Identifying Clusters in Bayesian Disease Mapping

Disease mapping is the field of spatial epidemiology interested in estimating the spatial pattern in disease risk across $n$ areal units. One aim is to identify units exhibiting elevated disease risks, so that public health interventions can be made. Bayesian hierarchical models with a spatially smooth conditional autoregressive prior are used for this purpose, but they cannot identify the spatial extent of high-risk clusters. Therefore we propose a two stage solution to this problem, with the first stage being a spatially adjusted hierarchical agglomerative clustering algorithm. This algorithm is applied to data prior to the study period, and produces $n$ potential cluster structures for the disease data. The second stage fits a separate Poisson log-linear model to the study data for each cluster structure, which allows for step-changes in risk where two clusters meet. The most appropriate cluster structure is chosen by model comparison techniques, specifically by minimising the Deviance Information Criterion. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland

Bayesian cluster detection via adjacency modelling

Disease mapping aims to estimate the spatial pattern in disease risk across an area, identifying units which have elevated disease risk. Existing methods use Bayesian hierarchical models with spatially smooth conditional autoregressive priors to estimate risk, but these methods are unable to identify the geographical extent of spatially contiguous high-risk clusters of areal units. Our proposed solution to this problem is a two-stage approach, which produces a set of potential cluster structures for the data and then chooses the optimal structure via a Bayesian hierarchical model. The first stage uses a spatially adjusted hierarchical agglomerative clustering algorithm. The second stage fits a Poisson log-linear model to the data to estimate the optimal cluster structure and the spatial pattern in disease risk. The methodology was applied to a study of chronic obstructive pulmonary disease (COPD) in local authorities in England, where a number of high risk clusters were identified

Spatial clustering of average risks and risk trends in Bayesian disease mapping

Spatiotemporal disease mapping focuses on estimating the spatial pattern in disease risk across a set of nonoverlapping areal units over a fixed period of time. The key aim of such research is to identify areas that have a high average level of disease risk or where disease risk is increasing over time, thus allowing public health interventions to be focused on these areas. Such aims are well suited to the statistical approach of clustering, and while much research has been done in this area in a purely spatial setting, only a handful of approaches have focused on spatiotemporal clustering of disease risk. Therefore, this paper outlines a new modeling approach for clustering spatiotemporal disease risk data, by clustering areas based on both their mean risk levels and the behavior of their temporal trends. The efficacy of the methodology is established by a simulation study, and is illustrated by a study of respiratory disease risk in Glasgow, Scotland

Recommendation Subgraphs for Web Discovery

Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate the website. Choosing an appropriate set of recommendations at each page is one of the key features of backend engines that have been deployed at several e-commerce sites. Specifically at BloomReach, an engine consisting of several independent components analyzes and optimizes its clients' websites. This paper focuses on the structure optimizer component which improves the website navigation experience that enables the discovery of novel content. We begin by formalizing the concept of recommendations used for discovery. We formulate this as a natural graph optimization problem which in its simplest case, reduces to a bipartite matching problem. In practice, solving these matching problems requires superlinear time and is not scalable. Also, implementing simple algorithms is critical in practice because they are significantly easier to maintain in production. This motivated us to analyze three methods for solving the problem in increasing order of sophistication: a sampling algorithm, a greedy algorithm and a more involved partitioning based algorithm. We first theoretically analyze the performance of these three methods on random graph models characterizing when each method will yield a solution of sufficient quality and the parameter ranges when more sophistication is needed. We complement this by providing an empirical analysis of these algorithms on simulated and real-world production data. Our results confirm that it is not always necessary to implement complicated algorithms in the real-world and that very good practical results can be obtained by using heuristics that are backed by the confidence of concrete theoretical guarantees

Pathogenesis of placentitis in the goat (Capra hircus) inoculated with Brucella abortus

A caprine model of ruminant brucellar placentitis was developed and used to determine the pathogenesis of placental infection and to characterize changes in trophoblasts infected with Brucella abortus. Tissues from the uterus and placentae were examined by light and electron microscopy at various post-inoculation intervals. B. abortus was identified in placentae by immunoperoxidase and immunogold cytochemistry. Placentitis was present by 5 days post-inoculation and abortions occurred by 11 days. Histologically, brucellae were first seen in placentomal erythrophagocytic trophoblasts and periplacentomal chorioallantoic trophoblasts. Necrosis of trophoblasts, chorioallantoic ulceration, and large numbers of brucellae in chorionic villi were present in later stages of infection. This study indicated that entry and replication of brucellae in trophoblasts precede placentome and fetal infection and that trophoblasts are the source of brucellae for these tissues;Ultrastructurally, brucellae were first seen in phagosomes of erythrophagocytic trophoblasts and in the rough endoplasmic reticulum of chorioallantoic trophoblasts. After intracellular bacterial replication caused trophoblast necrosis, large numbers of brucellae were in connective tissue of chorionic villi, placental vasculitis was present, and placentomal trophoblasts were separated from maternal syncytial epithelium. This study indicated that bacteremic brucellae are endocytosed by erythrophagocytic trophoblasts, brucellae likely replicate in trophoblastic rough endoplasmic reticulum, and that placental vasculitis is important in the pathogenesis of abortion;Trophoblasts in normal and brucellae-infected placentae were characterized by electron microscopic morphometry. Volume and surface density of normal rough endoplasmic reticulum decreased six-fold in brucellae-infected trophoblasts as compared to normal trophoblasts. The remainder of rough endoplasmic reticulum in infected trophoblasts was hypertrophied and distended by intracisternal brucellae. This decrease in normal rough endoplasmic reticulum and the corresponding hypertrophy of brucellae-filled rough endoplasmic reticulum indicates that B. abortus replicates in trophoblastic rough endoplasmic reticulum

The production of gum by certain species of Rhizobium

It has long been known that the legume root-nodule bacteria produce a bacterial gum, but knowledge of the exact role of gum production in the metabolism of the organism is still rather incomplete. The results secured by a number of investigators indicate that gum production may be intimately connected in some way with the mechanism of symbiotic nitrogen fixation. In addition, some studies have shown that considerable differences exist in the quantity and chemical nature of the gum produced by different species of Rhizobium

X-Ray Diffraction Analysis of the Pennsylvanian Clays of Mahaska County

This study involved five of the operating open-pit mines of Mahaska County, Iowa, which are located near the eastern edge of the Mid-Continent Basin. The mines were sampled from the underclay to the surface at two foot intervals and the clay fraction was separated and analyzed both qualitatively and quantitatively. Results of this investigation showed that the major component present besides illite and kaolinite in the hulk sample was quartz. However, the quartz was not present in the less-than-two micron fraction. The clay fraction analysis varied from 38 percent to 60 percent kaolin and 17 percent to 26 percent illite with the remainder being chlorite and non-swelling mixed-layered material; chlorite was present in only eleven of the samples collected. The mineralogy was used as evidence that these rocks were deposited in near shore environment. This interpretation when considered along with stratigraphic work of others suggests that the rocks are in the Cherokee Group