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Circadian rhythmicity in transcriptomic profiles has been shown in many physiological processes, and the disruption of circadian patterns has been found to associate with several diseases. In this paper, we developed a series of likelihood-based methods to detect (i) circadian rhythmicity (denoted as LR_rhythmicity) and (ii) differential circadian patterns comparing two experimental conditions (denoted as LR_diff). In terms of circadian rhythmicity detection, we demonstrated that our proposed LR_rhythmicity could better control the type I error rate compared to existing methods under a wide variety of simulation settings. In terms of differential circadian patterns, we developed methods in detecting differential amplitude, differential phase, differential basal level and differential fit, which also successfully controlled the type I error rate. In addition, we demonstrated that the proposed LR_diff could achieve higher statistical power in detecting differential fit, compared to existing methods. The superior performance of LR_rhythmicity and LR_diff was demonstrated in four real data applications, including a brain aging data (gene expression microarray data of human postmortem brain), a time-restricted feeding data (RNA sequencing data of human skeletal muscles) and a scRNAseq data (single cell RNA sequencing data of mouse suprachiasmatic nucleus). An R package for our methods is publicly available on GitHub  https://github.com/diffCircadian/diffCircadian .

Likelihood-based tests for detecting circadian rhythmicity and differential circadian patterns in transcriptomic applications