Generalized additive models for cancer mapping with incomplete covariates

Maps depicting cancer incidence rates have become useful tools in public health research, giving valuable information about the spatial variation in rates of disease. Typically, these maps are generated using count data aggregated over areas such as counties or census blocks. However, with the proliferation of geographic information systems and related databases, it is becoming easier to obtain exact spatial locations for the cancer cases and suitable control subjects. The use of such point data allows us to adjust for individual-level covariates, such as age and smoking status, when estimating the spatial variation in disease risk. Unfortunately, such covariate information is often subject to missingness. We propose a method for mapping cancer risk when covariates are not completely observed. We model these data using a logistic generalized additive model. Estimates of the linear and non-linear effects are obtained using a mixed effects model representation. We develop an EM algorithm to account for missing data and the random effects. Since the expectation step involves an intractable integral, we estimate the E-step with a Laplace approximation. This framework provides a general method for handling missing covariate values when fitting generalized additive models. We illustrate our method through an analysis of cancer incidence data from Cape Cod, Massachusetts. These analyses demonstrate that standard complete-case methods can yield biased estimates of the spatial variation of cancer risk.     

Delivering spatially comparable inference on the risks of multiple severities of respiratory disease from spatially misaligned disease count data

Population-level disease risk varies between communities, and public health professionals are interested in mapping this spatial variation to monitor the locations of high-risk areas and the magnitudes of health inequalities. Almost all of these risk maps relate to a single severity of disease outcome, such as hospitalization, which thus ignores any cases of disease of a different severity, such as a mild case treated in a primary care setting. These spatially-varying risk maps are estimated from spatially aggregated disease count data, but the set of areal units to which these disease counts relate often varies by severity. Thus, the statistical challenge is to provide spatially comparable inference from multiple sets of spatially misaligned disease count data, and an additional complexity is that the spatial extents of the areal units for some severities are partially unknown. This paper thus proposes a novel spatial realignment approach for multivariate misaligned count data, and applies it to the first study delivering spatially comparable inference for multiple severities of the same disease. Inference is via a novel spatially smoothed data augmented MCMC algorithm, and the methods are motivated by a new study of respiratory disease risk in Scotland in 2017.     

Spatial Epidemiology and GIS in Marine Mammal Conservation Medicine and Disease Research

The use of spatial epidemiology and geographical information systems (GIS) facilitates the incorporation of spatial relationships into epidemiological investigations of marine mammal diseases and conservation medicine. Spatial epidemiology is the study of the spatial variation in disease risk or incidence and explicitly addresses spatial structures and functions that factor into disease. The GIS consists of input, management, analysis, and presentation of spatial disease data and can act as an integrative tool so that a range of varied data sources can be combined to describe different environmental aspects of wild animals and their diseases. The use of modern spatial analyses and GIS is becoming well developed in the field of marine mammal ecology and biology, but has just recently started to gain more use in disease research. The use of GIS methodology and spatial analysis in nondisease marine mammal studies is briefly discussed, while examples of the specific uses of these tools in mapping, surveillance and monitoring, disease cluster detection, identification of environmental predictors of disease in wildlife populations, risk assessment, and modeling of diseases, is presented. Marine mammal disease investigations present challenges, such as less consistent access to animals for sampling, fewer baseline data on diseases in wild populations, and less robust epidemiologic study designs, but several recommendations for future research are suggested. Since location is an integral part of investigating disease, spatial epidemiology and GIS should be incorporated as a data management and analysis tool in the study of marine mammal diseases and conservation medicine.     

Estimation of Spatial Variation in Risk Using Matched Case‐control Data

A common problem in environmental epidemiology is to estimate spatial variation in disease risk after accounting for known risk factors. In this paper we consider this problem in the context of matched case‐control studies. We extend the generalised additive model approach of Kelsall and Diggle (1998) to studies in which each case has been individually matched to a set of controls. We discuss a method for fitting this model to data, apply the method to a matched study on perinatal death in the North West Thames region of England and explain why, if spatial variation is of particular scientific interest, matching is undesirable.     

Bayesian shared spatial‐component models to combine and borrow strength across sparse disease surveillance sources

When analyzing the geographical variations of disease risk, one common problem is data sparseness. In such a setting, we investigate the possibility of using Bayesian shared spatial component models to strengthen inference and correct for any spatially structured sources of bias, when distinct data sources on one or more related diseases are available. Specifically, we apply our models to analyze the spatial variation of risk of two forms of scrapie infection affecting sheep in Wales (UK) using three surveillance sources on each disease. We first model each disease separately from the combined data sources and then extend our approach to jointly analyze diseases and data sources. We assess the predictive performances of several nested joint models through pseudo cross‐validatory predictive model checks.     

The Impact of Spatial Scales and Spatial Smoothing on the Outcome of Bayesian Spatial Model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matérn correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.     

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

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

Mapping Risk of Malaria Transmission in Mainland Portugal Using a Mathematical Modelling Approach

Malaria is currently one of the world´s major health problems. About a half-million deaths are recorded every year. In Portugal, malaria cases were significantly high until the end of the 1950s but the disease was considered eliminated in 1973. In the past few years, endemic malaria cases have been recorded in some European countries. With the increasing human mobility from countries with endemic malaria to Portugal, there is concern about the resurgence of this disease in the country. Here, we model and map the risk of malaria transmission for mainland Portugal, considering 3 different scenarios of existing imported infections. This risk assessment resulted from entomological studies on An. atroparvus, the only known mosquito capable of transmitting malaria in the study area. We used the malariogenic potential (determined by receptivity, infectivity and vulnerability) applied over geospatial data sets to estimate spatial variation in malaria risk. The results suggest that the risk exists, and the hotspots are concentrated in the northeast region of the country and in the upper and lower Alentejo regions.     

Polytomous disease mapping to detect uncommon risk factors for related diseases

A statistical model for jointly analysing the spatial variation of incidences of three (or more) diseases, with common and uncommon risk factors, is introduced. Deaths for different diseases are described by a logit model for multinomial responses (multinomial logit or polytomous logit model). For each area and confounding strata population (i.e. age-class, sex, race) the probabilities of death for each cause (the response probabilities) are estimated. A specic disease, the one having a common risk factor only, acts as the baseline category. The log odds are decomposed additively into shared (common to diseases different by the reference disease) and specic structured spatial variability terms, unstructured unshared spatial terms and confounders terms (such as age, race and sex) to adjust the crude observed data for their effects. Disease specic spatially structured effects are estimated; these are considered as latent variables denoting disease-specic risk factors. The model is presented with reference to a specic application. We considered the mortality data (from 1990 to 1994) relative to oral cavity, larynx and lung cancers in 13 age groups of males, in the 287 municipalities of Region of Tuscany (Italy). All these pathologies share smoking as a common risk factor; furthermore, two of them (oral cavity and larynx cancer) share alcohol consumption as a risk factor. All studies suggest that smoking and alcohol consumption are the major known risk factors for oral cavity and larynx cancers; nevertheless, in this paper, we investigate the possibility of other different risk factors for these diseases, or even the presence of an interaction effect (between smoking and alcohol risk factors) but with different spatial patterns for oral and larynx cancer. For each municipality and age-class the probabilities of death for each cause (the response probabilities) are estimated. Lung cancer acts as the baseline category. The log odds are decomposed additively into shared (common to oral cavity and larynx diseases) and specic structured spatial variability terms, unstructured unshared spatial terms and an age-group term. It turns out that oral cavity and larynx cancer have different spatial patterns for residual risk factors which are not the typical ones such as smoking habits and alcohol consumption. But, possibly, these patterns are due to different spatial interactions between smoking habits and alcohol consumption for the first and the second disease.     

Health inequities in influenza transmission and surveillance

The lower an individual’s socioeconomic position, the higher their risk of poor health in low-, middle-, and high-income settings alike. As health inequities grow, it is imperative that we develop an empirically-driven mechanistic understanding of the determinants of health disparities, and capture disease burden in at-risk populations to prevent exacerbation of disparities. Past work has been limited in data or scope and has thus fallen short of generalizable insights. Here, we integrate empirical data from observational studies and large-scale healthcare data with models to characterize the dynamics and spatial heterogeneity of health disparities in an infectious disease case study: influenza. We find that variation in social and healthcare-based determinants exacerbates influenza epidemics, and that low socioeconomic status (SES) individuals disproportionately bear the burden of infection. We also identify geographical hotspots of influenza burden in low SES populations, much of which is overlooked in traditional influenza surveillance, and find that these differences are most predicted by variation in susceptibility and access to sickness absenteeism. Our results highlight that the effect of overlapping factors is synergistic and that reducing this intersectionality can significantly reduce inequities. Additionally, health disparities are expressed geographically, and targeting public health efforts spatially may be an efficient use of resources to abate inequities. The association between health and socioeconomic prosperity has a long history in the epidemiological literature; addressing health inequities in respiratory-transmitted infectious disease burden is an important step towards social justice in public health, and ignoring them promises to pose a serious threat.     

Spatio-temporal Transmission and Environmental Determinants of Schistosomiasis Japonica in Anhui Province,China

Background

Schistosomiasis japonica still remains of public health and economic significance in China, especially in the lake and marshland areas along the Yangtze River Basin, where the control of transmission has proven difficult. In the study, we investigated spatio-temporal variations of S. japonicum infection risk in Anhui Province and assessed the associations of the disease with key environmental factors with the aim of understanding the mechanism of the disease and seeking clues to effective and sustainable schistosomiasis control.

Methodology/Principal Findings

Infection data of schistosomiasis from annual conventional surveys were obtained at the village level in Anhui Province, China, from 2000 to 2010 and used in combination with environmental data. The spatio-temporal kriging model was used to assess how these environmental factors affected the spatio-temporal pattern of schistosomiasis risk. Our results suggested that seasonal variation of the normalized difference vegetation index (NDVI), seasonal variation of land surface temperature at daytime (LSTD), and distance to the Yangtze River were negatively significantly associated with risk of schistosomiasis. Predictive maps showed that schistosomiasis prevalence remained at a low level and schistosomiasis risk mainly evolved along the Yangtze River. Schistosomiasis risk also followed a focal spatial pattern, fluctuating temporally with a peak (the largest spatial extent) in 2005 and then contracting gradually but with a scattered distribution until 2010.

Conclusion

The fitted spatio-temporal kriging model can capture variations of schistosomiasis risk over space and time. Combined with techniques of geographic information system (GIS) and remote sensing (RS), this approach facilitates and enriches risk modeling of schistosomiasis, which in turn helps to identify prior areas for effective and sustainable control of schistosomiasis in Anhui Province and perhaps elsewhere in China.     

A heterogeneity measure for cluster identification with application to disease mapping

Mapping of disease incidence has long been of importance to epidemiology and public health. In this paper, we consider identification of clusters of spatial units with elevated disease rates and develop a new approach that estimates the relative disease risk in association with potential risk factors and simultaneously identifies clusters corresponding to elevated risks. A heterogeneity measure is proposed to enable the comparison of a candidate cluster and its complement under a pair of complementary models. A quasi-likelihood procedure is developed for estimating the model parameters and identifying the clusters. An advantage of our approach over traditional spatial clustering methods is the identification of clusters that can have arbitrary shapes due to abrupt or noncontiguous changes while accounting for risk factors and spatial correlation. Asymptotic properties of the proposed methodology are established and a simulation study shows empirically sound finite-sample properties. The mapping and clustering of enterovirus 71 infections in Taiwan are carried out for illustration.     

Non‐Parametric Ecological Regression and Spatial Variation

Ecological studies aim to analyse the variation of disease risk in relation to exposure variables that are measured at an area unit level. In practice it is rarely possible to use the exposure variables themselves, either because the corresponding data are not available or because the causes of the disease are not fully understood. It is therefore quite common to use crude proxies of the real exposure to the disease in question. These proxies are rarely able to explain the disease variation and hence additional area level random effects are introduced to account for the residual variation. In this paper we investigate the possibility to model the effect of ecological covariates non‐parametrically, with and without additional random effects for the residual spatial variation. We illustrate the issues arising through analyses of simulated and real data on larynx cancer mortality in Germany, during the years of 1986 to 1990, where we use the corresponding lung cancer rates as a proxy for smoking consumption.     

Spatial and temporal dynamics of blue agave (Agave tequilana Weber var. azul) wilt in Jalisco Mexico

Tequila is a Mexican alcoholic beverage made from the fermentation and distillation of the blue agave (Agave tequilana Weber var. azul) stem. This crop is affected by a wilt associated mainly with Fusarium oxysporum. This disease can produce considerable yield losses. Little is known about the spatial and temporal behaviour of blue agave wilt. In this work, the spatial and temporal dynamics of the disease in commercial blue agave plantations in the state of Jalisco, Mexico, were analysed. Four fields of approximately 1 ha were selected in the municipalities of Arandas and Magdalena, in which disease assessments were carried out over a year of evaluation. Each plant was categorized based on a scale with four severity classes (healthy plant, severity class 1, severity class 2 and severity class 3). Maps of disease distribution were made. The spatial pattern was analysed by means of four indicators of spatial variation for binomial data; the spatial and temporal variation was analysed by means of transition matrices. An aggregate spatial pattern was observed in all fields. The transitions in severity classes were not completely unidirectional; some plants showed symptom remission between the date of first and second disease assessment, while others remained at their original severity. Severity class 1 occurred most frequently in Arandas fields (from 12.9% to 40.3%). There was a notable increase in wilt severity to class 2 in the Magdalena fields (from 4% to 50.6%). The rates of disease development towards severity class 3 are low and do not suppose a significant loss for the crop; nevertheless, the rates of disease development towards the wilt severity class 2 do put in risk the health of the crop and the availability of the raw material for the making of tequila.     

Malaria in Africa: vector species' niche models and relative risk maps

A central theoretical goal of epidemiology is the construction of spatial models of disease prevalence and risk, including maps for the potential spread of infectious disease. We provide three continent-wide maps representing the relative risk of malaria in Africa based on ecological niche models of vector species and risk analysis at a spatial resolution of 1 arc-minute (9 185 275 cells of approximately 4 sq km). Using a maximum entropy method we construct niche models for 10 malaria vector species based on species occurrence records since 1980, 19 climatic variables, altitude, and land cover data (in 14 classes). For seven vectors (Anopheles coustani, A. funestus, A. melas, A. merus, A. moucheti, A. nili, and A. paludis) these are the first published niche models. We predict that Central Africa has poor habitat for both A. arabiensis and A. gambiae, and that A. quadriannulatus and A. arabiensis have restricted habitats in Southern Africa as claimed by field experts in criticism of previous models. The results of the niche models are incorporated into three relative risk models which assume different ecological interactions between vector species. The "additive" model assumes no interaction; the "minimax" model assumes maximum relative risk due to any vector in a cell; and the "competitive exclusion" model assumes the relative risk that arises from the most suitable vector for a cell. All models include variable anthrophilicity of vectors and spatial variation in human population density. Relative risk maps are produced from these models. All models predict that human population density is the critical factor determining malaria risk. Our method of constructing relative risk maps is equally general. We discuss the limits of the relative risk maps reported here, and the additional data that are required for their improvement. The protocol developed here can be used for any other vector-borne disease.     

Spatio-temporal variation in environmental features predicts the distribution and abundance of Ixodes scapularis

Many species have experienced dramatic changes in both geographic range and population sizes in recent history. Increases in the geographic range or population size of disease vectors have public health relevance as these increases often precipitate the emergence of infectious diseases in human populations. Accurately identifying environmental factors affecting the biogeographic patterns of vector species is a long-standing analytical challenge, stemming from a paucity of data capturing periods of rapid changes in vector demographics. We systematically investigated the occurrence and abundance of nymphal Ixodes scapularis ticks at 532 sampling locations throughout New York State (NY), USA, between 2008 and 2018, a time frame that encompasses the emergence of diseases vectored by these ticks. Analyses of these field-collected data demonstrated a range expansion into northern and western NY during the last decade. Nymphal abundances increased in newly colonised areas, while remaining stable in areas with long-standing populations over the last decade. These trends in the geographic range and abundance of nymphs correspond to both the geographic expansion of human Lyme disease cases and increases in incidence rates. Analytic models fitted to these data incorporating time, space, and environmental factors, accurately identified drivers of the observed changes in nymphal occurrence and abundance. These models accounted for the spatial and temporal variation in the occurrence and abundance of nymphs and can accurately predict nymphal population patterns in future years. Forecasting disease risk at fine spatial scales prior to the transmission season can influence both public health mitigation strategies and individual behaviours, potentially impacting tick-borne disease risk and subsequently human disease incidence.     

Semi-Parametric Spatial Joint Modeling of HIV and HSV-2 among Women in Kenya

Several diseases have common risk factors. The joint modeling of disease outcomes within a spatial statistical context may provide more insight on the interaction of diseases both at individual and at regional level. Spatial joint modeling allows for studying of the relationship between diseases and also between regions under study. One major approach for joint spatial modeling is the multivariate conditional autoregressive approach. In this approach, it is assumed that all the covariates in the study have linear effects on the multiple response variables. In this study, we relax this linearity assumption and allow some covariates to have nonlinear effects using the penalized regression splines. This model was used to jointly model the spatial variation of human immunodeficiency virus (HIV) and herpes simplex virus-type 2 (HSV-2) among women in Kenya. The model was applied to HIV and HSV-2 prevalence data among women aged 15–49 years in Kenya, derived from the 2007 Kenya AIDS indicator survey. A full Bayesian approach was used and the models were implemented in WinBUGS software. Both diseases showed significant spatial variation with highest disease burdens occurring around the Lake Victoria region. There was a nonlinear association between age of an individual and HIV and HSV-2 infection. The peak age for HIV was around 30 years while that of HSV-2 was about 40 years. A positive significant spatial correlation between HIV and HSV-2 was observed with a correlation of 0.6831(95% CI: 0.3859, 0.871).     

Spatial and temporal modelling for parasite transmission studies and risk assessment

Spatial and temporal modelling of parasite transmission and risk assessment require relevant spatial information at appropriate spatial and temporal scales. There is now a large literature that demonstrates the utility of satellite remote sensing and spatial modelling within geographical information systems (GIS) and firmly establishes these technologies as the key tools for spatial epidemiology. This review outlines the strength of satellite remotely sensed data for spatial mapping of landscape characteristics in relation to disease reservoirs, host distributions and human disease. It is suggested that current satellite technology can fulfill the spatial mapping needs of disease transmission and risk modelling, but that temporal resolution, which is a function of the satellite data acquisition characteristics, may be a limitating factor for applications requiring information about landscape or ecosystem dynamics. The potential of the Modis sensor for spatial epidemiology is illustrated with reference to mapping spatial and temporal vegetation dynamics and small mammal parasite hosts on the Tibetan plateau. Future research directions and priorities for landscape epidemiology are considered.     

Systematic neighborhood observations at high spatial resolution: methodology and assessment of potential benefits

There is a growing body of public health research documenting how characteristics of neighborhoods are associated with differences in the health status of residents. However, little is known about how the spatial resolution of neighborhood observational data or community audits affects the identification of neighborhood differences in health. We developed a systematic neighborhood observation instrument for collecting data at very high spatial resolution (we observe each parcel independently) and used it to collect data in a low-income minority neighborhood in Dallas, TX. In addition, we collected data on the health status of individuals residing in this neighborhood. We then assessed the inter-rater reliability of the instrument and compared the costs and benefits of using data at this high spatial resolution. Our instrument provides a reliable and cost-effect method for collecting neighborhood observational data at high spatial resolution, which then allows researchers to explore the impact of varying geographic aggregations. Furthermore, these data facilitate a demonstration of the predictive accuracy of self-reported health status. We find that ordered logit models of health status using observational data at different spatial resolution produce different results. This implies a need to analyze the variation in correlative relationships at different geographic resolutions when there is no solid theoretical rational for choosing a particular resolution. We argue that neighborhood data at high spatial resolution greatly facilitates the evaluation of alternative geographic specifications in studies of neighborhood and health.     

Exploration of methods to identify polymorphisms associated with variation in DNA repair capacity phenotypes

Elucidating the relationship between polymorphic sequences and risk of common disease is a challenge. For example, although it is clear that variation in DNA repair genes is associated with familial cancer, aging and neurological disease, progress toward identifying polymorphisms associated with elevated risk of sporadic disease has been slow. This is partly due to the complexity of the genetic variation, the existence of large numbers of mostly low frequency variants and the contribution of many genes to variation in susceptibility. There has been limited development of methods to find associations between genotypes having many polymorphisms and pathway function or health outcome. We have explored several statistical methods for identifying polymorphisms associated with variation in DNA repair phenotypes. The model system used was 80 cell lines that had been resequenced to identify variation; 191 single nucleotide substitution polymorphisms (SNPs) are included, of which 172 are in 31 base excision repair pathway genes, 19 in 5 anti-oxidation genes, and DNA repair phenotypes based on single strand breaks measured by the alkaline Comet assay. Univariate analyses were of limited value in identifying SNPs associated with phenotype variation. Of the multivariable model selection methods tested: the easiest that provided reduced error of prediction of phenotype was simple counting of the variant alleles predicted to encode proteins with reduced activity, which led to a genotype including 52 SNPs; the best and most parsimonious model was achieved using a two-step analysis without regard to potential functional relevance: first SNPs were ranked by importance determined by random forests regression (RFR), followed by cross-validation in a second round of RFR modeling that included ever more SNPs in declining order of importance. With this approach six SNPs were found to minimize prediction error. The results should encourage research into utilization of multivariate analytical methods for epidemiological studies of the association of genetic variation in complex genotypes with risk of common diseases.