Pittsburgh Mind-Body Center

4:00 pm - 5:00 pm, Social Room (3rd Floor) Mellon Institute, Carnegie Mellon University

"Rhythm and Blues: Statistical Models for Biological Rhythm Data"

Joel Greenhouse, Ph.D., and Howard Seltman, M.D., Ph.D., Department of Statistics, Carnegie Mellon University

Many behavioral and physiological processes are periodic with a period of approximately 24 hours. For descriptive purposes, linear regression using a simple sinusoid with a fixed 24 hour period is sometimes an adequate tool for analyzing data from such processes. Inference based on regression models under the assumption of independent and identically distributed errors, however, can often be misleading. The purpose of this talk is to introduce alternative statistical models for the analysis of biological rhythm data. First, we present a general class of models for fitting a single rhythm, fitting the underlying circadian signal using higher order harmonic terms and the error component using time series models. We next extend the basic model to incorporate variation across subjects. We illustrate the use of this multi-stage model using standard statistical software (PROC MIXED) to study changes in the 24 hour serum cortisol rhythm between depressed patients and healthy controls. Finally, we note that a limitation of the class of harmonic regression models for hormonal data such as cortisol is that they do not account for the fact that the concentration is the net result of periodic secretion and excretion/metabolism. We present a physiologically more realistic class of stochastic compartmental models where the underlying biological rhythm for a group of subjects is modeled as periodically varying transition probabilities that control a two-state (quiescent vs. secreting) hidden Markov chain in each subject. The emphasis of this presentation will be on concepts and illustrative examples.

Joel Greenhouse is a Professor of Statistics at Carnegie Mellon University and an Adjunct Professor of Psychiatry and Epidemiology at the University of Pittsburgh. His Ph.D. is in Biostatistics from the University of Michigan.  Howard Seltman is a Visiting Assistant Professor in Statistics at Carnegie Mellon University.   He has an M.D. from the Medical College of Pennsylvania, is a board certified Clinical Pathologist, and has a Ph.D. in Statistics from Carnegie Mellon University.