A flexible model for human circadian rhythms

Many hormones and other physiological processes vary in a circadian pattern. Although a sine/cosine function can be used to model these patterns, this functional form is not appropriate when there is asymmetry between the peak and nadir phases. In this paper we describe a semiparametric periodic spline function that can be fit to circadian rhythms. The model includes both phase and amplitude so that the time and the magnitude of the peak or nadir can be estimated. We also describe tests of fit for components in the model. Data from an experiment to study immunological responses in humans are used to demonstrate the methods.