Bayesian Spatial Random Effect Modelling for Analysing Burglary Risks Controlling for Offender, Socioeconomic, and Unknown Risk Factors

Biologists who develop and apply habitat models are often familiar with the statistical challenges posed by their data's spatial structure but are unsure of whether the use of complex spatial models will increase the utility of model results in planning. We compared the relative performance of nonspatial and hierarchical Bayesian spatial models for three vertebrate and invertebrate taxa of conservation concern (Church's sideband snails [Monadenia churchi], red tree voles [Arborimus longicaudus], and Pacific fishers [Martes pennanti pacifica]) that provide examples of a range of distributional extents and dispersal abilities. We used presence-absence data derived from regional monitoring programs to develop models with both landscape and site-level environmental covariates. We used Markov chain Monte Carlo algorithms and a conditional autoregressive or intrinsic conditional autoregressive model framework to fit spatial models. The fit of Bayesian spatial models was between 35 and 55% better than the fit of nonspatial analogue models. Bayesian spatial models outperformed analogous models developed with maximum entropy (Maxent) methods. Although the best spatial and nonspatial models included similar environmental variables, spatial models provided estimates of residual spatial effects that suggested how ecological processes might structure distribution patterns. Spatial models built from presence-absence data improved fit most for localized endemic species with ranges constrained by poorly known biogeographic factors and for widely distributed species suspected to be strongly affected by unmeasured environmental variables or population processes. By treating spatial effects as a variable of interest rather than a nuisance, hierarchical Bayesian spatial models, especially when they are based on a common broad-scale spatial lattice (here the national Forest Inventory and Analysis grid of 24 km(2) hexagons), can increase the relevance of habitat models to multispecies conservation planning.

My dissertation is motivated by the need for improved statistical approaches for understanding differences in cancer risk in rural vs. urban areas. To accomplish this goal, we develop three statistical methods that can be used to model and explain differences in age-adjusted rates between small areas with differing characteristics. These methods allow researchers to draw meaningful inferences from sparse spatial or spatio-temporal datasets at the ZIP code or county levels. Furthermore, they can be used to identify regions that might require public health interventions and to motivate costly data collection efforts at the individual level. The statistical methods we propose in this dissertation can be classified into two categories: estimation and mediation. Chapter 2 focuses on precisely estimating age-adjusted cancer mortality rates for small areas from spatio-temporal datasets with an excessive number of zeros. A large proportion of zeros are often present in datasets involving low-prevalence diseases and in datasets that include rural regions with small population sizes. When stratifying counts for each region and year by age group in the process of estimating age-adjusted rates, the proportion of zeros in the dataset is further inflated. We propose a novel Bayesian hierarchical hurdle model with spatial and temporal random effects for estimating age-adjusted rates in these settings. Via a simulation study and two data examples, we study the performance of this model and make recommendations as to when it should be used over a Bayesian hierarchical Poisson regression model for age-adjusted rates. Chapters 3 and 4 address the goal of mediation. Specifically, Chapter 3 focuses on a method for performing a mediation analysis and Chapter 4 introduces a method for performing a decomposition analysis. Both chapters aim to explain a difference in age-adjusted rates at the ZIP code level based on either a ZIP code-level exposure (mediation) or a fixed characteristic (decomposition). We develop flexible statistical methods that use Bayesian hierarchical models with spatial random effects and a Bayesian version of the g-computation technique from causal inference. Both methods were designed to create counterfactual small area estimates of age-adjusted rates within the analysis and consequently stable estimates of the effects of interest. Through a simulation study, we illustrate a high level of precision and minimal bias in the total, direct, and indirect effects when using our proposed mediation analysis method. We also compare our proposed mediation method to two methods used in the medical literature and show that our method exhibits the best trade-off of bias and variance. To demonstrate the performance of our decomposition method, we perform a data analysis to understand whether park access explains the disparity in age-adjusted colorectal cancer incidence rates in rural vs. urban ZIP codes in Iowa. We illustrate that precise inferences can be made from sparse ZIP code-level datasets when incorporating small area estimation techniques into each analysis.

Comparison of Multivariate Poisson lognormal spatial and temporal crash models to identify hot spots of intersections based on crash types

The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis was to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considered the skewnormal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considered non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model were evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD has shown the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.

Statistical models for landslide hazard enable mapping of risk factors and landslide occurrence intensity by using geomorphological covariates available at high spatial resolution. However, the spatial distribution of the triggering event (e.g., precipitation or earthquakes) is often not directly observed. In this paper we develop Bayesian spatial hierarchical models for point patterns of landslide occurrences using different types of log-Gaussian Cox processes. Starting from a competitive baseline model that captures the unobserved precipitation trigger through a spatial random effect at slope unit resolution, we explore novel complex model structures that take clusters of events arising at small spatial scales into account as well as nonlinear or spatially-varying covariate effects. For a 2009 event of around 5000 precipitation-triggered landslides in Sicily, Italy, we show how to fit our proposed models efficiently, using the integrated nested Laplace approximation (INLA), and rigorously compare the performance of our models both from a statistical and applied perspective. In this context we argue that model comparison should not be based on a single criterion and that different models of various complexity may provide insights into complementary aspects of the same applied problem. In our application our models are found to have mostly the same spatial predictive performance, implying that key to successful prediction is the inclusion of a slope-unit resolved random effect capturing the precipitation trigger. Interestingly, a parsimonious formulation of space-varying slope effects reflects a physical interpretation of the precipitation trigger: in subareas with weak trigger, the slope steepness is shown to be mostly irrelevant.

Environmental health studies are of great interest in research to evaluate the mortality-temperature relationship by adjusting spatially correlated random effects as well as identifying significant change points in temperature. However, this relationship is often not expressed using parametric models, which makes identifying change points an even more challenging problem. This paper proposes a unified semiparametric approach to simultaneously identify the nonlinear mortality-temperature relationship and detect spatially-dependent change points. A unified method is proposed for the model estimation, spatially dependent change points detection, and testing whether they are significant simultaneously by a permutation-based test. We operate under the assumption that change points remain constant, yet acknowledge the uncertainty regarding their precise number. These change points are influenced by the smoothing of an unknown function, which in turn relies on a smoothing variable and spatial random effects. Consequently, the detection of change points may be influenced by spatial effects. In this paper, several simulation studies are conducted to evaluate the performance of our proposed approach. The advantages of this unified approach are demonstrated using epidemiological data on mortality and temperature.

IntroductionThe pandemic had a profound impact on the provision of health services in Cúcuta, Colombia where the neighbourhood-level risk of Covid-19 has not been investigated. Identifying the sociodemographic and environmental risk factors of Covid-19 in large cities is key to better estimate its morbidity risk and support health strategies targeting specific suburban areas. This study aims to identify the risk factors associated with the risk of Covid-19 in Cúcuta considering inter -spatial and temporal variations of the disease in the city's neighbourhoods between 2020 and 2022. MethodsAge-adjusted rate of Covid-19 were calculated in each Cúcuta neighbourhood and each quarter between 2020 and 2022. A hierarchical spatial Bayesian model was used to estimate the risk of Covid-19 adjusting for socioenvironmental factors per neighbourhood across the study period. Two spatiotemporal specifications were compared (a nonparametric temporal trend; with and without space-time interaction). The posterior mean of the spatial and spatiotemporal effects was used to map the Covid-19 risk. ResultsThere were 65,949 Covid-19 cases in the study period with a varying standardized Covid-19 rate that peaked in October–December 2020 and April–June 2021. Both models identified an association of the poverty and stringency indexes, education level and PM10 with Covid-19 although the best fit model with a space-time interaction estimated a strong association with the number of high-traffic roads only. The highest risk of Covid-19 was found in neighbourhoods in west, central, and east Cúcuta. ConclusionsThe number of high-traffic roads is the most important risk factor of Covid-19 infection in Cucuta. This indicator of mobility and connectivity overrules other socioenvironmental factors when Bayesian models include a space-time interaction. Bayesian spatial models are important tools to identify significant determinants of Covid-19 and identifying at-risk neighbourhoods in large cities. Further research is needed to establish causal links between these factors and Covid-19.

A Bayesian spatial survival model was employed to assess geographical disparities and influential risk factors using retrospective data from oncology centers between 2019 and 2025. Central Local Government Areas (LGAs) such as Ikeja, Surulere, Oshodi-Isolo, and Mushin showed positive spatial effects, indicating that survival was higher than expected after adjusting for individual risk factors. The variation of surrounding regions in the Local Government Areas including Ibeju-Lekki, Epe, and parts of Eti-Osa recorded strongly negative spatial effects, suggesting substantially poorer survival not explained by observed covariates.

Spatial analysis of count data is important in epidemiology and other domains to identify spatial patterns. While Bayesian spatial models are a popular approach, they do require detailed knowledge of the process for model fitting, checking, and visualising results. Although a number of R packages are available to simplify running the model, there are still complexities when checking the model. This paper aims to provide a user-friendly and interactive R Shiny web application for the analysis of spatial data using Bayesian spatial Conditional Autoregressive Leroux models. The web application is built with the integration of the R packages shiny and CARBayes. The required data are the number of cases, population, and optionally some covariates for each region. In this case, we used Covid-19 data in 2021 in South Sulawesi province, Indonesia. This application enables fitting a Bayesian spatial CAR Leroux model under several hyperpriors and selecting the most appropriate through comparing several goodness of fit measures. The application also enables checking convergence, plus obtaining and visualising in an interactive map the relative risk of disease for each region.

A novel Bayesian spatial distributional regression model is presented to predict forest structural diversity in terms of the distributions of the stem diameter at breast height (DBH) in the protection forests in Ebensee, Austria. The distributional regression approach overcomes the limitations and uncertainties of traditional regression modeling, in which the conditional mean of the response is regressed against explanatory variables. The distributional regression addresses the complete conditional response distribution, instead. In total 36,338 sample trees were measured via a handheld mobile personal laser scanning system (PLS) on 273 sample plots each having a 20 m radius. Recent airborne laser scanning (ALS) data were used to derive regression covariates from the normalized digital vegetation height model (DVHM) and the digital terrain model (DTM). Candidate models were constructed that differed in their linear predictors of the two gamma distribution parameters. In the distributional regression approach, covariates can enter the model in a flexible form, such as via nonlinear smooth curves, cyclic smooths, or spatial effects. Supported by Bayesian diagnostics DIC and WAIC, nonlinear smoothing splines outperformed linear parametric slope coefficients, and the best implementation of spatial structured effects was achieved by a Gaussian process smooth. Model fitting and posterior parameter inference was achieved by using full Bayesian methodology and MCMC sampling algorithms implemented in the R-package BAMLSS. With BAMLSS, spatial interval predictions of the DBH distribution at any new geo-locations were enabled via straightforward access to the posterior predictive distributions of the model terms and by offering simple plug-in solutions for new covariate values. A cross-validation analysis validated the robustness of the proposed method’s parameter estimation and out-of-sample prediction. Spatial predictions of stem count proportions per DBH classes revealed that regeneration of smaller trees was lacking in certain areas of the protection forest landscape. Therefore, the intensity of final felling needs to be increased to reduce shading from the dense, overmature shelter trees and to promote sunlight for the young regeneration trees.

Chagas disease, caused by Trypanosoma cruzi, is still a public health problem in Latin America and in the Southern Cone countries, where Triatoma infestans is the main vector. We evaluated the relationships among the density of green vegetation around rural houses, sociodemographic characteristics, and domestic (re)infestation with T. infestans while accounting for their spatial dependence in the municipality of Pampa del Indio between 2007 and 2016. The study comprised sociodemographic and ecological variables from 734 rural houses with no missing data. Green vegetation density surrounding houses was estimated by the normalized difference vegetation index (NDVI). We used a hierarchical Bayesian logistic regression composed of fixed effects and spatial random effects to estimate domestic infestation risk and quantile regressions to evaluate the association between surrounding NDVI and selected sociodemographic variables. Qom ethnicity and the number of poultry were negatively associated with surrounding NDVI, whereas overcrowding was positively associated with surrounding NDVI. Hierarchical Bayesian models identified that domestic infestation was positively associated with surrounding NDVI, suitable walls for triatomines, and overcrowding over both intervention periods. Preintervention domestic infestation also was positively associated with Qom ethnicity. Models with spatial random effects performed better than models without spatial effects. The former identified geographic areas with a domestic infestation risk not accounted for by fixed-effect variables. Domestic infestation with T. infestans was associated with the density of green vegetation surrounding rural houses and social vulnerability over a decade of sustained vector control interventions. High density of green vegetation surrounding rural houses was associated with households with more vulnerable social conditions. Evaluation of domestic infestation risk should simultaneously consider social, landscape and spatial effects to control for their mutual dependency. Hierarchical Bayesian models provided a proficient methodology to identify areas for targeted triatomine and disease surveillance and control.

The near-shore ocean ecosystem is influenced by catchment runoff. The Great Barrier Reef has been experiencing significant water quality deterioration over the past 150 years, due in part to agricultural intensification and urban settlement in adjacent catchments (Thorburn et al., 2013). There is a need for us to understand the influences of catchment characteristics on stream water quality, with an aim to mitigate and manage the water quality issue in the terrestrial stream runoff derived from the adjacent Great Barrier Reef catchments. The event-based water quality monitoring data set from the Paddock to Reef Integrated Monitoring Program across six Natural Management Regions provides a potential opportunity to develop a data-driven understanding of catchment characteristics affecting water quality at the catchment scale. This requires a robust and reliable modelling tool to relate the monitoring data to anthropogenic and natural processes. In this study, monitoring data of Total Suspended Solids (TSS) and dissolved Oxidised Nitrogen (NOX) from 32 sites across the Great Barrier Reef catchments are selected as case study constituents due to the high risk they pose to reef health when exported from catchments to the receiving marine environment. Also, these two constituents have distinct biogeochemical processes in catchments. Specifically, TSS is typically conserved (although mobilized and deposited) while travelling through river systems; while NOX can be potentially processed and removed from the system altogether. A Bayesian hierarchical linear modelling framework is adopted, due to its ability to borrow strength among sites, allowing information to be transferred across space, and due to its ability to provide uncertainty of the predictions. The Bayesian hierarchical linear regression model in this study is developed to evaluate the significance of various catchment characteristics (e.g., land uses, catchment topography and geology) on spatial variation in water quality. The main findings of this study are listed as follows, • Sites located in the Burdekin and Fitzroy Natural Management Regions tend to have greater TSS concentrations, illustrated by the modelled site-specific spatial random effects (deviation from the overall average concentration). Additionally, grazing and dry land agriculture land uses are positively correlated with the spatial random effect on TSS. The complexity of interaction between different catchment characteristics (e.g., land use and topography) can potentially result in a negative spatial random effect on TSS, which is reduced in the relatively steeper Great Barrier Reef catchments with a denser stream network. • Sugar cane is one of the most significant NOX contributors according to the modelling results, likely partially due to the excessive application of fertilizers; however, conservation land use has limited effect on NOX removal, indicating denitrification process alone may not be sufficient to remove NOX. The modelling results demonstrate different land management strategies are required for the purpose of reducing different constituents. This work will provide scientific insights for water quality management at the catchment scale.

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matern covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

BackgroundThe evidence is sparse regarding the associations between serious mental illnesses (SMIs) prevalence and environmental factors in adulthood as well as the geographic distribution and variability of these associations. In this study, we evaluated the association between availability and proximity of green and blue space with SMI prevalence in England as a whole and in its major conurbations (Greater London, Birmingham, Liverpool and Manchester, Leeds, and Newcastle).Methods and findingsWe carried out a retrospective analysis of routinely collected adult population (≥18 years) data at General Practitioner Practice (GPP) level. We used data from the Quality and Outcomes Framework (QOF) on the prevalence of a diagnosis of SMI (schizophrenia, bipolar affective disorder and other psychoses, and other patients on lithium therapy) at the level of GPP over the financial year April 2014 to March 2018. The number of GPPs included ranged between 7,492 (April 2017 to March 2018) to 7,997 (April 2014 to March 2015) and the number of patients ranged from 56,413,719 (April 2014 to March 2015) to 58,270,354 (April 2017 to March 2018). Data at GPP level were converted to the geographic hierarchy unit Lower Layer Super Output Area (LSOA) level for analysis. LSOAs are a geographic unit for reporting small area statistics and have an average population of around 1,500 people. We employed a Bayesian spatial regression model to explore the association of SMI prevalence in England and its major conurbations (greater London, Birmingham, Liverpool and Manchester, Leeds, and Newcastle) with environmental characteristics (green and blue space, flood risk areas, and air and noise pollution) and socioeconomic characteristics (age, ethnicity, and index of multiple deprivation (IMD)). We incorporated spatial random effects in our modelling to account for variation at multiple scales.Across England, the environmental characteristics associated with higher SMI prevalence at LSOA level were distance to public green space with a lake (prevalence ratio [95% credible interval]): 1.002 [1.001 to 1.003]), annual mean concentration of PM2.5 (1.014 [1.01 to 1.019]), and closeness to roads with noise levels above 75 dB (0.993 [0.992 to 0.995]). Higher SMI prevalence was also associated with a higher percentage of people above 24 years old (1.002 [1.002 to 1.003]), a higher percentage of ethnic minorities (1.002 [1.001 to 1.002]), and more deprived areas.Mean SMI prevalence at LSOA level in major conurbations mirrored the national associations with a few exceptions. In Birmingham, higher average SMI prevalence at LSOA level was positively associated with proximity to an urban green space with a lake (0.992 [0.99 to 0.998]). In Liverpool and Manchester, lower SMI prevalence was positively associated with road traffic noise ≥75 dB (1.012 [1.003 to 1.022]). In Birmingham, Liverpool, and Manchester, there was a positive association of SMI prevalence with distance to flood zone 3 (land within flood zone 3 has ≥1% chance of flooding annually from rivers or ≥0.5% chance of flooding annually from the sea, when flood defences are ignored): Birmingham: 1.012 [1.000 to 1.023]; Liverpool and Manchester: 1.016 [1.006 to 1.026]. In contrast, in Leeds, there was a negative association between SMI prevalence and distance to flood zone 3 (0.959 [0.944 to 0.975]). A limitation of this study was because we used a cross-sectional approach, we are unable to make causal inferences about our findings or investigate the temporal relationship between outcome and risk factors. Another limitation was that individuals who are exclusively treated under specialist mental health care and not seen in primary care at all were not included in this analysis.ConclusionsOur study provides further evidence on the significance of socioeconomic associations in patterns of SMI but emphasises the additional importance of considering environmental characteristics alongside socioeconomic variables in understanding these patterns. In this study, we did not observe a significant association between green space and SMI prevalence, but we did identify an apparent association between green spaces with a lake and SMI prevalence. Deprivation, higher concentrations of air pollution, and higher proportion of ethnic minorities were associated with higher SMI prevalence, supporting a social-ecological approach to public health prevention. It also provides evidence of the significance of spatial analysis in revealing the importance of place and context in influencing area-based patterns of SMI.

Variation in the risk of colorectal cancer in families with Lynch syndrome: a retrospective cohort study.