A Bayesian Long‐term Survival Model Parametrized in the Cured Fraction

The main goal of this paper is to investigate a cure rate model that comprehends some well‐known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.     

A Bayesian Two‐Part Latent Class Model for Longitudinal Medical Expenditure Data: Assessing the Impact of Mental Health and Substance Abuse Parity

Summary In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four‐year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two‐part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two‐part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class‐varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.     

Log‐gamma linear‐mixed effects models for multiple outcomes with application to a longitudinal glaucoma study

Glaucoma is a progressive disease due to damage in the optic nerve with associated functional losses. Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non‐Gaussian linear‐mixed models to estimate the correlations among subject‐specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject‐specific effects by modeling the skewed random effects through the log‐gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log‐gamma assumption against the usual normality assumption of the random effects, we propose a lack‐of‐fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time.     

Modeling Inter‐Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model

Summary The aim of this article is to develop a spatial model for multi‐subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi‐subject data, some work on spatial modeling of single‐subject data, and some recent work on spatial modeling of multi‐subject data. However, there has been no work on spatial models that explicitly account for inter‐subject variability in activation locations. In this article, we use the idea of activation centers and model the inter‐subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass‐univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.