Circadian rhythms are endogenous oscillations that regulate various physiological processes and their disruption has been linked to many diseases, making it important to determine how gene-expression rhythms are altered across genotypes, treatments, or environmental exposures. Existing approaches for circadian transcriptomic analysis are often limited to pairwise comparisons or to a single aspect of rhythmic behavior, making them inadequate for comprehensive inference in multi-condition experimental designs. We propose CARhy (Comprehensive Analysis of Rhythmicity), a unified statistical framework for transcriptomic data collected under more than two conditions. Based on first-harmonic Fourier regression, CARhy provides formal tests for the presence of rhythmicity and for differences across conditions in rhythmicity, amplitude, phase, and baseline level. By allowing condition-specific variances and accommodating unbalanced designs, the framework remains reliable under heteroscedastic noise and realistic sampling constraints. Simulations show that CARhy controls type I error and false discovery rates well while achieving higher power than existing approaches in challenging settings. In mouse liver transcriptomic data, CARhy offers an interpretable and practical tool for characterizing how circadian rhythms differ across multiple experimental conditions. CARhy is implemented as an R package and is publicly available at: https://github.com/DrHuang123/Comprehensive-Analyses-of-Circadian-Rhythms-CARhy.git.

翻译：生物钟节律是调控多种生理过程的内源性振荡，其紊乱与多种疾病相关，因此明确基因表达节律如何随基因型、处理或环境暴露而改变具有重要意义。现有的生物钟转录组分析方法通常限于成对比较或单一节律特征分析，难以满足多条件实验设计中的综合推断需求。我们提出CARhy（节律性综合分析）框架，这是一个针对两个以上条件转录组数据的统一统计框架。基于一次谐波傅里叶回归，CARhy可对节律是否存在、不同条件下节律性、振幅、相位及基线水平的差异进行正式检验。该框架允许条件特异性方差并适应非平衡设计，从而在异方差噪声和实际采样约束下保持可靠性。模拟实验表明，CARhy在有效控制第一类错误率和错误发现率的同时，在挑战性场景下比现有方法具有更高统计功效。在小鼠肝脏转录组数据中，CARhy为表征多实验条件下生物钟节律差异提供了可解释且实用的工具。该框架以R语言包形式实现，开源代码见：https://github.com/DrHuang123/Comprehensive-Analyses-of-Circadian-Rhythms-CARhy.git。