cosinoRmixedeffects: an R package for mixed-effects cosinor models

Background Wearable devices enable monitoring and measurement of physiological parameters over a 24-h period, and some of which exhibit circadian rhythm characteristics. However, the currently available R package cosinor could only analyze daily cross-sectional data and compare the parameters between groups with two levels. To evaluate longitudinal changes in the circadian patterns, we need to extend the model to a mixed-effect model framework, allowing for random effects and interaction between COSINOR parameters and time-varying covariates. Results We developed the cosinoRmixedeffects R package for modelling longitudinal periodic data using mixed-effects cosinor models. The model allows for covariates and interactions with the non-linear parameters MESOR, amplitude, and acrophase. To facilitate ease of use, the package utilizes the syntax and functions of the widely used emmeans package to obtain estimated marginal means and contrasts. Estimation and hypothesis testing involving the non-linear circadian parameters are carried out using bootstrapping. We illustrate the package functionality by modelling daily measurements of heart rate variability (HRV) collected among health care workers over several months. Differences in circadian patterns of HRV between genders, BMI, and during infection with SARS-CoV2 are evaluated to illustrate how to perform hypothesis testing. Conclusion cosinoRmixedeffects package provides the model fitting, estimation and hypothesis testing for the mixed-effects COSINOR model, for the linear and non-linear circadian parameters MESOR, amplitude and acrophase. The model accommodates factors with any number of categories, as well as complex interactions with circadian parameters and categorical factors.

Ten years of chronic cluster – attacks still cluster

The chronic variant can be found in 10–20% of all cluster headache patients. While circadian and circannual rhythmicity are characteristic of the episodic variant, little is known on chronobiology in chronic cluster headache. We report a patient with chronic cluster evolved from episodic who recorded a total of 5447 attacks over 10 years. After spectral analysis, cosinor models were calculated within the frequency ranges of 23–25 h (circadian) and 11–13 months (circannual), respectively. Significant results ( P < 0.01) were found for 24-h periods, but not for circannual intervals (12 months). However, with regard to circannual periodicity, a semi-circannual rhythm (5–7 months) was suitable for curve fit and yielded significant results in the cosinor analysis at 6 months ( P < 0.05). This remarkable long observation period of 10 years shows that, at least for secondary chronic cluster headache which evolved from the episodic form, a typical circadian and circannual rhythmicity comparable to that of episodic cluster headache exists.

Cosinor Analysis for Temperature Time Series Data of Long Duration

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.