CARhy: Comprehensive Analyses of Circadian Rhythms in Transcriptomic Experiments with Multiple Conditions

TL;DR

CARhy is a new R package that enables comprehensive analysis of circadian gene expression rhythms across multiple conditions, overcoming limitations of existing methods.

Contribution

It introduces a unified statistical framework based on Fourier regression for multi-condition circadian transcriptomic analysis, handling heteroscedastic noise and unbalanced designs.

Findings

CARhy controls type I error and false discovery rates effectively.

It achieves higher power than existing methods in simulations.

Applied to mouse liver data, it characterizes differences in circadian rhythms across conditions.

Abstract

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.