A mixed-effects cosinor modelling framework for circadian gene expression

Many behavioral, molecular, and physiological phenomena oscillate on an approximately 24-h cycle, or display a circadian rhythm. One phenomenon of particular interest is gene expression, as multiple studies have identified associations between the oscillations in gene expression levels and a person's health. A challenge in identifying these associations for a population is that the circadian rhythm is unique to each person. Specifically, the times at which a gene's expression levels peak and trough are based on a person's internal circadian clock, and each person's internal circadian clock time is uniquely offset relative to the 24-h day-night cycle time. If each person's offset is not taken into account when estimating the parameters of a population-level cosinor model, which is commonly used to represent how gene expression levels oscillate, then the population-level amplitude parameter estimate for this model could be erroneously attenuated. This attenuation bias would increase the likelihood of falsely concluding that a gene's expression levels do not oscillate. While laboratory tests can mitigate attenuation bias by determining each person's offset, these laboratory tests are often expensive to perform. To address attenuation bias without performing laboratory tests, we propose a new method for estimating the parameters of a population-level cosinor model using longitudinal data from multiple genes and people. First, the parameters of a population-level cosinor model are estimated for each gene without considering each person's offset. Second, the parameters of an individual-level cosinor model are estimated for each person and each gene. Third, a data-driven offset is computed for each person using the parameter estimates of these models. Fourth, the parameters of a new population-level cosinor model are estimated for each gene incorporating these data-driven offsets. Simulation studies show that this method mitigates attenuation bias in population-level amplitude parameter estimates and in hypothesis test statistics that are computed to determine whether or not a gene's expression levels oscillate. Application of this method on data from three different studies demonstrates that this method consistently produces population-level parameter estimates and hypothesis test statistics that closely match those obtained when each person's offset is determined from laboratory tests.