Likelihood-based Tests for Detecting Circadian Rhythmicity and Differential Circadian Patterns in Transcriptomic Applications

Abstract

Circadian rhythmicity in transcriptomic profiles has been shown in many physiological processes, and the disruption of circadian patterns has been founded 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 two real data applications, including a brain aging data (gene expression microarray data of human postmortem brain) and a time-restricted feeding data (RNA sequencing data of human skeletal muscles). An R package for our methods is publicly available on GitHub https://github.com/diffCircadian/diffCircadian

Experimental Design and Power Calculation in Omics Circadian Rhythmicity Detection

“…To evaluate the impact of outliers on type I error control, we replace q % of the expression values with outliers, where q =(5,10,20). To be specific, for a gene g , there is q % chance that the expression level is simulated from UNIF(M..A;M + A); and 1 q % chance that the expression level is simulated independently based on Equation 1 under H 0 : A = 0 (i.e., y gi = M + ε gi , )).…”

“…Additional modeling is needed to extend for valid false discovery rate (FDR) control. Secondly, in addition to detecting genes with rhythmic pattern, another important research question is to identify differential circadian pattern (10, 35, 40, 46) (i.e., the circadian pattern is disrupted because of the treatment or condition). Extending the CircaPower framework to include power calculation for differential circadian analysis will be another future direction.…”

“…Lastly, our work is based on a single cosinor model for circadian rhythmicity detection. While the cosinor model is advantageous statistically and show better type I error control when circadian assumption holds (10), extending the current framework to a more flexible family of circadian pattern is of biological interests to the general circadian research field.…”

“…To fill in these research gaps, we propose a model-based approach to accurately calculate the circadian power (namely CircaPower), based on a cosinor model (7, 10). In the literature, several other computational or non-model-based algorithms have been developed to detect circadian rhythmicity, including Lomb-Scargle periodograms (12), COSOPT (43), ARSER (48), RAIN (45), and JTK CYCLE (18).…”

Nitecap: An Exploratory Circadian Analysis Web Application

“…Recent work has focused on comparisons of rhythmicity across different conditions ( Thaben and Westermark, 2016 ; Singer and Hughey, 2019 ), but these methods report only p -values for an aggregate change in rhythmicity and cannot isolate changes in amplitude or phase specifically. While the theory for doing so is well developed ( Bingham et al, 1982 ), tests of these differences have only recently had modern implementations ( Moskon, 2020 ; Parsons et al, 2020 ; Ding et al, 2021 ; Weger et al, 2021 ). Investigators still lack exploratory tools for visualization and understanding these studies or for running these analyses without informatics training.…”