Journal of Data Science

Abstract: The application of linear mixed models or generalized linear mixed models to large databases in which the level 2 units (hospitals) have a wide variety of characteristics is a problem frequently encountered in studies of medical quality. Accurate estimation of model parameters and standard errors requires accounting for the grouping of outcomes within hospitals. Including the hospitals as random effect in the model is a common method of doing so. However in a large, diverse population, the required assump tions are not satisfied, which can lead to inconsistent and biased parameter estimates. One solution is to use cluster analysis with clustering variables distinct from the model covariates to group the hospitals into smaller, more homogeneous groups. The analysis can then be carried out within these groups. We illustrate this analysis using an example of a study of hemoglobin A1c control among diabetic patients in a national database of United States Department of Veterans’ Affairs (VA) hospitals.

Abstract: Response variables that are scored as counts, for example, number of mastitis cases in dairy cattle, often arise in quantitative genetic analysis. When the number of zeros exceeds the amount expected such as under the Poisson density, the zero-inflated Poisson (ZIP) model is more appropriate. In using the ZIP model in animal breeding studies, it is necessary to accommodate genetic and environmental covariances. For that, this study proposes to model the mixture and Poisson parameters hierarchically, each as a function of two random effects, representing the genetic and environmental sources of variability, respectively. The genetic random effects are allowed to be correlated, leading to a correlation within and between clusters. The environmental effects are introduced by independent residual terms, accounting for overdispersion above that caused by extra-zeros. In addition, an inter correlation structure between random genetic effects affecting mixture and Poisson parameters is used to infer pleiotropy, an expression of the extent to which these parameters are influenced by common genes. The methods described here are illustrated with data on number of mastitis cases from Norwegian Red cows. Bayesian analysis yields posterior distributions useful for studying environmental and genetic variability, as well as genetic correlation.

Abstract: Information regarding small area prevalence of chronic disease is important for public health strategy and resourcing equity. This paper develops a prevalence model taking account of survey and census data to derive small area prevalence estimates for diabetes. The application involves 32000 small area subdivisions (zip code census tracts) of the US, with the prevalence estimates taking account of information from the US-wide Behavioral Risk Factor Surveillance System (BRFSS) survey on population prevalence differentials by age, gender, ethnic group and education. The effects of such aspects of population composition on prevalence are widely recognized. However, the model also incorporates spatial or contextual influences via spatially structured effects for each US state; such contextual effects are allowed to differ between ethnic groups and other demographic categories using a multivariate spatial prior. A Bayesian estimation approach is used and analysis demonstrates the considerably improved fit of a fully specified compositional-contextual model as compared to simpler ‘standard’ approaches which are typically limited to age and area effects.

Abstract: A core task in analyzing randomized clinical trials based on longitudinal data is to find the best way to describe the change over time for each treatment arm. We review the implementation and estimation of a flexible piecewise Hierarchical Linear Model (HLM) to model change over time. The flexible piecewise HLM consists of two phases with differing rates of change. The breakpoints between these two phases, as well as the rates of change per phase are allowed to vary between treatment groups as well as individuals. While this approach may provide better model fit, how to quantify treatment differences over the longitudinal period is not clear. In this paper, we develop a procedure for summarizing the longitudinal data for the flexible piecewise HLM on the lines of Cook et al. (2004). We focus on quantifying the overall treatment efficacy using the area under the curve (AUC) of the individual flexible piecewise HLM models. Methods are illustrated through data from a placebo-controlled trial in the treatment of depression comparing psychotherapy and pharmacotherapy.

Abstract: We propose two simple, easy-to-implement methods for obtaining simultaneous credible bands in hierarchical models from standard Markov chain Monte Carlo output. The methods generalize Scheff´e’s (1953) approach to this problem, but in a Bayesian context. A small simulation study is followed by an application of the methods to a seasonal model for Ache honey gathering.