I'm interested in developing a model for the circadian rhythm of hormone levels via a cosinor analysis. I just started looking into cosinor analyses so I have a few questions.

The data is being collected at the moment, but I'm trying to get a better understanding of the method before the actual data arrives. This is how the data should look like: a total of 12 subjects with each subjects' hormone levels measured every 30 minutes over a period of 6 days. On days 1-3 subjects were administered drug A and on days 4-6 drug B. A 24 hour cycle is expected and therefore I'm interested in developing a model for a 24h circadian rhythm for each of the two drugs. This means I have multiple cycles - 24hours each - per person for each of the two drugs.

After reading the following two reviews (Fernandez et al., 2009; Cornelissen 2014) on cosinor it seems that I want to perform a population-mean cosinor analysis. Assuming that the necessary assumptions are met and in the simplest case of a single-component cosinor, I'm wondering how I would go ahead and do the analysis.

My understanding is that I should first calculate a single-component cosinor for each subject and then average the parameter estimates to get the population mean estimates. Say for drug A, can I simply combine the first three days of data for each subject to compute the single-component cosinors? Once I have those 12 single-component cosinors can I then just average them to get the population mean estimates? Do I have to account for the fact that I have repeated cycles for each subject, for example in the computation of variance estimates?


1 Answer 1


The way I understand the cosinor is that it can and is recommended to be performed over several cycles. The reason is Nyquist frequency i.e. you can reliably detect a frequency with at least 2 cycles of it and the more cycles you have, the better estimation you get (assuming stationary rhythm). In your case I would definitely perform single cosinor analyses for every subject and treatment. The problem here is repeated measures. As cosinor is a special case of linear regression, it probably can be combined with linear mixed model approach. Although I have not read them myself but these references could probably help:

Mikulich SK, Zerbe GO, Jones RH, Crowley TJ. Comparing linear and nonlinear mixed model approaches to cosinor analysis.

Weaver, Royal John Analysis of rhythmic biological data: The mixed-effects cosinor model.


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