Fitting a sinusoid to biological rhythm data using ranks

Biological data are frequently collected with small numbers of observations from several subjects. Often a linear model is fitted to the data by averaging over subjects. Frequently there are considerable between-subject differences, and due allowance should be made for these when the model is fitted by parametric techniques. In this paper it is proposed that the model should be fitted by using the within-subject ranks of the observations. The technique is applied to the problem of estimating the 'cosinor' diagram for biological rhythm data. An example involving melatonin levels, in which there are considerable between-subject differences, is considered. The results obtained by use of the ranks are compared with those of a parametric analysis which makes allowance for the between-subject differences. The results are very similar, but the rank analysis requires much less computation.