@article {788, title = {A unifying framework for marginalized random intercept models of correlated binary outcomes.}, journal = {Int Stat Rev}, volume = {82}, year = {2014}, month = {2014 Aug}, pages = {275-295}, abstract = {

We demonstrate that many current approaches for marginal modeling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalized random intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

}, issn = {0306-7734}, doi = {10.1111/insr.12035}, author = {Swihart, Bruce J and Caffo, Brian S and Crainiceanu, Ciprian M} } @article {810, title = {Combining hidden Markov models for comparing the dynamics of multiple sleep electroencephalograms.}, journal = {Stat Med}, volume = {32}, year = {2013}, month = {2013 Aug 30}, pages = {3342-56}, abstract = {

In this manuscript, we consider methods for the analysis of populations of electroencephalogram signals during sleep for the study of sleep disorders using hidden Markov models (HMMs). Notably, we propose an easily implemented method for simultaneously modeling multiple time series that involve large amounts of data. We apply these methods to study sleep-disordered breathing (SDB) in the Sleep Heart Health Study (SHHS), a landmark study of SDB and cardiovascular consequences. We use the entire, longitudinally collected, SHHS cohort to develop HMM population parameters, which we then apply to obtain subject-specific Markovian predictions. From these predictions, we create several indices of interest, such as transition frequencies between latent states. Our HMM analysis of electroencephalogram signals uncovers interesting findings regarding differences in brain activity during sleep between those with and without SDB. These findings include stability of the percent time spent in HMM latent states across matched diseased and non-diseased groups and differences in the rate of transitioning.

}, keywords = {Data Interpretation, Statistical, Electroencephalography, Female, Humans, Longitudinal Studies, Male, Markov Chains, Middle Aged, Models, Statistical, Sleep Apnea Syndromes}, issn = {1097-0258}, doi = {10.1002/sim.5747}, author = {Langrock, Roland and Swihart, Bruce J and Caffo, Brian S and Punjabi, Naresh M and Crainiceanu, Ciprian M} } @article {821, title = {Practical Marginalized Multilevel Models.}, journal = {Stat}, volume = {2}, year = {2013}, month = {2013}, abstract = {

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate the MMM and approximate MMM approaches on a cerebrovascular deficiency crossover trial using SAS and an epidemiological study on race and visual impairment using R. Datasets, SAS and R code are included as supplemental materials.

}, issn = {0038-9986}, doi = {10.1002/sta4.22}, author = {Griswold, Michael E and Swihart, Bruce J and Caffo, Brian S and Zeger, Scott L} }