Enhancing cosinor analysis of circadian phase markers using the gamma distribution

The cosinor model, in which a cosine curve is fitted to periodic data within a regression model, is a frequently used method for describing patterns of cyclical activity such as circadian rhythms. For circadian variables of interest (eg, melatonin and heart rate) that do not take on negative values, the assumption of normally distributed residuals required by the general linear model, which is most commonly used for cosinor analysis, may not be appropriate. Alternatively, a generalized linear model with the gamma distribution (GZLM-gamma) is specifically defined to accommodate non-negative outcomes. Herein, we demonstrate the improved fit and gains of efficiency in detection of circadian rhythm afforded by using the GZLM-gamma in cosinor models of heart rate, actigraphic activity, and urinary 6-sulfatoxymelatonin. Notably, this improved detection of circadian rhythm allows retention of additional patients for downstream analyses, further improving study power.