A mixed effects cosinor modelling framework for circadian gene expression

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.