Joint Spatial Model Research Articles

Bayesian two-part spatial models for semicontinuous data with application to emergency department expenditures.

In health services research, it is common to encounter semicontinuous data characterized by a point mass at zero and a continuous distribution of positive values. Examples include medical expenditures, in which the zeros represent patients who do not use health services, while the continuous distribution describes the level of expenditures among users. Semicontinuous data are customarily analyzed using two-part mixture models. In the spatial analysis of semicontinuous data, two-part models are especially appealing because they provide a joint picture of how health services utilization and associated expenditures vary across geographic regions. However, when applying these models, careful attention must be paid to distributional choices, as model misspecification can lead to biased and imprecise inferences. This paper introduces a broad class of Bayesian two-part models for the spatial analysis of semicontinuous data. Specific models considered include two-part lognormal, log skew-elliptical, and Bayesian non-parametric models. Multivariate conditionally autoregressive priors are used to link model components and provide spatial smoothing across neighboring regions, resulting in a joint spatial modeling framework for health utilization and expenditures. We develop a fully conjugate Gibbs sampling scheme, leading to efficient posterior computation. We illustrate the approach using data from a recent study of emergency department expenditures.

Off-grid direction of arrival estimation based on joint spatial sparsity for distributed sparse linear arrays.

In the design phase of sensor arrays during array signal processing, the estimation performance and system cost are largely determined by array aperture size. In this article, we address the problem of joint direction-of-arrival (DOA) estimation with distributed sparse linear arrays (SLAs) and propose an off-grid synchronous approach based on distributed compressed sensing to obtain larger array aperture. We focus on the complex source distribution in the practical applications and classify the sources into common and innovation parts according to whether a signal of source can impinge on all the SLAs or a specific one. For each SLA, we construct a corresponding virtual uniform linear array (ULA) to create the relationship of random linear map between the signals respectively observed by these two arrays. The signal ensembles including the common/innovation sources for different SLAs are abstracted as a joint spatial sparsity model. And we use the minimization of concatenated atomic norm via semidefinite programming to solve the problem of joint DOA estimation. Joint calculation of the signals observed by all the SLAs exploits their redundancy caused by the common sources and decreases the requirement of array size. The numerical results illustrate the advantages of the proposed approach.

Joint spatial modeling to identify shared patterns among chronic related potentially preventable hospitalizations.

BackgroundRates of Potentially Preventable Hospitalizations (PPH) are used to evaluate access of territorially delimited populations to high quality ambulatory care. A common geographic pattern of several PPH would reflect the performance of healthcare providers. This study is aimed at modeling jointly the geographical variation in six chronic PPH conditions in one Spanish Autonomous Community for describing common and discrepant patterns, and to assess the relative weight of the common pattern on each condition.MethodsData on the 39,970 PPH hospital admissions for diabetes short term complications, chronic obstructive pulmonary disease (COPD), congestive heart failure, dehydration, angina admission and adult asthma, between 2007 and 2009 were extracted from the Hospital Discharge Administrative Databases and assigned to one of the 240 Basic Health Zones. Rates and Standardized Hospitalization Ratios per geographic unit were estimated. The spatial analysis was carried out jointly for PPH conditions using Shared Component Models (SCM).ResultsThe component shared by the six PPH conditions explained about the 36% of the variability of each PPH condition, ranging from the 25.9 for dehydration to 58.7 for COPD. The geographical pattern found in the latent common component identifies territorial clusters with particularly high risk. The specific risk pattern that each isolated PPH does not share with the common pattern for all six conditions show many non-significant areas for most PPH, but with some exceptions.ConclusionsThe geographical distribution of the risk of the PPH conditions is captured in a 36% by a unique latent pattern. The SCM modeling may be useful to evaluate healthcare system performance.

Joint spatial Bayesian modeling for studies combining longitudinal and cross-sectional data

Design for intervention studies may combine longitudinal data collected from sampled locations over several survey rounds and cross-sectional data from other locations in the study area. In this case, modeling the impact of the intervention requires an approach that can accommodate both types of data, accounting for the dependence between individuals followed up over time. Inadequate modeling can mask intervention effects, with serious implications for policy making. In this paper we use data from a large-scale larviciding intervention for malaria control implemented in Dar es Salaam, United Republic of Tanzania, collected over a period of almost 5 years. We apply a longitudinal Bayesian spatial model to the Dar es Salaam data, combining follow-up and cross-sectional data, treating the correlation in longitudinal observations separately, and controlling for potential confounders. An innovative feature of this modeling is the use of Ornstein-Uhlenbeck process to model random time effects. We contrast the results with other Bayesian modeling formulations, including cross-sectional approaches that consider individual-level random effects to account for subjects followed up in two or more surveys. The longitudinal modeling approach indicates that the intervention significantly reduced the prevalence of malaria infection in Dar es Salaam by 20% whereas the joint model did not suggest significance within the results. Our results suggest that the longitudinal model is to be preferred when longitudinal information is available at the individual level.

Joint Statistics of Radio Frequency Interference in Multiantenna Receivers

Many wireless data communications systems, such as LTE, Wi-Fi, and Wimax, have become or are rapidly becoming interference limited due to radio frequency interference (RFI) generated by both human-made and natural sources. Human-made sources of RFI include uncoordinated devices operating in the same frequency band, devices communicating in adjacent frequency bands, and computational platform subsystems radiating clock frequencies and their harmonics. Additive RFI for these wireless systems has predominantly non-Gaussian statistics, and is well modeled by the Middleton Class A distribution for centralized networks, and the symmetric alpha stable distribution for decentralized networks. Our primary contribution is the derivation of joint spatial statistical models of RFI generated from uncoordinated interfering sources randomly distributed around a multiantenna receiver. The derivation is based on statistical-physical interference generation and propagation mechanisms. Prior results on joint statistics of multiantenna interference model either spatially independent or spatially isotropic interference, and do not provide a statistical-physical derivation for certain network environments. Our proposed joint spatial statistical model captures a continuum between spatially independent and spatially isotropic statistics, and hence includes many previous results as special cases. Practical applications include co-channel interference modeling for various wireless network environments, including wireless ad hoc, cellular, local area, and femtocell networks.

El Niño–Southern Oscillation influence on winter maximum daily precipitation in California in a spatial model

Recent studies have found that the El Niño–Southern Oscillation (ENSO) has statistically significant influences on extreme precipitation. A limitation of most existing work is that a separate generalized extreme value (GEV) distribution is fitted for each individual site. Such models cannot address important questions that involve events jointly defined across multiple sites; for instance, what is the probability that the 50 year return levels of three sites in the vicinity of a city occur in the same season? With the latest statistical methodology for spatial extremes, we fit max‐stable process models to winter maximum daily precipitation of 192 sites in California over 55 years. A composite likelihood approach is used since the full likelihood is unavailable either analytically or numerically. In addition to latitude, longitude, and elevation, the Southern Oscillation Index (SOI) is incorporated into the parameters of the marginal GEV models. We find that, in a spatial context, the ENSO has a significant influence on the extreme precipitation in California by shifting the location parameter of the GEV distributions, with higher values of the SOI corresponding to lower maximum winter daily precipitation. The joint spatial model is used to assess risks concerning joint extremal events at network of sites with spatial dependence properly accounted for. The probability of extremal events occurring at multiple sites in the same season is found to be much higher than what would be expected under the independence assumption.

Joint Spatial Modeling of Recurrent Infection and Growth with Processes under Intermittent Observation

In this article, we present a new statistical methodology for longitudinal studies in forestry, where trees are subject to recurrent infection, and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations, which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed wherein a mixed nonhomogeneous Poisson process, governing recurring infection, is linked with a spatially dynamic nonlinear model representing the underlying height growth trajectories. These trajectories are based on the von Bertalanffy growth model and a spatially varying parameterization is employed. Spatial variability in growth parameters is modeled through a multivariate spatial process derived through kernel convolution. Inference is conducted in a Bayesian framework with implementation based on hybrid Monte Carlo. Our methodology is applied for analysis in an 11-year study of recurrent weevil infestation of white spruce in British Columbia.

On Bayesian shared component disease mapping and ecological regression with errors in covariates

Recent literature on Bayesian disease mapping presents shared component models (SCMs) for joint spatial modeling of two or more diseases with common risk factors. In this study, Bayesian hierarchical formulations of shared component disease mapping and ecological models are explored and developed in the context of ecological regression, taking into consideration errors in covariates. A review of multivariate disease mapping models (MultiVMs) such as the multivariate conditional autoregressive models that are also part of the more recent Bayesian disease mapping literature is presented. Some insights into the connections and distinctions between the SCM and MultiVM procedures are communicated. Important issues surrounding (appropriate) formulation of shared- and disease-specific components, consideration/choice of spatial or non-spatial random effects priors, and identification of model parameters in SCMs are explored and discussed in the context of spatial and ecological analysis of small area multivariate disease or health outcome rates and associated ecological risk factors. The methods are illustrated through an in-depth analysis of four-variate road traffic accident injury (RTAI) data: gender-specific fatal and non-fatal RTAI rates in 84 local health areas in British Columbia (Canada). Fully Bayesian inference via Markov chain Monte Carlo simulations is presented.

Joint spatial survival modeling for the age at diagnosis and the vital outcome of prostate cancer

Prostate cancer (PrCA) is the most common malignancy in men and a leading cause of cancer mortality among males in the United States. Large geographical variation and racial disparities exist in both the incidence of PrCA and the survival rate after diagnosis. In this population-based study, a joint spatial survival model is constructed to investigate factors that affect the age at diagnosis of PrCA and the subsequent survival. The joint model for these two time-to-event outcomes is specified through parametric models for age at diagnosis and survival time conditional on diagnosis age. To account for possible correlation in these outcomes among men from the same geographical region, frailty terms are included in the survival model. Both spatially correlated and uncorrelated frailties are incorporated in each model considered. The deviance information criterion is used to select a best-fitting model within the Bayesian framework. The results from our final best-fitting model indicate that race, marital status at diagnosis, and cancer stage are significantly associated with both of the two time-to-event outcomes. No pattern emerged in the geographical distribution of age at PrCA diagnosis. In contrast, a spatially clustered pattern was observed in the geographic distribution of survival experience post diagnosis.

Open Space at the Rural-Urban Fringe: A Joint Spatial Hedonic Model of Developed and Undeveloped Land Values

We examine the impacts of different open space amenities on sales prices of developed and undeveloped land in two time periods ten years apart in a rapidly urbanizing county in central Ohio. Buffers within 0.25 and 0.5 miles are created that include percentages of agricultural, residential, park and golf course uses around each land sale and are used as explanatory variables. We contribute to the literature by estimating a unified model that accounts for spatial heterogeneity as well as for cross-correlations in developed and undeveloped land sales. Our findings suggest interactions between the land markets examined are complex and dynamic.