A SAS macro for modelling periodic data using cosinor analysis

Cosinor analysis, developed by Franz Hallberg and colleagues in the 1960s, allows for the fitting of a cosine curve to data of a known period. Cosinor analysis is frequently used in the analysis of biological rhythm data. While software exists to perform these analyses, we are not aware of any published SAS procedures or macros which would facilitate them.

To meet this gap, we herein describe SAS macros which perform cosinor analyses that assume either normally or gamma distributed outcomes and fixed period. The macros can 1) produce datasets with cosinor parameters including acrophase, mesor, amplitude, nadir and test for rhythmicity 2) output datasets with fitted and observed values from the model, and 3) plot the resulting curve and underlying data.

We demonstrate the use of these macros with data from our research on circadian rhythms of heart rate and sleep in critically ill patients.

Cosinor analysis provides a parsimonious and intuitive set of estimates to summarize periodic data. We are hopeful that the publication of our macro will allow a wider spectrum of users to avail themselves of this technique.