-hour cycle, or display circadian rhythms. Many circadian biology studies have investigated how these rhythms vary across cohorts, uncovering associations between atypical rhythms and diseases such as cancer, metabolic syndrome, and sleep disorders. A challenge in analyzing circadian biology data is that the oscillation peak and trough times for a phenomenon differ across individuals. If these individual-level differences are not accounted for in trigonometric regression, which is prevalent in circadian biology studies, then estimates of the population-level amplitude parameters can suffer from attenuation bias. This attenuation bias could lead to inaccurate study conclusions. To address attenuation bias, we propose a refined two-stage (RTS) method for trigonometric regression given longitudinal data obtained from each individual participating in a study. In the first stage, the parameters of individual-level models are estimated. In the second stage, transformations of these individual-level estimates are aggregated to produce population-level parameter estimates for inference. Simulation studies show that our RTS method mitigates bias in parameter estimation, obtains greater statistical power, and maintains appropriate type I error control when compared to the standard two-stage (STS) method, which ignores individual-level differences in peak and trough times. The only exception for parameter estimation and statistical power occurs when the oscillation amplitudes are weak relative to random variability in the data and the sample size is small. Illustrations with cortisol level data and heart rate data show that our RTS method obtains larger population-level amplitude parameter estimates and smaller $p$-values for multiple hypothesis tests when compared to the STS method.