Hierarchical and Joint Site‐Edge Methods for Medicare Hospice Service Region Boundary Analysis

Summary Hospice service offers a convenient and ethically preferable health‐care option for terminally ill patients. However, this option is unavailable to patients in remote areas not served by any hospice system. In this article, we seek to determine the service areas of two particular cancer hospice systems in northeastern Minnesota based only on death counts abstracted from Medicare billing records. The problem is one of spatial boundary analysis, a field that appears statistically underdeveloped for irregular areal (lattice) data, even though most publicly available human health data are of this type. In this article, we suggest a variety of hierarchical models for areal boundary analysis that hierarchically or jointly parameterize both the areas and the edge segments. This leads to conceptually appealing solutions for our data that remain computationally feasible. While our approaches parallel similar developments in statistical image restoration using Markov random fields, important differences arise due to the irregular nature of our lattices, the sparseness and high variability of our data, the existence of important covariate information, and most importantly, our desire for full posterior inference on the boundary. Our results successfully delineate service areas for our two Minnesota hospice systems that sometimes conflict with the hospices' self‐reported service areas. We also obtain boundaries for the spatial residuals from our fits, separating regions that differ for reasons yet unaccounted for by our model.     

Testing random effects in linear mixed‐effects models with serially correlated errors

In linear mixed‐effects models, random effects are used to capture the heterogeneity and variability between individuals due to unmeasured covariates or unknown biological differences. Testing for the need of random effects is a nonstandard problem because it requires testing on the boundary of parameter space where the asymptotic chi‐squared distribution of the classical tests such as likelihood ratio and score tests is incorrect. In the literature several tests have been proposed to overcome this difficulty, however all of these tests rely on the restrictive assumption of i.i.d. measurement errors. The presence of correlated errors, which often happens in practice, makes testing random effects much more difficult. In this paper, we propose a permutation test for random effects in the presence of serially correlated errors. The proposed test not only avoids issues with the boundary of parameter space, but also can be used for testing multiple random effects and any subset of them. Our permutation procedure includes the permutation procedure in Drikvandi, Verbeke, Khodadadi, and Partovi Nia (2013) as a special case when errors are i.i.d., though the test statistics are different. We use simulations and a real data analysis to evaluate the performance of the proposed permutation test. We have found that random slopes for linear and quadratic time effects may not be significant when measurement errors are serially correlated.     

Spatial modelling-based approach to phytogeographical regionalization using grassland vegetation data

We presented a methodology for drawing continuous boundaries in the landscape differentiating between regions with different floristic composition. A region in Central Slovakia covering 2,445 km² was investigated. Ecological indicator values for temperature (EIT) in 1,978 grassland polygons were analysed. Ordinary kriging was used to interpolate EIT across the study region. Lattice wombling was used to identify the most intensive gradients in EIT and to draw boundaries, while ANOVA was used for post-classification analysis. A strong pattern of spatial continuity was present in EIT assigned to species in grassland polygons allowing for drawing continuous boundaries in the landscape. The study region was divided into 15 districts using the proposed method. Post-classification analysis indicated that 17 out of 23 adjacent districts were found to differ significantly in term of mean value of source samples. The results implied the need for incorporating spatial autocorrelation in sample data into post-classification analysis; such factor is often neglected in ecological research. The presented findings suggested broader applicability of the proposed method for spatial modelling, as vegetation data is widely accessible in databases for many regions of Europe.     

Local signal time-series during rest used for areal boundary mapping in individual human brains

It is widely thought that resting state functional connectivity likely reflects functional interaction among brain areas and that different functional areas interact with different sets of brain areas. A method for mapping areal boundaries has been formulated based on the large-scale spatial characteristics of regional interaction revealed by resting state functional connectivity. In the present study, we present a novel analysis for areal boundary mapping that requires only the signal timecourses within a region of interest, without reference to the information from outside the region. The areal boundaries were generated by the novel analysis and were compared with those generated by the previously-established standard analysis. The boundaries were robust and reproducible across the two analyses, in two regions of interest tested. These results suggest that the information for areal boundaries is readily available inside the region of interest.     

Vegetation controls vary across space and spatial scale in a historic grassland‐forest biome boundary

Ecological boundaries are critical landscape regions of transition between adjacent ecological systems. While environmental controls of boundaries may operate in a scale‐dependent manner, multiple‐scale comparisons of vegetation–environment relationships have been characterized for few boundary systems. We used approximately 250 000 point records on the occurrence of woody versus grassland vegetation in conjunction with climatic, topographical, and soils data to evaluate scale effects and spatial heterogeneity in a 650‐km section of the historic prairie–forest biome boundary of Minnesota, USA. We chose this as a model system because of the availability of historical vegetation data, a considerable spatial extent, a sharp ecological transition, and the ability to avoid confounding from more recent anthropogenic land use change. We developed modeling techniques using hierarchical variance partitioning in a spatially‐structured format that allowed us to simultaneously evaluate vegetation–environment relationships across two‐dimensional space (i.e. the prairie‐forest boundary) and across spatial scales (i.e. varying extents). Soils variables displayed the least spatial autocorrelation at shortest lag distances and tended to be the least important predictors of woody vegetation at all spatial extents. Topographical variables displayed greater spatial heterogeneity in regions dominated by forest compared with prairie and were more important at fine‐intermediate spatial scales, highlighting their likely control on fire regimes. An integrated climatic variable (precipitation minus potential evapotranspiration) displayed a trend of increasing spatial variance across the study region and was unambiguously the strongest biome boundary control, although its joint influence with fire was difficult to characterize. Spatially heterogeneous vegetation–environment relationships were observed at all scales, especially at finer scales. Our results suggest that the importance of environmental controls changes smoothly rather than discretely across scales and demonstrate the need to account for spatial non‐stationarity and scale to predict and understand vegetation distribution across ecological boundaries.     

Generalized hierarchical multivariate CAR models for areal data

In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p>/= 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B64, 583-639). Finally, we offer a real-data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991-1998 in Minnesota counties.     

Second-order analysis of inhomogeneous spatial point processes using case-control data

Summary Methods for the statistical analysis of stationary spatial point process data are now well established, methods for nonstationary processes less so. One of many sources of nonstationary point process data is a case–control study in environmental epidemiology. In that context, the data consist of a realization of each of two spatial point processes representing the locations, within a specified geographical region, of individual cases of a disease and of controls drawn at random from the population at risk. In this article, we extend work by Baddeley, Møller, and Waagepetersen (2000, Statistica Neerlandica 54 , 329–350) concerning estimation of the second‐order properties of a nonstationary spatial point process. First, we show how case–control data can be used to overcome the problems encountered when using the same data to estimate both a spatially varying intensity and second‐order properties. Second, we propose a semiparametric method for adjusting the estimate of intensity so as to take account of explanatory variables attached to the cases and controls. Our primary focus is estimation, but we also propose a new test for spatial clustering that we show to be competitive with existing tests. We describe an application to an ecological study in which juvenile and surviving adult trees assume the roles of controls and cases.     

Moving window analysis and riparian boundary delineation on the Northern Plains of Kruger National Park,South Africa

Landscapes commonly comprise of mosaics, patches and boundaries. Riparian boundaries are complex to delineate and characterize, with a multitude of variables available for delineation. Multiple methods exist for boundary delineation such as two-dimensional wombling, constrained classification techniques and discontinuity detection. One method that has proven to be reliable in boundary delineation with one-dimensional transect data is the moving split window (MSW) analysis. This study demonstrates the efficacy of MSW to delineate grass species turnover and environmental boundaries across two geologically dissimilar riparian zones in the Kruger National Park, South Africa. There are few studies that have delineated riparian boundaries of Kruger National Park, and none that have used the MSW analysis. MSW detects significant changes in dissimilarity indices of variables along gradients. Significant shifts in dissimilarity designate boundaries at various spatial scales dictated by window sizes. Significant boundaries emerge by altering window sizes, increasing quadrat width and removing infrequent herbaceous species. By utilizing these three methods, MSW background variance was reduced and riparian and wetland/upland boundaries were sharper and more easily defined.     

Retrospective versus prospective score tests for genetic association with case‐control data

Since the seminal work of Prentice and Pyke, the prospective logistic likelihood has become the standard method of analysis for retrospectively collected case‐control data, in particular for testing the association between a single genetic marker and a disease outcome in genetic case‐control studies. In the study of multiple genetic markers with relatively small effects, especially those with rare variants, various aggregated approaches based on the same prospective likelihood have been developed to integrate subtle association evidence among all the markers considered. Many of the commonly used tests are derived from the prospective likelihood under a common‐random‐effect assumption, which assumes a common random effect for all subjects. We develop the locally most powerful aggregation test based on the retrospective likelihood under an independent‐random‐effect assumption, which allows the genetic effect to vary among subjects. In contrast to the fact that disease prevalence information cannot be used to improve efficiency for the estimation of odds ratio parameters in logistic regression models, we show that it can be utilized to enhance the testing power in genetic association studies. Extensive simulations demonstrate the advantages of the proposed method over the existing ones. A real genome‐wide association study is analyzed for illustration.     

Evaluating methods to quantify spatial variation in the velocity of biological invasions

Invading species rarely spread homogeneously through a landscape and invasion patterns typically display irregular frontal boundaries as the invasion progresses through space. Those irregular patterns are generally produced by local environmental factors that may slow or accelerate movement of the frontal boundary. While there is an abundant literature on species distribution modelling methods that quantify local suitability for species establishment, comparatively few studies have examined methods for measuring the local velocity of invasions that can then be statistically analysed in relation to spatially variable environmental factors. Previous studies have used simulations to compare different methods for estimating the overall rate of spread of an invasion. We adopted a similar approach of simulating invasions that resemble two real case‐studies, both in terms of their spatial resolution (i.e. considering the size of one cell as one km) and their spatial extent (> 600 000 km²). Simulations were sampled to compare how different methods used to measure local spread rate, namely the neighbouring, nearest distance and Delaunay methods, perform for spatio‐temporal comparisons. We varied the assessment using three levels of complexity of the spatio‐temporal pattern of invasion, three sample sizes (500, 1000 and 2000 points), three different spatial sampling patterns (stratified, random, aggregated), three interpolation methods (generalized linear model, kriging, thin plate spline regression) and two spatio‐temporal modelling structures (trend surface analysis and boundary displacement), resulting in a total of 486 different scenarios. The thin plate spline regression interpolation method, in combination with trend surface analysis, was found to provide the most robust local spread rate quantification as it was able to reliably accommodate different sampling conditions and invasion patterns. This best approach was successfully applied to two case‐studies, the invasion of France by the horse‐chestnut leafminer Cameraria ohridella and by the bluetongue virus, generally in agreement with previously published values of spread rates. Potential avenues for further research are discussed.     

Modeling disease incidence data with spatial and spatio temporal dirichlet process mixtures

Disease incidence or mortality data are typically available as rates or counts for specified regions, collected over time. We propose Bayesian nonparametric spatial modeling approaches to analyze such data. We develop a hierarchical specification using spatial random effects modeled with a Dirichlet process prior. The Dirichlet process is centered around a multivariate normal distribution. This latter distribution arises from a log-Gaussian process model that provides a latent incidence rate surface, followed by block averaging to the areal units determined by the regions in the study. With regard to the resulting posterior predictive inference, the modeling approach is shown to be equivalent to an approach based on block averaging of a spatial Dirichlet process to obtain a prior probability model for the finite dimensional distribution of the spatial random effects. We introduce a dynamic formulation for the spatial random effects to extend the model to spatio-temporal settings. Posterior inference is implemented through Gibbs sampling. We illustrate the methodology with simulated data as well as with a data set on lung cancer incidences for all 88 counties in the state of Ohio over an observation period of 21 years.     

A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using MRI

Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the smooth boundary curves using functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation we show that our method is robust to shape of the target zone and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonance imaging.     

A geostatistical approach to large-scale disease mapping with temporal misalignment

Summary Temporal boundary misalignment occurs when area boundaries shift across time (e.g., census tract boundaries change at each census year), complicating the modeling of temporal trends across space. Large area-level datasets with temporal boundary misalignment are becoming increasingly common in practice. The few existing approaches for temporally misaligned data do not account for correlation in spatial random effects over time. To overcome issues associated with temporal misalignment, we construct a geostatistical model for aggregate count data by assuming that an underlying continuous risk surface induces spatial correlation between areas. We implement the model within the framework of a generalized linear mixed model using radial basis splines. Using this approach, boundary misalignment becomes a nonissue. Additionally, this disease-mapping framework facilitates fast, easy model fitting by using a penalized quasilikelihood approximation to maximum likelihood estimation. We anticipate that the method will also be useful for large disease-mapping datasets for which fully Bayesian approaches are infeasible. We apply our method to assess socioeconomic trends in breast cancer incidence in Los Angeles between the periods 1988-1992 and 1998-2002.     

Mapping Cancer Risk in Southwestern Ontario with Changing Census Boundaries

Summary Mapping disease risk often involves working with data that have been spatially aggregated to census regions or postal regions, either for administrative reasons or confidentiality. When studying rare diseases, data must be collected over a long time period in order to accumulate a meaningful number of cases. These long time periods can result in spatial boundaries of the census regions changing over time, as is the case with the motivating example of exploring the spatial structure of mesothelioma lung cancer risk in Lambton County and Middlesex County of southwestern Ontario, Canada. This article presents a local‐EM kernel smoothing algorithm that allows for the combining of data from different spatial maps, being capable of modeling risk for spatially aggregated data with time‐varying boundaries. Inference and uncertainty estimates are carried out with parametric bootstrap procedures, and cross‐validation is used for bandwidth selection. Results for the lung cancer study are shown and discussed.     

Comparison of One‐Step and Two‐Step Meta‐Analysis Models Using Individual Patient Data

The problem of combining information from separate trials is a key consideration when performing a meta‐analysis or planning a multicentre trial. Although there is a considerable journal literature on meta‐analysis based on individual patient data (IPD), i.e. a one‐step IPD meta‐analysis, versus analysis based on summary data, i.e. a two‐step IPD meta‐analysis, recent articles in the medical literature indicate that there is still confusion and uncertainty as to the validity of an analysis based on aggregate data. In this study, we address one of the central statistical issues by considering the estimation of a linear function of the mean, based on linear models for summary data and for IPD. The summary data from a trial is assumed to comprise the best linear unbiased estimator, or maximum likelihood estimator of the parameter, along with its covariance matrix. The setup, which allows for the presence of random effects and covariates in the model, is quite general and includes many of the commonly employed models, for example, linear models with fixed treatment effects and fixed or random trial effects. For this general model, we derive a condition under which the one‐step and two‐step IPD meta‐analysis estimators coincide, extending earlier work considerably. The implications of this result for the specific models mentioned above are illustrated in detail, both theoretically and in terms of two real data sets, and the roles of balance and heterogeneity are highlighted. Our analysis also shows that when covariates are present, which is typically the case, the two estimators coincide only under extra simplifying assumptions, which are somewhat unrealistic in practice.     

Opportunistic data reveal widespread species turnover in Enallagma damselflies at biogeographical scales

An information tradeoff exists between systematic presence/absence surveys and purely opportunistic (presence‐only) records for investigating the geography of community structure. Opportunistic species occurrence data may be of relatively limited quality, but typically involves numerous observations and species. Given the quality–quantity tradeoff, what can opportunistic data reveal about spatial patterns in community structure? Here we explore opportunistic data in describing geographic patterns of species composition, using over 4600 occurrence records of Enallagma damselflies in the United States. We tested phylogenetic scale (genus level, Enallagma major clades, Enallagma subclades) and spatial extent (U.S. vs watershed regions), hypothesizing that nonrandom structure is more likely at larger spatial extents. We also used three sets of systematic presence/absence surveys as a benchmark for validating opportunistic presence‐only records. Null model analysis of matrix coherence and species replacements showed many cases of nonrandom structure and widespread species turnover. This outcome was repeated across spatial and environmental gradients and community composition scenarios. Turnover dominated across the U.S. and two watersheds spanning biogeographic boundaries, but random assemblages were prevalent in a third watershed with limited longitudinal extent. Turnover also pervaded each level of phylogeny. Opportunistic presence‐only datasets showed identical patterns as systematic presence/absence datasets. These results indicate that extensive opportunistic data can be used to detect species turnover, especially at geographic scales where range margins are crossed.     

SHOOT MERISTEMLESS trafficking controls axillary meristem formation,meristem size and organ boundaries in Arabidopsis

The shoot stem cell niche, contained within the shoot apical meristem (SAM) is maintained in Arabidopsis by the homeodomain protein SHOOT MERISTEMLESS (STM). STM is a mobile protein that traffics cell‐to‐cell, presumably through plasmodesmata. In maize, the STM homolog KNOTTED1 shows clear differences between mRNA and protein localization domains in the SAM. However, the STM mRNA and protein localization domains are not obviously different in Arabidopsis, and the functional relevance of STM mobility is unknown. Using a non‐mobile version of STM (2xNLS‐YFP‐STM), we show that STM mobility is required to suppress axillary meristem formation during embryogenesis, to maintain meristem size, and to precisely specify organ boundaries throughout development. STM and organ boundary genes CUP SHAPED COTYLEDON1 (CUC1), CUC2 and CUC3 regulate each other during embryogenesis to establish the embryonic SAM and to specify cotyledon boundaries, and STM controls CUC expression post‐embryonically at organ boundary domains. We show that organ boundary specification by correct spatial expression of CUC genes requires STM mobility in the meristem. Our data suggest that STM mobility is critical for its normal function in shoot stem cell control.     

Barriers to dispersal of rain forest butterflies in tropical agricultural landscapes

Fragmentation of natural habitats can be detrimental for species if individuals fail to cross habitat boundaries to reach new locations, thereby reducing functional connectivity. Connectivity is crucial for species shifting their ranges under climate change, making it important to understand factors that might prevent movement through human‐modified landscapes. In tropical regions, rain forests are being fragmented by agricultural expansion, potentially isolating populations of highly diverse forest‐dependent species. The likelihood of crossing habitat boundaries is an important determinant of species dispersal through fragmented landscapes, and so we examined movement across rain forest‐oil palm plantation boundaries on Borneo by using relatively mobile nymphalid butterflies as our model study taxon. We marked 1666 individuals from 65 species, and 19 percent (100/527) of recaptured individuals crossed the boundary. Boundary crossing was relatively frequent in some species, and net movement of individuals was from forest into plantation. However, boundary crossing from forest into plantation was detected in less than 50 percent (12/28) of recaptured species and was dominated by small‐sized butterfly species whose larval host plants occurred within plantations. Thus, while oil palm plantations may be relatively permeable to some species, they may act as barriers to the movement of forest‐dependent species (i.e., species that require rain forest habitat to breed), highlighting the importance of maintaining forest connectivity for conserving rain forest species.     

Comparative phylogeography of three common Neotropical tree species

Aim To determine spatial and temporal commonalities in patterns of chloroplast DNA (cpDNA) variation in three widespread Neotropical tree species. We examine whether patterns of genetic variation are more consistent with Pliocene or Pleistocene divergence. Location Central American forests, located in El Salvador, Nicaragua, Costa Rica and Panama. Methods We collected sequences from two cpDNA loci from c. 30 locations for each of three species –Bursera simaruba (Burseraceae; n = 278), Brosimum alicastrum (Moraceae; n = 210) and Ficus insipida (Moraceae; n = 222) – and additionally sequenced one nuclear locus for Bursera simaruba (n = 45). We used Monmonier’s algorithm to detect genetic barriers between regions. Divergence times between these regions were estimated using coalescent analyses. Results Spatial genetic boundaries were found in similar areas for these species, namely between Costa Rica and Nicaragua for all three species, and between El Salvador and Nicaragua for two species. These boundaries visually coincide with the spatial delimitations of Pliocene islands and previously hypothesized Pleistocene refugia. Divergence time estimates between regions are more consistent with Pleistocene divergence in two of the three species. Main conclusions Our results point to strong commonalities in the spatial locations of genetic boundaries in these three species, despite the complex geological and climatological history of this region, and ecological differences between the species. While spatial genetic boundaries coincide conspicuously with possible Pliocene and Pleistocene barriers to gene flow, we cannot distinguish between the two scenarios because of the strong spatial overlap of both barriers. However, the temporal data tentatively suggest that some of this divergence occurred in the Pleistocene, although limitations in the analysis cannot confirm Pleistocene divergence without external, corroborating data. While we cannot definitively implicate a single historical process as driving patterns of genetic differentiation in all three species, our results represent an initial step towards identifying a common history of Central American tree species.