A local join counts methodology for spatial clustering in disease from relative risk models

ABSTRACT

This paper considers adaptation of hierarchical models for small area disease counts to detect disease clustering. A high risk area may be an outlier (in local terms) if surrounded by low risk areas, whereas a high risk cluster requires that both the focus area and surrounding areas demonstrate common elevated risk. A local join count method is suggested to detect local clustering of high disease risk in a single health outcome, and extends to assessing bivariate spatial clustering in relative risk. Applications include assessing spatial heterogeneity in effects of area predictors according to local clustering configuration, and gauging sensitivity of bivariate clustering to random effect assumptions.     

Semiparametric Proportional Odds Models for Spatially Correlated Survival Data

The last decade has witnessed major developments in Geographical Information Systems (GIS) technology resulting in the need for statisticians to develop models that account for spatial clustering and variation. In public health settings, epidemiologists and health-care professionals are interested in discerning spatial patterns in survival data that might exist among the counties. This paper develops a Bayesian hierarchical model for capturing spatial heterogeneity within the framework of proportional odds. This is deemed more appropriate when a substantial percentage of subjects enjoy prolonged survival. We discuss the implementation issues of our models, perform comparisons among competing models and illustrate with data from the SEER (Surveillance Epidemiology and End Results) database of the National Cancer Institute, paying particular attention to the underlying spatial story.     

Geographic distribution of cardiovascular comorbidities in South Africa: a national cross-sectional analysis

Objectives: We sought to estimate the spatial coexistence of hypertension, coronary heart disease (CHD), stroke and hypercholesterolaemia in South Africa. Design: Cross-sectional. Setting: Sub-Saharan Africa and South Africa. Participants: Data were from 13,827 adults (mean±SD age 39±18 years, 58.4% women) interviewed in the 1998 South African Health and Demographic Survey. Interventions: N/A. Primary and secondary outcome measures: We used multivariate spatial disease models to estimate district-level shared and disease-specific spatial risk components, controlling for known individual risk factors. Results: In univariate analysis, observed prevalence of hypertension and CHD is was high in the south-western parts, and low in the north east. Stroke and high blood cholesterol prevalence appeared to be evenly distributed across the country. In multivariate analysis (adjusting for age, gender, ethnicity, education, urban-dwelling, smoking, alcohol consumption and obesity), hypertension and stroke prevalence were highly concentrated in the south-western parts, whilst CHD and hypercholesterolaemia were highly prevalent in central and top north-eastern corridor, respectively. The shared component, which we took to represent nutrition and other lifestyle factors not accounted for in the model, had a larger effect on cardiovascular disease prevalence in the south-western areas of the country. It appeared to have greater effect on hypertension and CHD. Conclusion: This study suggests a clear geographic distribution of cardiovascular disease in South Africa, driven possibly by shared lifestyle behaviours. These findings might be useful for public health resource allocation in low-income settings.     

Vector-borne infectious disease mapping with stochastic difference equations: an analysis of dengue disease in Malaysia

Few publications consider the estimation of relative risk for vector-borne infectious diseases. Most of these articles involve exploratory analysis that includes the study of covariates and their effects on disease distribution and the study of geographic information systems to integrate patient-related information. The aim of this paper is to introduce an alternative method of relative risk estimation based on discrete time–space stochastic SIR-SI models (susceptible–infective–recovered for human populations; susceptible–infective for vector populations) for the transmission of vector-borne infectious diseases, particularly dengue disease. First, we describe deterministic compartmental SIR-SI models that are suitable for dengue disease transmission. We then adapt these to develop corresponding discrete time–space stochastic SIR-SI models. Finally, we develop an alternative method of estimating the relative risk for dengue disease mapping based on these models and apply them to analyse dengue data from Malaysia. This new approach offers a better model for estimating the relative risk for dengue disease mapping compared with the other common approaches, because it takes into account the transmission process of the disease while allowing for covariates and spatial correlation between risks in adjacent regions.     

Calibrated predictions for multivariate competing risks models

Prediction models for time-to-event data play a prominent role in assessing the individual risk of a disease, such as cancer. Accurate disease prediction models provide an efficient tool for identifying individuals at high risk, and provide the groundwork for estimating the population burden and cost of disease and for developing patient care guidelines. We focus on risk prediction of a disease in which family history is an important risk factor that reflects inherited genetic susceptibility, shared environment, and common behavior patterns. In this work family history is accommodated using frailty models, with the main novel feature being allowing for competing risks, such as other diseases or mortality. We show through a simulation study that naively treating competing risks as independent right censoring events results in non-calibrated predictions, with the expected number of events overestimated. Discrimination performance is not affected by ignoring competing risks. Our proposed prediction methodologies correctly account for competing events, are very well calibrated, and easy to implement.     

Finite mixtures approach to ecological regression

During past few years great attention has been devoted to the analysis of disease incidence and mortality rates, with an explicit focus on modelling geographical variation of rates observed in spatially adjacent regions. The general aim of these contributes has been both to highlight clusters of regions with homogeneous relative risk and to determine the effects of observed and unobserved risk factors related to the analyzed disease. Most of the proposed modelling approaches can be derived as alternative specifications of the components of a general convolution model (Molliè, 1996). In this paper, we consider the semiparametric approach discussed by Schlattmann and Böhning (1993); in particular, we focus on models with an explicit spatially structured component (see Biggeri et al., 2000), and propose alternative choices for the structure of the spatial component.     

Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared gamma frailty model and the inverse Gaussian frailty model with the reversed hazard rate. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. We also apply the proposed models to the Australian twin data set and a better model is suggested.     

A new approach to investigating spatial variations of disease

Summary.  For rare diseases the observed disease count may exhibit extra Poisson variability, particularly in areas with low or sparse populations. Hence the variance of the estimates of disease risk, the standardized mortality ratios, may be highly unstable. This overdispersion must be taken into account otherwise subsequent maps based on standardized mortality ratios will be misleading and, rather than displaying the true spatial pattern of disease risk, the most extreme values will be highlighted. Neighbouring areas tend to exhibit spatial correlation as they may share more similarities than non-neighbouring areas. The need to address overdispersion and spatial correlation has led to the proposal of Bayesian approaches for smoothing estimates of disease risk. We propose a new model for investigating the spatial variation of disease risks in conjunction with an alternative specification for estimates of disease risk in geographical areas—the multivariate Poisson–gamma model. The main advantages of this new model lie in its simplicity and ability to account naturally for overdispersion and spatial auto-correlation. Exact expressions for important quantities such as expectations, variances and covariances can be easily derived.     

Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions

The last decade has seen an explosion of work on the use of mixture models for clustering. The use of the Gaussian mixture model has been common practice, with constraints sometimes imposed upon the component covariance matrices to give families of mixture models. Similar approaches have also been applied, albeit with less fecundity, to classification and discriminant analysis. In this paper, we begin with an introduction to model-based clustering and a succinct account of the state-of-the-art. We then put forth a novel family of mixture models wherein each component is modeled using a multivariate t-distribution with an eigen-decomposed covariance structure. This family, which is largely a t-analogue of the well-known MCLUST family, is known as the tEIGEN family. The efficacy of this family for clustering, classification, and discriminant analysis is illustrated with both real and simulated data. The performance of this family is compared to its Gaussian counterpart on three real data sets.     

Hierarchical Bayesian bivariate disease mapping: analysis of children and adults asthma visits to hospital

In spatial epidemiology, detecting areas with high ratio of disease is important as it may lead to identifying risk factors associated with disease. This in turn may lead to further epidemiological investigations into the nature of disease. Disease mapping studies have been widely performed with considering only one disease in the estimated models. Simultaneous modelling of different diseases can also be a valuable tool both from the epidemiological and also from the statistical point of view. In particular, when we have several measurements recorded at each spatial location, one can consider multivariate models in order to handle the dependence among the multivariate components and the spatial dependence between locations. In this paper, spatial models that use multivariate conditionally autoregressive smoothing across the spatial dimension are considered. We study the patterns of incidence ratios and identify areas with consistently high ratio estimates as areas for further investigation. A hierarchical Bayesian approach using Markov chain Monte Carlo techniques is employed to simultaneously examine spatial trends of asthma visits by children and adults to hospital in the province of Manitoba, Canada, during 2000–2010.     

Spatio-temporal modeling of infectious disease dynamics

A stochastic model, which is well suited to capture space–time dependence of an infectious disease, was employed in this study to describe the underlying spatial and temporal pattern of measles in Barisal Division, Bangladesh. The model has two components: an endemic component and an epidemic component; weights are used in the epidemic component for better accounting of the disease spread into different geographical regions. We illustrate our findings using a data set of monthly measles counts in the six districts of Barisal, from January 2000 to August 2009, collected from the Expanded Program on Immunization, Bangladesh. The negative binomial model with both the seasonal and autoregressive components was found to be suitable for capturing space–time dependence of measles in Barisal. Analyses were done using general optimization routines, which provided the maximum likelihood estimates with the corresponding standard errors.     

Bayesian analysis of spatial data using different variance and neighbourhood structures

In disease mapping, the overall goal is to study the incidence or mortality risk caused by a specific disease in a number of geographical regions. It is common to assume that the response variable follows a Poisson distribution, whose average rate can be explained by a group of covariates and a random effect. For this random effect, it is considered conditional autoregressive (CAR) models, which carry information about the neighbourhood relationship between the regions. The focus of this paper was to explore and compare some CAR models proposed in the literature. An application with epidemiological data was conducted to model the risk of death due to Crohn's Disease and Ulcerative Colitis in the State of São Paulo – Brazil. Finally, a simulation study was done to strengthen the results and assess the performance of the models in the presence of various levels of spatial dependence.     

Multilevel modelling of the geographical distributions of diseases

Multilevel modelling is used on problems arising from the analysis of spatially distributed health data. We use three applications to demonstrate the use of multilevel modelling in this area. The first concerns small area all-cause mortality rates from Glasgow where spatial autocorrelation between residuals is examined. The second analysis is of prostate cancer cases in Scottish counties where we use a range of models to examine whether the incidence is higher in more rural areas. The third develops a multiple-cause model in which deaths from cancer and cardiovascular disease in Glasgow are examined simultaneously in a spatial model. We discuss some of the issues surrounding the use of complex spatial models and the potential for future developments.     

Constrained clustering of irregularly sampled spatial data

Many spatial data such as those in climatology or environmental monitoring are collected over irregular geographical locations. Furthermore, it is common to have multivariate observations at each location. We propose a method of segmentation of a region of interest based on such data that can be carried out in two steps: (1) clustering or classification of irregularly sample points and (2) segmentation of the region based on the classified points.

We develop a spatially-constrained clustering algorithm for segmentation of the sample points by incorporating a geographical-constraint into the standard clustering methods. Both hierarchical and nonhierarchical methods are considered. The latter is a modification of the seeded region growing method known in image analysis. Both algorithms work on a suitable neighbourhood structure, which can for example be defined by the Delaunay triangulation of the sample points. The number of clusters is estimated by testing the significance of successive change in the within-cluster sum-of-squares relative to a null permutation distribution. The methodology is validated on simulated data and used in construction of a climatology map of Ireland based on meteorological data of daily rainfall records from 1294 stations over the period of 37 years.     

A Bayesian latent spatial model for mapping the cortical signature of progression to Alzheimer's disease

Prior studies have shown that atrophy in vulnerable cortical regions is associated with an increased risk of progression to clinical dementia. In this work, we utilize the longitudinal structural magnetic resonance imaging (MRI) data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) to investigate the relationship between the temporally changing spatial topography of cortical thickness and conversion from mild cognitive impairment to Alzheimer's disease (AD). We develop a novel Bayesian latent spatial model that employs the spatial information underlying the thickness effects across the cortical surface. The proposed method facilitates the development of imaging markers by reliably quantifying and mapping the regional vulnerability to AD progression across the cortical surface. Simulation results showed substantial gains in statistical power and estimation performance by accounting for the spatial structure of the association. Using MRI data from ADNI, we examined the topographic patterns of anatomic regions where cortical thinning is associated with an increased risk of developing AD.     

A spatial structural equation model with an application to area health needs

Indices of population ‘health need’ are often used to distribute health resources or assess equity in service provision. This article describes a spatial structural equation model incorporating multiple indicators of need and multiple population health risks that affect need (analogous to multiple indicators–multiple causes models). More specifically, the multiple indicator component of the model involves health outcomes such as hospital admissions or mortality, whereas the multiple risk component models the impact on the need for area social and demographic indicators, which proxy population-level risk factors for different diseases. The latent need construct is allowed (under a Bayesian approach) to be spatially correlated, though the prior assumed for need allows a mix of spatially structured and unstructured influences. A case study considers variations in need for coronary heart disease (CHD) care over 625 small areas in London, using recent mortality and hospitalization data (the ‘indicators’) and measures of general ill-health, income and unemployment, which proxy variations in population risk for CHD.     

Geometric consistency of principal component scores for high-dimensional mixture models and its application

In this article, we consider clustering based on principal component analysis (PCA) for high-dimensional mixture models. We present theoretical reasons why PCA is effective for clustering high-dimensional data. First, we derive a geometric representation of high-dimension, low-sample-size (HDLSS) data taken from a two-class mixture model. With the help of the geometric representation, we give geometric consistency properties of sample principal component scores in the HDLSS context. We develop ideas of the geometric representation and provide geometric consistency properties for multiclass mixture models. We show that PCA can cluster HDLSS data under certain conditions in a surprisingly explicit way. Finally, we demonstrate the performance of the clustering using gene expression datasets.     

Predicting infectious disease outbreak risk via migratory waterfowl vectors

The spread of an emerging infectious disease is a major public health threat. Given the uncertainties associated with vector-borne diseases, in terms of vector dynamics and disease transmission, it is critical to develop statistical models that address how and when such an infectious disease could spread throughout a region such as the USA. This paper considers a spatio-temporal statistical model for how an infectious disease could be carried into the USA by migratory waterfowl vectors during their seasonal migration and, ultimately, the risk of transmission of such a disease to domestic fowl. Modeling spatio-temporal data of this type is inherently difficult given the uncertainty associated with observations, complexity of the dynamics, high dimensionality of the underlying process, and the presence of excessive zeros. In particular, the spatio-temporal dynamics of the waterfowl migration are developed by way of a two-tiered functional temporal and spatial dimension reduction procedure that captures spatial and seasonal trends, as well as regional dynamics. Furthermore, the model relates the migration to a population of poultry farms that are known to be susceptible to such diseases, and is one of the possible avenues toward transmission to domestic poultry and humans. The result is a predictive distribution of those counties containing poultry farms that are at the greatest risk of having the infectious disease infiltrate their flocks assuming that the migratory population was infected. The model naturally fits into the hierarchical Bayesian framework.     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.