Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow 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 piecewise constant hazards. This relationship allows us to synthesize 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.

ESTIMATING TEMPORAL ASSOCIATIONS IN ELECTROCORTICOGRAPHIC (ECoG) TIME SERIES WITH FIRST ORDER PRUNING

Granger causality (GC) is a statistical technique used to estimate temporal associations in multivariate time series. Many applications and extensions of GC have been proposed since its formulation by Granger in 1969. Here we control for potentially mediating or confounding associations between time series in the context of event-related electrocorticographic (ECoG) time series. A pruning approach to remove spurious connections and simultaneously reduce the required number of estimations to fit the effective connectivity graph is proposed. Additionally, we consider the potential of adjusted GC applied to independent components as a method to explore temporal relationships between underlying source signals. Both approaches overcome limitations encountered when estimating many parameters in multivariate time-series data, an increasingly common predicament in today's brain mapping studies.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.