On Analyzing Circadian Rhythms Data Using Nonlinear Mixed Models
with Harmonic Terms
Biometrics, 61 (4):
1115--1120 (December 2005)Abstract
SummaryWang, Ke, and Brown (2003, Biometrics59, 804–812) developed
a smoothing-based approach for modeling circadian rhythms with random
effects. Their approach is flexible in that fixed and random covariates
can affect both the amplitude and phase shift of a nonparametrically
smoothed periodic function. In motivating their approach, Wang et
al. stated that a simple sinusoidal function is too restrictive.
In addition, they stated that “although adding harmonics can improve
the fit, it is difficult to decide how many harmonics to include
in the model, and the results are difficult to interpret.” We disagree
with the notion that harmonic models cannot be a useful tool in modeling
longitudinal circadian rhythm data. In this note, we show how nonlinear
mixed models with harmonic terms allow for a simple and flexible
alternative to Wang et al.'s approach. We show how to choose the
number of harmonics using penalized likelihood to flexibly model
circadian rhythms and to estimate the effect of covariates on the
rhythms. We fit harmonic models to the cortisol circadian rhythm
data presented by Wang et al. to illustrate our approach. Furthermore,
we evaluate the properties of our procedure with a small simulation
study. The proposed parametric approach provides an alternative to
Wang et al.'s semiparametric approach and has the added advantage
of being easy to implement in most statistical software packages.