A mixed effects cosinor modelling framework for circadian gene expression

Abstract

The cosinor model is frequently used to represent the oscillatory behavior of different genes over time. When data are collected from multiple individuals, the cosinor model is estimated with recorded gene expression levels and the 24 hour day-night cycle time at which gene expression levels are observed. 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 individual-specific offsets are unknown, they pose a challenge in performing statistical analyses with a cosinor model. Specifically, when each individual participating in a study has a different offset, the parameter estimates of a population cosinor model obtained with day-night cycle time are attenuated. These attenuated parameter estimates also attenuate test statistics, which inflate type II error rates in identifying genes with oscillatory behavior. To address this attenuation bias, this paper proposes a method when data are collected in a longitudinal design. This method involves first estimating individual-specific and population cosinor models for each gene, and then translating the times at which an individual's gene expression levels are recorded based on the parameter estimates of these models. Simulation studies confirm that this method mitigates bias in estimation and inference. Illustrations with data from three circadian biology studies highlight that this method produces parameter estimates and test statistics akin to those obtained when each individual's offset is known.