Hierarchical Bayes estimation of hunting success rates with spatial correlations

A Bayesian hierarchical generalized linear model is used to estimate hunting success rates at the subarea level for postseason harvest surveys. The model includes fixed week effects, random geographic effects, and spatial correlations between neighboring subareas. The computation is done by Gibbs sampling and adaptive rejection sampling techniques. The method is illustrated using data from the Missouri Turkey Hunting Survey in the spring of 1996. Bayesian model selection methods are used to demonstrate that there are significant week differences and spatial correlations of hunting success rates among counties. The Bayesian estimates are also shown to be quite robust in terms of changes of hyperparameters.     

Hierarchical Bayesian Analysis of Correlated Zero‐inflated Count Data

This article presents two‐component hierarchical Bayesian models which incorporate both overdispersion and excess zeros. The components may be resultants of some intervention (treatment) that changes the rare event generating process. The models are also expanded to take into account any heterogeneity that may exist in the data. Details of the model fitting, checking and selecting alternative models from a Bayesian perspective are also presented. The proposed methods are applied to count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zero‐inflated spatio‐temporal models for disease mapping

In this paper, our aim is to analyze geographical and temporal variability of disease incidence when spatio‐temporal count data have excess zeros. To that end, we consider random effects in zero‐inflated Poisson models to investigate geographical and temporal patterns of disease incidence. Spatio‐temporal models that employ conditionally autoregressive smoothing across the spatial dimension and B‐spline smoothing over the temporal dimension are proposed. The analysis of these complex models is computationally difficult from the frequentist perspective. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning method provides a frequentist approach to mixed models that is also computationally convenient. We propose to use data cloning, which yields to maximum likelihood estimation, to conduct frequentist analysis of zero‐inflated spatio‐temporal modeling of disease incidence. One of the advantages of the data cloning approach is that the prediction and corresponding standard errors (or prediction intervals) of smoothing disease incidence over space and time is easily obtained. We illustrate our approach using a real dataset of monthly children asthma visits to hospital in the province of Manitoba, Canada, during the period April 2006 to March 2010. Performance of our approach is also evaluated through a simulation study.     

Small Sample Comparison of Modified Chi‐Square Test Statistics for Survey Data

The problem of categorial data analysis in survey sampling arises because of non‐independence of sample elements of the sample obtained through imposed sampling design. In this article the performance of modified χ² statistic for testing independence of attributes have been evaluated for small sample sizes with the help of log‐linear models with respect to its achieved level of significance for fixed nominal level at 5%, through simulation technique. It hase been observed that the perfiormance of these test statistics depends on average and coefficient of variation of eigen values of design effect matrix. The first order corrected statistic is able to capture the effect of sampling design to a great extent but the performance of second order corrected statistic is much better. Further, these modified χ² test statistics were applied to a real survey data and their performance were evaluated with respect to their achievied level of significance.     

Notes on Estimation of the General Odds Ratio and the General Risk Difference for Paired‐Sample Data

Under the matched‐pair design, this paper discusses estimation of the general odds ratio OR_G for ordinal exposure in case‐control studies and the general risk difference RD_G for ordinal outcomes in cross‐sectional or cohort studies. To illustrate the practical usefulness of interval estimators of OR_G and RD_G developed here, this paper uses the data from a case‐control study investigating the effect of the number of beverages drunk at “burning hot” temperature on the risk of possessing esophageal cancer, and the data from a cross‐sectional study comparing the grade distributions of unaided distance vision between two eyes. Finally, this paper notes that using the commonly‐used statistics related to odds ratio for dichotomous data by collapsing the ordinal exposure into two categories: the exposure versus the non‐exposure, tends to be less efficient than using the statistics related to OR_G proposed herein.     

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.