Bayesian Simultaneous Intervals for Small Areas: An Application to Mapping Mortality Rates in U.S. Health Service Areas

It is customary when presenting a choropleth map of rates or counts to present only the estimates (mean or mode) of the parameters of interest. While this technique illustrates spatial variation, it ignores the variation inherent in the estimates. We describe an approach to present variability in choropleth maps by constructing 100(1-alpha)% simultaneous intervals. The result provides three maps (estimate with two bands). We propose two methods to construct simultaneous intervals from the optimal individual highest posterior density (HPD) intervals to ensure joint simultaneous coverage of 100(1-alpha)%. Both methods exhibit the main feature of multiplying the lower bound and dividing the upper bound of the individual HPD intervals by parameters

A double-dichotomy clustering of dual pathology dementia patients

Introduction: Subcortical ischemic vascular disease (SIVD) and Alzheimer's disease (AD) related dementia can coexist in older subjects, leading to mixed dementia (MX). Identification of dementia sub-groups is important for designing proper treatment plans and clinical trials. Method: An Alzheimer's disease severity (ADS) score and a vascular disease severity (VDS) score are calculated from CSF and MRI biomarkers, respectively. These scores, being sensitive to different Alzheimer's and vascular disease processes are combined orthogonally in a double-dichotomy plot. This formed an objective basis for clustering the subjects into four groups, consisting of AD, SIVD, MX and leukoaraiosis (LA). The relationship of these four groups is examined with respect to cognitive assessments and clinical diagnosis. Results: Cluster analysis had at least 83% agreement with the clinical diagnosis for groups based either on Alzheimer's or on vascular sensitive biomarkers, and a combined agreement of 68.8% for clustering the four groups. The VDS score was correlated to executive function (r = -0.28, p < 0.01) and the ADS score to memory function (r = −0.35, p < 0.002) after adjusting for age, sex, and education. In the subset of patients for which the cluster scores and clinical diagnoses agreed, the correlations were stronger (VDS score-executive function: r = −0.37, p < 0.006 and ADS score-memory function: r = −0.58, p < 0.0001). Conclusions: The double-dichotomy clustering based on imaging and fluid biomarkers offers an unbiased method for identifying mixed dementia patients and selecting better defined sub-groups. Differential correlations with neuropsychological tests support the hypothesis that the categories of dementia represent different etiologies