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A linear mixed model approach to compare the evolution of multiple biological rhythms


Correspondence to: Andrea Fontana, Unit of Biostatistics, IRCCS “Casa Sollievo della Sofferenza”, Viale Cappuccini 1, 71013 San Giovanni Rotondo (FG), Italy.



The assessment and comparison of multiple biological rhythms represent an important challenge in chronobiology. They allow the investigation of whether a well-defined time-qualified relationship between biorhythms of the same frequency range is maintained in the presence of functional alterations, which may lead to chronodisruption or internal desynchronization. We propose a multivariate linear mixed model approach where functions of several biorhythms are jointly modeled in a multivariate longitudinal fashion, handling both the correlation between biorhythms of multiple outcomes and the correlation between measurements collected over time within the same biological entity. Furthermore, between-subject heterogeneity is also taken into account with the inclusion of random effects. Pairwise comparisons between biorhythms are performed by means of proper contrasts. As an example, we define contrasts which allow us testing whether or not two biorhythms are identical or opposing, providing additional support in clinical practice. Moreover, we illustrate the proposed method using both simulated and biological real data, concerning the comparison of three specific lymphocytes profiles which modulate the function of immune system between healthy subjects and non-small lung cancer patients. Finally, the corresponding SAS syntax is provided. Copyright © 2012 John Wiley & Sons, Ltd.