The cosinor model is frequently used to represent gene expression given the 24 hour day-night cycle time at which a corresponding tissue sample is collected. However, the timing of many biological processes are based on individual-specific internal timing systems that are offset relative to day-night cycle time. When these offsets are unknown, they pose a challenge in performing statistical analyses with a cosinor model. To clarify, when sample collection times are mis-recorded, cosinor regression can yield attenuated parameter estimates, which would also attenuate test statistics. This attenuation bias would inflate type II error rates in identifying genes with oscillatory behavior. This paper proposes a heuristic method to account for unknown offsets when tissue samples are collected in a longitudinal design. Specifically, this method involves first estimating individual-specific cosinor models for each gene. The times of sample collection for that individual are then translated based on the estimated phase-shifts across every gene. Simulation studies confirm that this method mitigates bias in estimation and inference. Illustrations with real data from three circadian biology studies highlight that this method produces parameter estimates and inferences akin to those obtained when each individual's offset is known.

翻译：余弦模型常用于表征与24小时昼夜节律时间对应的组织样本基因表达模式。然而，许多生物过程的时序依赖于个体特异性内部计时系统，这类系统相对于昼夜节律时间存在偏移。当这些偏移未知时，会给基于余弦模型的统计分析带来挑战。具体而言，若样本采集时间记录存在误差，余弦回归将产生衰减的参数估计值，进而导致检验统计量的衰减。这种衰减偏差会扩大基因振荡行为识别中的第二类错误率。本文提出一种启发式方法，用于解决纵向设计中组织样本采集时间未知偏移的问题。该方法首先为每个基因构建个体特异性余弦模型，随后基于所有基因估计的相位偏移量对个体的样本采集时间进行校正。模拟研究证实该方法能有效缓解估计与推断中的偏差。基于三项昼夜节律生物学研究的真实数据验证表明，该方法可产出与已知个体偏移时相同的参数估计与推断结果。