Comparison of estimation methods for creating small area rates of acute myocardial infarction among Medicare beneficiaries in California

Creating local population health measures from administrative data would be useful for health policy and public health monitoring purposes. While a wide range of options – from simple spatial smoothers to model-based methods – for estimating such rates exists, there are relatively few side-by-side comparisons, especially not with real-world data. In this paper, we compare methods for creating local estimates of acute myocardial infarction rates from Medicare claims data. A Bayesian Monte Carlo Markov Chain estimator that incorporated spatial and local random effects performed best, followed by a method-of-moments spatial Empirical Bayes estimator. As the former is more complicated and time-consuming, spatial linear Empirical Bayes methods may represent a good alternative for non-specialist investigators.     

Modelling spatial disease rates using maximum likelihood

This paper concerns maximum likelihood estimation for a generalized linear mixed model (GLMM) useful for modelling spatial disease rates. The model allows for log-linear covariate adjustment and local smoothing of rates through estimation of spatially correlated random effects. The covariance structure of the random effects is based on a recently proposed model which parameterizes spatial dependence through the inverse covariance matrix. A Markov chain Monte Carlo algorithm for performing maximum likelihood estimation for this model is described. Results of a computer simulation study that compared maximum likelihood (ML) and penalized quasi-likelihood (PQL) estimators are presented. Compared with PQL, ML produced less biased estimates of the intercept but the ML estimates were slightly more variable. Estimates of the other regression coefficients were unbiased and nearly identical for the two methods. ML estimators of the random effects standard deviation and spatial correlation were more biased than the corresponding PQL estimators. The conclusion is that ML estimators for GLMMs cannot be expected to perform better than PQL for small samples.     

A functional-model-adjusted spatial scan statistic

This paper introduces a new spatial scan statistic designed to adjust cluster detection for longitudinal confounding factors indexed in space. The functional-model-adjusted statistic was developed using generalized functional linear models in which longitudinal confounding factors were considered to be functional covariates. A general framework was developed for application to various probability models. Application to a Poisson model showed that the new method is equivalent to a conventional spatial scan statistic that adjusts the underlying population for covariates. In a simulation study with single and multiple covariate models, we found that our new method adjusts the cluster detection procedure more accurately than other methods. Use of the new spatial scan statistic was illustrated by analyzing data on premature mortality in France over the period from 1998 to 2013, with the quarterly unemployment rate as a longitudinal confounding factor.     

Simulation study of power and sample size for repeated measures with multinomial outcomes: an application to sound direction identification experiments (SDIE)

This study focuses on sample size determination in repeated measures studies with multinomial outcomes from multiple factors. In settings where multiple factors have repeated measures, a single subject could have hundreds of observations. Sample size selection may then refer to the number of subjects, the number of levels within a factor, or the number of repetitions within the level. We simulate multinomial data through a generalized linear mixed model (GLMM) with and without overdispersion, compute the empirical power of detecting group difference for several analytical methods and contrast their performance in group comparison studies with repeated multinomial data. We use four spatial functions to model the spatial correlation structures among observations. We evaluate the factors affecting the power under various scenarios. We also present a dataset typical in hearing studies for sound localization, in which a spatially distributed array of audio loudspeakers plays multiple sounds in order to compare two programming schemes for a hearing aid device.     

A multi-modal relative spatial access assessment approach to measure spatial accessibility to primary care providers

Two-step floating catchment area (2SFCA) methods that account for multiple transportation modes provide more realistic accessibility representation than single-mode methods. However, the use of the impedance coefficient in an impedance function (e.g., Gaussian function) introduces uncertainty to 2SFCA results. This paper proposes an enhancement to the multi-modal 2SFCA methods through incorporating the concept of a spatial access ratio (SPAR) for spatial access measurement. SPAR is the ratio of a given place’s access score to the mean of all access scores in the study area. An empirical study on spatial access to primary care physicians (PCPs) in the city of Albuquerque, NM, USA was conducted to evaluate the effectiveness of SPAR in addressing uncertainty introduced by the choice of the impedance coefficient in the classic Gaussian impedance function. We used ESRI StreetMap Premium and General Transit Specification Feed (GTFS) data to calculate the travel time to PCPs by car and bus. We first generated two spatial access scores—using different catchment sizes for car and bus, respectively—for each demanding population location: an accessibility score for car drivers and an accessibility score for bus riders. We then computed three corresponding spatial access ratios of the above scores for each population location. Sensitivity analysis results suggest that the spatial access scores vary significantly when using different impedance coefficients (p?<?0.05); while SPAR remains stable (p?=?1). Results from this paper suggest that a spatial access ratio can significantly reduce impedance coefficient-related uncertainties in multi-modal 2SFCA methods.     

Asthma and air pollution in the Bronx: methodological and data considerations in using GIS for environmental justice and health research

This paper examines methods of environmental justice assessment with Geographic Information Systems, using research on the spatial correspondence between asthma and air pollution in the Bronx, New York City as a case study. Issues of spatial extent and resolution, the selection of environmental burdens to analyze, data and methodological limitations, and different approaches to delineating exposure are discussed in the context of the asthma study, which, through proximity analysis, found that people living near (within specified distance buffers) noxious land uses were up to 66 percent more likely to be hospitalized for asthma, and were 30 percent more likely to be poor and 13 percent more likely to be a minority than those outside the buffers.     

Spatial modelling of disease using data- and knowledge-driven approaches

The purpose of spatial modelling in animal and public health is three-fold: describing existing spatial patterns of risk, attempting to understand the biological mechanisms that lead to disease occurrence and predicting what will happen in the medium to long-term future (temporal prediction) or in different geographical areas (spatial prediction). Traditional methods for temporal and spatial predictions include general and generalized linear models (GLM), generalized additive models (GAM) and Bayesian estimation methods. However, such models require both disease presence and absence data which are not always easy to obtain. Novel spatial modelling methods such as maximum entropy (MAXENT) and the genetic algorithm for rule set production (GARP) require only disease presence data and have been used extensively in the fields of ecology and conservation, to model species distribution and habitat suitability. Other methods, such as multicriteria decision analysis (MCDA), use knowledge of the causal factors of disease occurrence to identify areas potentially suitable for disease. In addition to their less restrictive data requirements, some of these novel methods have been shown to outperform traditional statistical methods in predictive ability (Elith et al., 2006). This review paper provides details of some of these novel methods for mapping disease distribution, highlights their advantages and limitations, and identifies studies which have used the methods to model various aspects of disease distribution.     

Geographic analysis of diabetes prevalence in an urban area

The objective of this research is to identify the sociodemographic, environmental, and lifestyle factors associated with the geographic variability of Diabetes Mellitus (DM) prevalence in the City of Winnipeg, Manitoba in Canada. An ecological regression study design was employed for this purpose. The study population included all prevalent cases of DM in 1998 for Winnipeg. Predictor and outcome data were aggregated for analysis using two methods. First, the spatial scan statistic was used to aggregate study data into highly probable diabetes prevalence clusters. Secondly, predictor and outcome data were aggregated to existing administrative health areas. Analysis of variance and spatial and non-spatial linear regression techniques were used to explore the relationship between predictor and outcome variables. The results of the two methods of data aggregation on regression results were compared. Mapping and statistical analysis revealed substantial clustering and small-area variations in the prevalence of DM in the City of Winnipeg. The observed variations were associated with variations in socioeconomic, environmental and lifestyle characteristics of the population. The two methods of data aggregation used in the study generated very similar results in terms of identifying the geographic location of DM clusters and of the population characteristics ecologically correlated to those clusters. High rates of DM prevalence are strongly correlated with indicators of low socioeconomic status, poor environmental quality and poor lifestyles. This analysis further illustrates what a useful tool the spatial scan statistic can be when used in conjunction with ecological regression to explore the etiology of chronic disease.     

An examination of five spatial disease clustering methodologies for the identification of childhood cancer clusters in Alberta, Canada

Cluster detection is an important part of spatial epidemiology because it may help suggest potential factors associated with disease and thus, guide further investigation of the nature of diseases. Many different methods have been proposed to test for disease clusters. In this paper, we study five popular methods for detecting spatial clusters. These methods are Besag-Newell (BN), circular spatial scan statistic (CSS), flexible spatial scan statistic (FSS), Tango's maximized excess events test (MEET), and Bayesian disease mapping (BYM). We study these five different methods by analyzing a data set of malignant cancer diagnoses in children in the province of Alberta, Canada during 1983-2004. Our results show that the potential clusters are located in the south-central part of the province. Although, all methods performed very well to detect clusters, the BN and MEET methods identified local as well as general clusters.     

Regression B-spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

In the context of Bayesian disease mapping, recent literature presents generalized linear mixed models that engender spatial smoothing. The methods assume spatially varying random effects as a route to partially pooling data and 'borrowing strength' in small-area estimation. When spatiotemporal disease rates are available for sequential risk mapping of several time periods, the 'smoothing' issue may be explored by considering spatial smoothing, temporal smoothing and spatiotemporal interaction. In this paper, these considerations are motivated and explored through development of a Bayesian semiparametric disease mapping model framework which facilitates temporal smoothing of rates and relative risks via regression B-splines with mixed-effect representation of coefficients. Specifically, we develop spatial priors such as multivariate Gaussian Markov random fields and non-spatial priors such as unstructured multivariate Gaussian distributions and illustrate how time trends in small-area relative risks may be explored by splines which vary in either a spatially structured or unstructured manner. In particular, we show that with suitable prior specifications for the random effects ensemble, small-area relative risk trends may be fit by 'spatially varying' or randomly varying B-splines. A recently developed Bayesian hierarchical model selection criterion, the deviance information criterion, is used to assess the trade-off between goodness-of-fit and smoothness and to select the number of knots. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risks and to quantify uncertainty. The study offers a disease and health outcome surveillance methodology for flexible and efficient exploration and assessment of emerging risk trends and clustering. The methods are motivated and illustrated through a Bayesian analysis of adverse medical events (also known as iatrogenic injuries) among hospitalized elderly patients in British Columbia, Canada.     

Likelihood based tests for spatial randomness

Many different methods have been proposed to test the spatial randomness of a point pattern adjusting for an inhomogeneous background population. These tests can be classified into cluster detection tests, concerned with the detection and inference of local clusters, and global clustering tests, which collect evidence for clustering throughout the study region. This paper is mainly concerned about global clustering tests.Some tests for spatial randomness are based on likelihoods, which include the spatial and space-time scan statistics with variable window size and Gangnon and Clayton's weighted average likelihood ratio tests. Both of these tests perform well compared to other tests for cluster detection and global clustering, respectively. In this study, we develop other likelihood based tests for global clustering and we explore the use of different weight functions with these tests. The power of these tests is evaluated using simulated data set and compared with existing methods.     

Breast cancer in West Islip, NY: A spatial clustering analysis with covariates

This paper presents the results of an exploratory spatial analysis of breast cancer clustering in the community of West Islip on Long Island. Using address-level data from a survey of women in West Islip, we analyze the existence and locations of breast cancer clusters among long-term community residents. Statistical and geographical methods are used to first, estimate a logistic regression model of disease as a function of known risk factors and second, analyze spatial clustering among the cases of breast cancer not explained by the modeled risk factors. The method determines the actual locations of clusters so that if there is a potential causal factor in the environment it can be identified for further study. Although little evidence of clustering is uncovered, the methods described here have utility for exploratory spatial analysis in many health contexts.     

A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome

Several methods for the estimation and comparison of rates of change in longitudinal studies with staggered entry and informative drop-outs have been recently proposed. For multivariate normal linear models, REML estimation is used. There are various approaches to maximizing the corresponding log-likelihood; in this paper we use a restricted iterative generalized least squares method (RIGLS) combined with a nested EM algorithm. An important statistical problem in such approaches is the estimation of the standard errors adjusted for the missing data (observed data information matrix). Louis has provided a general technique for computing the observed data information in terms of completed data quantities within the EM framework. The multiple imputation (MI) method for obtaining variances can be regarded as an alternative to this. The aim of this paper is to develop, apply and compare the Louis and a modified MI method in the setting of longitudinal studies where the source of missing data is either death or disease progression (informative) or end of the study (assumed non-informative). Longitudinal data are simultaneously modelled with the missingness process. The methods are illustrated by modelling CD4 count data from an HIV-1 clinical trial and evaluated through simulation studies. Both methods, Louis and MI, are used with Monte Carlo simulations of the missing data using the appropriate conditional distributions, the former with 100 simulations, the latter with 5 and 10. It is seen that naive SEs based on the completed data likelihood can be seriously biased. This bias was largely corrected by Louis and modified MI methods, which gave broadly similar estimates. Given the relative simplicity of the modified MI method, it may be preferable.     

A weighted average likelihood ratio test for spatial clustering of disease

We consider methods proposed for detecting localized spatial clustering. We propose a new test statistic, the weighted average likelihood ratio test, as an alternative to the spatial scan (maximum likelihood ratio) test statistic. Two different types of weights are considered. We propose an unbiased cluster selection criterion and evaluate the bias of the tests through simulation. We also examine the power of the tests through simulations and apply the methods to the well-known New York leukaemia data.     

Geographic information systems: their use in environmental epidemiologic research.

Advances in geographic information system (GIS) technology, developed by geographers, provide new opportunities for environmental epidemiologists to study associations between environmental exposures and the spatial distribution of disease. A GIS is a powerful computer mapping and analysis technology capable of integrating large quantities of geographic (spatial) data as well as linking geographic with nongeographic data (e.g., demographic information, environmental exposure levels). In this paper we provide an overview of some of the capabilities and limitations of GIS technology; we illustrate, through practical examples, the use of several functions of a GIS including automated address matching, distance functions, buffer analysis, spatial query, and polygon overlay; we discuss methods and limitations of address geocoding, often central to the use of a GIS in environmental epidemiologic research; and we suggest ways to facilitate its use in future studies. Collaborative efforts between epidemiologists, biostatisticians, environmental scientists, GIS specialists, and medical geographers are needed to realize the full potential of GIS technology in environmental health research and may lead to innovative solutions to complex questions.     

Need for improved methods to collect and present spatial epidemiologic data for vectorborne diseases

Improved methods for collection and presentation of spatial epidemiologic data are needed for vectorborne diseases in the United States. Lack of reliable data for probable pathogen exposure site has emerged as a major obstacle to the development of predictive spatial risk models. Although plague case investigations can serve as a model for how to ideally generate needed information, this comprehensive approach is cost-prohibitive for more common and less severe diseases. New methods are urgently needed to determine probable pathogen exposure sites that will yield reliable results while taking into account economic and time constraints of the public health system and attending physicians. Recent data demonstrate the need for a change from use of the county spatial unit for presentation of incidence of vectorborne diseases to more precise ZIP code or census tract scales. Such fine-scale spatial risk patterns can be communicated to the public and medical community through Web-mapping approaches.     

Using survival analysis to study spatial point patterns in geographical epidemiology

The spatial K-function has become a well accepted method of investigating whether significant clustering can be detected in spatial point patterns. Unlike nearest neighbor-based methods, the K-function approach has the advantage of exploring spatial pattern across a range of spatial scales. However, K-functions still have a number of drawbacks. For instance, although K-functions are based on inter-event distances, they only use a count of the number of point events within successive distance bands. This represents data aggregation and information loss. Secondly, and perhaps more significantly, K-functions are based on a cumulative count of point events with distance. This feature raises the possibility that the investigation of pattern at different scales is compromised by the dependency of any one count to previous counts. This paper proposes a new approach to the analysis of spatial point patterns based upon survival analysis. Although typically used in the temporal domain, there is no reason why survival analysis cannot be applied to any positively-valued, continuous variable as well as time. In this paper, survival analysis is applied to the inter-event distance measures of bivariate spatial point patterns to investigate the 'random labeling' hypothesis. It is shown, through both a controlled data situation and empirical epidemiological applications, that such an approach may be a very useful complement to K-function analysis.     

The topography of poverty in the United States: a spatial analysis using county-level data from the Community Health Status Indicators project

Socioeconomic and health-related data at the county level are now available through the Community Health Status Indicators (CHSI) database. These data are useful for assessing the health of communities and regions. Users of the CHSI data can access online reports and an online mapping application for visualizing patterns in various community-related measures. It also is possible to download these data to conduct local analyses. This paper describes a spatial analysis of poverty in the United States at the county level for 2000. Spatial statistical techniques in a geographic information system were used to quantify significant spatial patterns, such as concentrated poverty rates and spatial outliers. The analysis revealed significant and stark patterns of poverty. A distinctive north–south demarcation of low versus high poverty concentrations was found, along with isolated pockets of high and low poverty within areas in which the predominant poverty rates were opposite. This pattern can be described as following a continental poverty divide. These insights can be useful in explicating the underlying processes involved in forming such spatial patterns that result in concentrated wealth and poverty. The spatial analytic techniques are broadly applicable to socioeconomic and health-related data and can provide important information about the spatial structure of datasets, which is important for choosing appropriate analysis methods.     

Application of geographical information systems in epidemiological studies exemplified by the ISAAC study in Munich

Geographical Information Systems (GIS) are increasingly applied as modern tools for analysis and visualization of health-related spatial data, especially in epidemiological research. GIS are used by medical researchers and executives in the public health service. A community-based survey was conducted according to the phase II protocol of the International Study of Asthma and Allergies in Childhood (ISAAC) in Munich. The spatial patterns of disease incidence were analysed and related to exposure data by GIS. The prevalence study on fourth-grade pupils (n = 3354) and school beginners (n = 2890) was conducted during the school term 1995/96 in Munich. Parental questionnaires and measurements of lung function and immunological parameters were used. The questionnaire data were integrated in a GIS database. In this paper we discuss methodological aspects of GIS-based spatial analysis related to epidemiological data. In addition, we investigate whether there were spatial clusters of children with wheeze in the last 12 months of a magnitude unlikely to occur by chance and which could indicate local health risks. The study was based on permutation tests where global and local methods were applied. No spatial clusters of children with asthma symptoms were identified in the city of Munich.     

A Bayesian space varying parameter model applied to estimating fertility schedules

We propose a spatial generalized linear model (GLM) to analyse the vital rates for small areas. In each small area, we have a response vector and covariates to explain its variability. The statistical methodology is based on a spatial Bayesian approach and it allows the covariates' parameters of the generalized linear model to vary smoothly on space. Hence, the effect of a covariate on the response varies depending on the random variables measurement location. Our model is an extension of disease mapping models allowing the space-covariate interaction to be modelled in a natural way and giving space a position of intrinsic interest. We introduce the model in the context of fertility curve estimation. In each small area, we have a curve describing the variation of fertility rates by age modelled by Coale's fertility model, which implies a GLM in each area. A simulation shows the advantages of our approach. In addition, the paper applies the procedure to census data used to study the diffusion of low fertility behaviour in Brazil.