Bayesian Poisson log-linear multilevel models scalable to epidemiological studies are proposed to investigate population variability in sleep state transition rates. Hierarchical random effects are used to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of importance. Essentially, non-parametric piecewise constant hazards are estimated and smoothed, allowing for time-varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming exponentially distributed survival times. Such re-derivation allows synthesis of two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed. This paper is a revamping of "Modeling multilevel sleep transitional data via Poisson log-linear multilevel models" available at: http://www.bepress.com/jhubiostat/paper212/
Swihart, Bruce J.; Caffo, Brian S. PhD; Crainiceanu, Ciprian PhD; and Punjabi, Naresh M. PhD, MD, "Mixed effect Poisson log-linear models for clinical and epidemiological sleep hypnogram data" (August 2010). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 215.