Diffusion and prediction of Leishmaniasis in a large metropolitan area in Brazil with a Bayesian space-time model

A scalable approach for short-term disease forecasting in high spatial resolution areal data

Short-term disease forecasting at specific discrete spatial resolutions has become a high-impact decision-support tool in health planning. However, when the number of areas is very large obtaining predictions can be computationally intensive or even unfeasible using standard spatiotemporal models. The purpose of this paper is to provide a method for short-term predictions in high-dimensional areal data based on a newly proposed "divide-and-conquer" approach. We assess the predictive performance of this method and other classical spatiotemporal models in a validation study that uses cancer mortality data for the 7907 municipalities of continental Spain. The new proposal outperforms traditional models in terms of mean absolute error, root mean square error, and interval score when forecasting cancer mortality 1, 2, and 3 years ahead. Models are implemented in a fully Bayesian framework using the well-known integrated nested Laplace estimation technique.

Time series analysis of leishmaniasis incidence in Sri Lanka: evidence for humidity-associated fluctuations

Leishmaniasis is a vector-borne disease of which the transmission is highly influenced by climatic factors, whereas the nature and magnitude differ between geographical regions. The effects of climatic variables on leishmaniasis in Sri Lanka are poorly investigated. The present study focused on time-series analysis of leishmaniasis cases reported from Sri Lanka with selected climatic variables. Variance stabilized time series of leishmaniasis patients of entire Sri Lanka and major districts from 2014 to 2018 was fitted to autoregressive integrated moving average (ARIMA) models. All the possible models were generated by assigning different values for autoregression and moving average terms using a function written in R statistical program. The top ten models with the lowest Akaike information criterion (AIC) values were selected by writing another function. These models were further evaluated using RMSE and MAPE error parameters to select the optimal model for each area. Cross-autocorrelation analyses were performed to assess the associations between climate and the leishmaniasis incidence. Most associated lags of each variable were integrated into the optimal models to determine the true effects imposed. The optimal models varied depending on the area. SARIMA (0,1,1) (1,0,0)₁₂ was optimal for the country level. All the forecasts were within the 95% confidence intervals. Humidity was the most notable factor associated with leishmaniasis, which could be attributed to the positive impacts on sand fly activity. Rainfall showed a negative impact probably as a result of flooding of sand fly larval habitats. The ARIMA-based models performed well for the prediction of leishmaniasis in the short term.

Space-time interactions in Bayesian disease mapping with recent tools: Making things easier for practitioners

Spatio-temporal disease mapping studies the distribution of mortality or incidence risks in space and its evolution in time, and it usually relies on fitting hierarchical Poisson mixed models. These models are complex for practitioners as they generally require adding constraints to correctly identify and interpret the different model terms. However, including constraints may not be straightforward in some recent software packages. This paper focuses on NIMBLE, a library of algorithms that contains among others a configurable system for Markov chain Monte Carlo (MCMC) algorithms. In particular, we show how to fit different spatio-temporal disease mapping models with NIMBLE making emphasis on how to include sum-to-zero constraints to solve identifiability issues when including spatio-temporal interactions. Breast cancer mortality data in Spain during the period 1990-2010 is used for illustration purposes. A simulation study is also conducted to compare NIMBLE with R-INLA in terms of parameter estimates and relative risk estimation. The results are very similar but differences are observed in terms of computing time.

Investigation of canine visceral leishmaniasis in a non-endemic area in Brazil and the comparison of serological and molecular diagnostic tests

INTRODUCTION:

Visceral leishmaniasis (VL) is an important zoonosis in Brazil. Previous identification of parasitized dogs can also help prevent the disease in humans, even in non-endemic areas of the country. The Brazilian Ministry of Health recommends diagnosis in dogs using a DPP^® (rapid test) as a screening test and an immunoenzymatic assay (ELISA) as a confirmatory test (DPP^®+ELISA), and culling infected dogs as a legal control measure. However, the accuracy of these serological tests has been questioned.

METHODS:

VL in dogs was investigated in a non-endemic area of the São Paulo state for three consecutive years, and the performances of different diagnostic tests were compared.

RESULTS:

A total of 331 dog samples were collected in 2015, 373 in 2016, and 347 in 2017. The seroprevalence by DPP^®+ELISA was 3.3, 3.2, and 0.3%, respectively, and by indirect immunofluorescence assay (IFA), it was 3.0, 5.6, and 5.5%, respectively. ELISA confirmed 18.4% of DPP^® positive samples. The concordance between the IFA and DPP^® was 83.9%. The concordance between IFA and DPP^®+ELISA was 92.9%. A molecular diagnostic test (PCR) was performed in 63.2% of the seropositive samples, all of which were negative.

CONCLUSIONS:

In non-endemic areas, diagnostic tests in dogs should be carefully evaluated to avoid false results.

Human visceral leishmaniasis in Central-Western Brazil: Spatial patterns and its correlation with socioeconomic aspects, environmental indices and canine infection

In this ecological study, we investigated spatial patterns of human visceral leishmaniasis (VL) incidence, its correlation with socioeconomic aspects, environmental indices (obtained through remote sensing) and canine VL during 2011-2016 in the municipality of Rondonópolis, a relevant endemic area for VL in Central-Western Brazil. Human VL cases were georeferenced and point patterns were analyzed by univariate Ripley's K function and Kernel density estimation (KDE). Poisson-based scan statistics were used to investigate spatial and spatiotemporal clusters of human VL incidence at the neighborhood level. Socioeconomic and environmental characteristics were compared between neighborhoods within and outside spatial human VL clusters. Also, we assessed the correlation between smoothed human VL incidence and canine VL seropositivity rates within and between neighborhoods. Human VL cases were clustered up to 2000 m; four hotspots were identified by KDE in peripheral areas. Spatial and spatiotemporal low-risk clusters for human VL were identified in central and southern areas. Neighborhoods within spatial low-risk cluster presented higher mean income, literacy rate, sanitary sewage service coverage and lower altitude, compared to the rest of the municipality. A positive correlation was found between the occurrence of human and canine VL. On the northern outskirts, high human VL incidence was spatially correlated with high canine VL seropositivity in surrounding neighborhoods. In conclusion, human VL demonstrated a heterogeneous, aggregated and peripheral spatial pattern. This distribution was correlated with intra-urban socioeconomic differences and canine VL seropositivity at the neighborhood level.

Bayesian hierarchical models for disease mapping applied to contagious pathologies

Disease mapping aims to determine the underlying disease risk from scattered epidemiological data and to represent it on a smoothed colored map. This methodology is based on Bayesian inference and is classically dedicated to non-infectious diseases whose incidence is low and whose cases distribution is spatially (and eventually temporally) structured. Over the last decades, disease mapping has received many major improvements to extend its scope of application: integrating the temporal dimension, dealing with missing data, taking into account various a prioris (environmental and population covariates, assumptions concerning the repartition and the evolution of the risk), dealing with overdispersion, etc. We aim to adapt this approach to model rare infectious diseases proposing specific and generic variants of this methodology. In the context of a contagious disease, the outcome of a primary case can in addition generate secondary occurrences of the pathology in a close spatial and temporal neighborhood; this can result in local overdispersion and in higher spatial and temporal dependencies due to direct and/or indirect transmission. In consequence, we test models including a Negative Binomial distribution (instead of the usual Poisson distribution) to deal with local overdispersion. We also use a specific spatio-temporal link in order to better model the stronger spatial and temporal dependencies due to the transmission of the disease. We have proposed and tested 60 Bayesian hierarchical models on 400 simulated datasets and bovine tuberculosis real data. This analysis shows the relevance of the CAR (Conditional AutoRegressive) processes to deal with the structure of the risk. We can also conclude that the negative binomial models outperform the Poisson models with a Gaussian noise to handle overdispersion. In addition our study provided relevant maps which are congruent with the real risk (simulated data) and with the knowledge concerning bovine tuberculosis (real data).

Spatiotemporal Analysis of Influenza in China, 2005-2018

Influenza is a major cause of morbidity and mortality worldwide, as well as in China. Knowledge of the spatial and temporal characteristics of influenza is important in evaluating and developing disease control programs. This study aims to describe an accurate spatiotemporal pattern of influenza at the prefecture level and explore the risk factors associated with influenza incidence risk in mainland China from 2005 to 2018. The incidence data of influenza were obtained from the Chinese Notifiable Infectious Disease Reporting System (CNIDRS). The Besag York Mollié (BYM) model was extended to include temporal and space-time interaction terms. The parameters for this extended Bayesian spatiotemporal model were estimated through integrated nested Laplace approximations (INLA) using the package R-INLA in R. A total of 702,226 influenza cases were reported in mainland China in CNIDRS from 2005–2018. The yearly reported incidence rate of influenza increased 15.6 times over the study period, from 3.51 in 2005 to 55.09 in 2008 per 100,000 populations. The temporal term in the spatiotemporal model showed that much of the increase occurred during the last 3 years of the study period. The risk factor analysis showed that the decreased number of influenza vaccines for sale, the new update of the influenza surveillance protocol, the increase in the rate of influenza A (H1N1)pdm09 among all processed specimens from influenza-like illness (ILI) patients, and the increase in the latitude and longitude of geographic location were associated with an increase in the influenza incidence risk. After the adjusting for fixed covariate effects and time random effects, the map of the spatial structured term shows that high-risk areas clustered in the central part of China and the lowest-risk areas in the east and west. Large space-time variations in influenza have been found since 2009. In conclusion, an increasing trend of influenza was observed from 2005 to 2018. The insufficient flu vaccine supplements, the newly emerging influenza A (H1N1)pdm09 and expansion of influenza surveillance efforts might be the major causes of the dramatic changes in outbreak and spatio-temporal epidemic patterns. Clusters of prefectures with high relative risks of influenza were identified in the central part of China. Future research with more risk factors at both national and local levels is necessary to explain the changing spatiotemporal patterns of influenza in China.

Effects of time-lagged meteorological variables on attributable risk of leishmaniasis in central region of Afghanistan

BACKGROUND

Leishmaniasis remains one of the world's most neglected vector-borne diseases, affecting predominantly poor communities mainly in developing countries. Previous studies have shown that the distribution and dynamics of leishmaniasis infections are sensitive to environmental factors, however, there are no studies on the burden of leishmaniasis attributable to time-varying meteorological variables.

METHODS

This study used data from 3 major leishmaniosis afflicted provinces of Afghanistan, between 2003 and 2009, to provide empirical analysis of change in heat/cold-leishmaniosis association. Non-linear and delayed exposure-lag-response relationship between meteorological variables and leishmaniasis were fitted with a distributed lag non-linear model applying a spline function which describes the dependency along the range of values with a lag of up to 12 months. We estimated the risk of leishmaniasis attributable to high and low temperature.

RESULTS

The median monthly mean temperature and rainfall were 16.1 °C and 0.6 in., respectively. Seasonal variations of leishmaniasis were consistent between males and females, however significant differences were observed among different age groups. Temperature effects were immediate and persistent (lag 0-12 months). The cumulative risks were highest at cold temperatures. The cumulative relative risks (logRR) for leishmaniasis were 6.16 (95% CI: 5.74-6.58) and 1.15 (95% CI: 1.32-1.31) associated with the 10th percentile temperature (2.16 °C) and the 90th percentile temperature (28.46 °C). The subgroup analysis showed increased risk for males as well as young and middle aged people at cold temperatures, however, higher risk was observed for the elderly in heat. The overall leishmaniasis-temperature attributable fractions was estimated to be 7.6% (95% CI: 7.5%-7.7%) and mostly due to cold.

CONCLUSION

Findings in this study highlight the non-linearity, delay of effects and magnitude of leishmaniasis risk associated with temperature. The disparity of risk between different subgroups can hopefully advise policy makers and assist in leishmaniasis control program.

Spatially varying auto-regressive models for prediction of new human immunodeficiency virus diagnoses

In demand of predicting new HIV diagnosis rates based on publicly available HIV data that is abundant in space but has few points in time, we propose a class of spatially varying autoregressive (SVAR) models compounded with conditional autoregressive (CAR) spatial correlation structures. We then propose to use the copula approach and a flexible CAR formulation to model the dependence between adjacent counties. These models allow for spatial and temporal correlation as well as space-time interactions and are naturally suitable for predicting HIV cases and other spatio-temporal disease data that feature a similar data structure. We apply the proposed models to HIV data over Florida, California and New England states and compare them to a range of linear mixed models that have been recently popular for modeling spatio-temporal disease data. The results show that for such data our proposed models outperform the others in terms of prediction.

Lung Cancer Mortality in Tuscany from 1971 to 2010 and Its Connections with Silicosis: A Space-Cohort Analysis Based on Shared Models

Lung cancer mortality in Tuscany (Italy) for males, from 1971 and 2010, is investigated. A hierarchical Bayesian model for space-time disease mapping is introduced. Such a model belongs to the class of shared random effect models and exploits the birth-cohort as the relevant time dimension. It allows for highlighting common and specific patterns of risk for each birth-cohort. The results show that different birth-cohorts exhibit quite different spatial patterns, even if the socioeconomic status is taken into account. In fact, there were different occupational exposures before and after the Second World War. The birth-cohort 1930-35 exhibits high relative risks related to particular areas. This fact could be connected with occupational exposure to risk factors for silicosis, perhaps a prognostic status for lung cancer.

Application of SCM with Bayesian B-Spline to Spatio-Temporal Analysis of Hypertension in China

Most previous research on the disparities of hypertension risk has neither simultaneously explored the spatio-temporal disparities nor considered the spatial information contained in the samples, thus the estimated results may be unreliable. Our study was based on the China Health and Nutrition Survey (CHNS), including residents over 12 years old in seven provinces from 1991 to 2011. Bayesian B-spline was used in the extended shared component model (SCM) for fitting temporal-related variation to explore spatio-temporal distribution in the odds ratio (OR) of hypertension, reveal gender variation, and explore latent risk factors. Our results revealed that the prevalence of hypertension increased from 14.09% in 1991 to 32.37% in 2011, with men experiencing a more obvious change than women. From a spatial perspective, a standardized prevalence ratio (SPR) remaining at a high level was found in Henan and Shandong for both men and women. Meanwhile, before 1997, the temporal distribution of hypertension risk for both men and women remained low. After that, notably since 2004, the OR of hypertension in each province increased to a relatively high level, especially in Northern China. Notably, the OR of hypertension in Shandong and Jiangsu, which was over 1.2, continuously stood out after 2004 for males, while that in Shandong and Guangxi was relatively high for females. The findings suggested that obvious spatial-temporal patterns for hypertension exist in the regions under research and this pattern was quite different between men and women.

Risk analysis and prediction of visceral leishmaniasis dispersion in São Paulo State, Brazil

Visceral leishmaniasis (VL) is an important neglected disease caused by a protozoan parasite, and represents a serious public health problem in many parts of the world. It is zoonotic in Europe and Latin America, where infected dogs constitute the main domestic reservoir for the parasite and play a key role in VL transmission to humans. In Brazil this disease is caused by the protozoan Leishmania infantum chagasi, and is transmitted by the sand fly Lutzomyia longipalpis. Despite programs aimed at eliminating infection sources, the disease continues to spread throughout the Country. VL in São Paulo State, Brazil, first appeared in the northwestern region, spreading in a southeasterly direction over time. We integrate data on the VL vector, infected dogs and infected human dispersion from 1999 to 2013 through an innovative spatial temporal Bayesian model in conjunction with geographic information system. This model is used to infer the drivers of the invasion process and predict the future progression of VL through the State. We found that vector dispersion was influenced by vector presence in nearby municipalities at the previous time step, proximity to the Bolívia-Brazil gas pipeline, and high temperatures (i.e., annual average between 20 and 23°C). Key factors affecting infected dog dispersion included proximity to the Marechal Rondon Highway, high temperatures, and presence of the competent vector within the same municipality. Finally, vector presence, presence of infected dogs, and rainfall (approx. 270 to 540mm/year) drove the dispersion of human VL cases. Surprisingly, economic factors exhibited no noticeable influence on disease dispersion. Based on these drivers and stochastic simulations, we identified which municipalities are most likely to be invaded by vectors and infected hosts in the future. Prioritizing prevention and control strategies within the identified municipalities may help halt the spread of VL while reducing monitoring costs. Our results contribute important knowledge to public and animal health policy planning, and suggest that prevention and control strategies should focus on vector control and on blocking contact between vectors and hosts in the priority areas identified to be at risk.

Leishmania infantum: illness, transmission profile and risk factors for asymptomatic infection in an endemic metropolis in Brazil

To evaluate the distribution of asymptomatic infection by Leishmania infantum in a metropolis in Brazil with different relative risks (RRs) for disease and risk factors associated with the infection, an ecological study was conducted using a Bayesian approach to estimate the RR of human visceral leishmaniasis (HVL) based on cases between 2008 and 2011. The areas were categorized and selected according to disease incidence: low (area-1), medium (area-2) and high (area-3). Cross-sectional study enrolling 935 children was used to estimate the prevalence of infection by L. infantum. Volunteers from these three areas were tested for L. infantum infection by ELISA (rK39 and soluble antigens). Infection prevalence rates were estimated and compared with the RR of disease. Multilevel logistic regression model evaluated the relationship between infection and the analysed variables. The RR of HVL was distributed heterogeneously in the municipality. The infection prevalence rates were: 34·9% in area-1; 29·3% in area-2; and 33·6% in area-3, with no significant differences between these areas. The variables 'Presence of backyards in the neighbourhood' and 'Younger children' were associated with L. infantum infection. We conclude that infection by L. infantum affects a significant proportion of the infant population regardless of the RR of disease.

Bayesian penalized spline models for the analysis of spatio-temporal count data

In recent years, the availability of infectious disease counts in time and space has increased, and consequently, there has been renewed interest in model formulation for such data. In this paper, we describe a model that was motivated by the need to analyze hand, foot, and mouth disease surveillance data in China. The data are aggregated by geographical areas and by week, with the aims of the analysis being to gain insight into the space-time dynamics and to make short-term predictions, which will aid in the implementation of public health campaigns in those areas with a large predicted disease burden. The model we develop decomposes disease-risk into marginal spatial and temporal components and a space-time interaction piece. The latter is the crucial element, and we use a tensor product spline model with a Markov random field prior on the coefficients of the basis functions. The model can be formulated as a Gaussian Markov random field and so fast computation can be carried out using the integrated nested Laplace approximation approach. A simulation study shows that the model can pick up complex space-time structure and our analysis of hand, foot, and mouth disease data in the central north region of China provides new insights into the dynamics of the disease.

A Four Dimensional Spatio-Temporal Analysis of an Agricultural Dataset

While a variety of statistical models now exist for the spatio-temporal analysis of two-dimensional (surface) data collected over time, there are few published examples of analogous models for the spatial analysis of data taken over four dimensions: latitude, longitude, height or depth, and time. When taking account of the autocorrelation of data within and between dimensions, the notion of closeness often differs for each of the dimensions. Here, we consider a number of approaches to the analysis of such a dataset, which arises from an agricultural experiment exploring the impact of different cropping systems on soil moisture. The proposed models vary in their representation of the spatial correlation in the data, the assumed temporal pattern and choice of conditional autoregressive (CAR) and other priors. In terms of the substantive question, we find that response cropping is generally more effective than long fallow cropping in reducing soil moisture at the depths considered (100 cm to 220 cm). Thus, if we wish to reduce the possibility of deep drainage and increased groundwater salinity, the recommended cropping system is response cropping.

On fitting spatio-temporal disease mapping models using approximate Bayesian inference

Spatio-temporal disease mapping comprises a wide range of models used to describe the distribution of a disease in space and its evolution in time. These models have been commonly formulated within a hierarchical Bayesian framework with two main approaches: an empirical Bayes (EB) and a fully Bayes (FB) approach. The EB approach provides point estimates of the parameters relying on the well-known penalized quasi-likelihood (PQL) technique. The FB approach provides the posterior distribution of the target parameters. These marginal distributions are not usually available in closed form and common estimation procedures are based on Markov chain Monte Carlo (MCMC) methods. However, the spatio-temporal models used in disease mapping are often very complex and MCMC methods may lead to large Monte Carlo errors and a huge computation time if the dimension of the data at hand is large. To circumvent these potential inconveniences, a new technique called integrated nested Laplace approximations (INLA), based on nested Laplace approximations, has been proposed for Bayesian inference in latent Gaussian models. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with PQL via a simulation study. The spatio-temporal distribution of male brain cancer mortality in Spain during the period 1986-2010 is also analysed.

Relative risk of visceral leishmaniasis in Brazil: a spatial analysis in urban area

Background

Visceral leishmaniasis (VL) is a vector-borne disease whose factors involved in transmission are poorly understood, especially in more urban and densely populated counties. In Brazil, the VL urbanization is a challenge for the control program. The goals were to identify the greater risk areas for human VL and the risk factors involved in transmission.

Methodology

This is an ecological study on the relative risk of human VL. Spatial units of analysis were the coverage areas of the Basic Health Units (146 small-areas) of Belo Horizonte, Minas Gerais State, Brazil. Human VL cases, from 2007 to 2009 (n = 412), were obtained in the Brazilian Reportable Disease Information System. Bayesian approach was used to model the relative risk of VL including potential risk factors involved in transmission (canine infection, socioeconomic and environmental features) and to identify the small-areas of greater risk to human VL.

Principal Findings

The relative risk of VL was shown to be correlated with income, education, and the number of infected dogs per inhabitants. The estimates of relative risk of VL were higher than 1.0 in 54% of the areas (79/146). The spatial modeling highlighted 14 areas with the highest relative risk of VL and 12 of them are concentrated in the northern region of the city.

Conclusions

The spatial analysis used in this study is useful for the identification of small-areas according to risk of human VL and presents operational applicability in control and surveillance program in an urban environment with an unequal spatial distribution of the disease. Thus the frequent monitoring of relative risk of human VL in small-areas is important to direct and prioritize the actions of the control program in urban environment, especially in big cities.

Visceral leishmaniasis (VL) is a vector-borne disease whose factors involved in transmission are poorly understood, especially in more urban and densely populated counties. In Brazil, the increasing occurrence of human VL cases in urban centers is a challenge for the control program. We aimed to identify the risk areas for VL and the risk factors involved in transmission in Belo Horizonte, a large urban area of the Brazil. At the same geographical space, we analyzed human VL cases (n = 412), canine infection and socioeconomic and environmental features. We identified a concentration of high-risk small-areas of human VL cases in the northern part of the city, marked by worse levels of education and income, and higher number of infected dogs per inhabitants. The spatial analysis used is useful for the identification of small-areas with a greater risk of VL and displays operational applicability in the control program in an urban environment with an unequal spatial distribution of the disease. Thus, the frequent monitoring of risk of human VL according to small-areas is important to direct and prioritize the actions of the control program in urban environment, especially in big cities.

Bayesian geostatistical modeling of leishmaniasis incidence in Brazil

Background

Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries.

Methodology

We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001–2010). Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis.

Principal Findings

For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676) for cutaneous leishmaniasis and 4,889 (SD: 288) for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively.

Conclusions/Significance

Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.

Leishmaniasis is a neglected tropical disease that causes approximately 20 to 40 thousand deaths every year. In Brazil, more than 600,000 clinical cases of leishmaniasis have been reported since 1990. Almost 90% of these cases are due to cutaneous leishmaniasis, whereas the remaining 10% are due to visceral leishmaniasis. Understanding of disease transmission, together with model-based incidence maps, will assist in designing and optimizing control efforts. We used reported leishmaniasis incidence data in Brazil covering the period between 2001 and 2010 to explore the association of the disease with climatic, environmental, and socioeconomic variables, and to predict its spatial distribution using Bayesian geostatistical models. We produced countrywide high spatial resolution maps for both forms of leishmaniasis and estimated the number of infected people, stratified by state. We believe that our incidence maps are useful to prioritize the spatial targeting of prevention and control.

Polynomial Spline Estimation for A Generalized Additive Coefficient Model

We study a semiparametric generalized additive coefficient model, in which linear predictors in the conventional generalized linear models is generalized to unknown functions depending on certain covariates, and approximate the nonparametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the nonparametric part is established. Semiparametric generalized likelihood ratio test is also proposed to check if a nonparametric coefficient can be simplified as a parametric one. A conditional bootstrap version is suggested to approximate the distribution of the test under the null hypothesis. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed methods. We further apply the proposed model and methods to a data set from a human visceral Leishmaniasis (HVL) study conduced in Brazil from 1994 to 1997. Numerical results outperform the traditional generalized linear model and the proposed generalized additive coefficient model is preferable.

Evaluating the effect of neighbourhood weight matrices on smoothing properties of Conditional Autoregressive (CAR) models

BACKGROUND

The Conditional Autoregressive (CAR) model is widely used in many small-area ecological studies to analyse outcomes measured at an areal level. There has been little evaluation of the influence of different neighbourhood weight matrix structures on the amount of smoothing performed by the CAR model. We examined this issue in detail.

METHODS

We created several neighbourhood weight matrices and applied them to a large dataset of births and birth defects in New South Wales (NSW), Australia within 198 Statistical Local Areas. Between the years 1995-2003, there were 17,595 geocoded birth defects and 770,638 geocoded birth records with available data. Spatio-temporal models were developed with data from 1995-2000 and their fit evaluated within the following time period: 2001-2003.

RESULTS

We were able to create four adjacency-based weight matrices, seven distance-based weight matrices and one matrix based on similarity in terms of a key covariate (i.e. maternal age). In terms of agreement between observed and predicted relative risks, categorised in epidemiologically relevant groups, generally the distance-based matrices performed better than the adjacency-based neighbourhoods. In terms of recovering the underlying risk structure, the weight-7 model (smoothing by maternal-age 'Covariate model') was able to correctly classify 35/47 high-risk areas (sensitivity 74%) with a specificity of 47%, and the 'Gravity' model had sensitivity and specificity values of 74% and 39% respectively.

CONCLUSION

We found considerable differences in the smoothing properties of the CAR model, depending on the type of neighbours specified. This in turn had an effect on the models' ability to recover the observed risk in an area. Prior to risk mapping or ecological modelling, an exploratory analysis of the neighbourhood weight matrix to guide the choice of a suitable weight matrix is recommended. Alternatively, the weight matrix can be chosen a priori based on decision-theoretic considerations including loss, cost and inferential aims.

Zoonotic cutaneous leishmaniasis in central Tunisia: spatio temporal dynamics

BACKGROUND

Zoonotic cutaneous leishmaniasis (ZCL) is endemic in many rural areas of the Southern and Eastern Mediterranean region where different transmission patterns of the disease have been described. This study was carried out in a region located in Central Tunisia and aimed to investigate the spatio-temporal dynamics of the disease from 1999 to 2004.

METHODS

Incident ZCL cases were defined by clinical diagnosis, confirmed by a positive skin test and/or parasitological examination. Annual ZCL rates were calculated for 94 regional sectors that comprise the study region of Sidi-Bouzid. Spatial and temporal homogeneity were initially investigated by chi-squared tests. Next, spatial scan statistics were used to identify spatial, temporal and spatio-temporal clusters that display abnormally high incidence rates. A hierarchical Bayesian Poisson regression model with spatial effects was fitted to signify explanatory socio-geographic factors related to spatial rate variability. Temporal ZCL dynamics for the 94 sectors were described via a linear mixed model.

RESULTS

A total of 15 897 ZCL cases were reported in the 6-year study period, with an annual incidence rate of 669.7/100 000. An outbreak of the disease was detected in 2004 (1114/100 000). Spatial clustering is evident for the whole time period. The most likely cluster according to the spatial scan statistic, contains seven sectors with abnormally high incidence rates and approximately 5% of the total population. ZCL rates per sector are mostly related to the urban/rural index; sectoral population density and the number of inhabitants per household do not appear to contribute much to the explanation of rate variability. The dynamics of the disease within the study period are satisfactorily described by quadratic curves that differ for urban and rural areas.

CONCLUSIONS

ZCL rates vary across space and time; rural/urban areas and environmental factors may explain part of this variation. In the study region, the Sidi Saâd dam-constructed in the early eighties and identified by previous studies as a major reason for the first outbreak of the disease-seems to be still related to increased ZCL rates. The most likely spatial cluster of high incidence rates contains regions located close to the dam. Our findings of increased incidences in urban areas support the hypothesis of increased incidences in peri-urban environments due to changes in sandfly/rodent living habits over recent years.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Empirical bayes estimation of demographic schedules for small areas

In this article, we analyze empirical Bayes (EB) methods for estimating small-area rate schedules. We develop EB methods that treat schedules as vectors and use adaptive neighborhoods to keep estimates appropriately local. This method estimates demographic rates for local subpopulations by borrowing strength not only from similar individuals elsewhere but also from other groups in the same area and from regularities in schedules across locations. EB is substantially better than standard methods when rates have strong spatial and age patterns. We illustrate this method with estimates of age-specific fertility schedules for over 3,800 Brazilian municipalities.

Bayesian extrapolation of space-time trends in cancer registry data

We apply a full Bayesian model framework to a dataset on stomach cancer mortality in West Germany. The data are stratified by age group, year, and district. Using an age-period-cohort model with an additional spatial component, our goal is to investigate whether there is evidence for space-time interactions in these data. Furthermore, we will determine whether a period-space or a cohort-space interaction model is more appropriate to predict future mortality rates. The setup will be fully Bayesian based on a series of Gaussian Markov random field priors for each of the components. Statistical inference is based on efficient algorithms to block update Gaussian Markov random fields, which have recently been proposed in the literature.

A Bayesian-based approach for spatio-temporal modeling of county level prevalence of Schistosoma japonicum infection in Jiangsu province, China

Spatio-temporal variations of Schistosoma japonicum infection risk in Jiangsu province, China, were examined and the relationships between key climatic factors and infection prevalence at the county level were determined. The parasitological data were collected annually by means of cross-sectional surveys carried out in 47 counties from 1990 to 1998. Climatic factors, namely land surface temperature (LST) and normalized difference vegetation index (NDVI), were obtained from remote sensing satellite sensors. Bayesian spatio-temporal models were employed to analyze the data. The best fitting model showed that spatial autocorrelation in Jiangsu province decreased dramatically from 1990 to 1992 and increased gradually thereafter. A likely explanation of this finding arises from the large-scale administration of praziquantel for morbidity control of schistosomiasis. Our analysis suggested a negative association between NDVI and risk of S. japonicum infection. On the other hand, an increase in LST contributed to a significant increase in S. japonicum infection prevalence. We conclude that combining geographic information system, remote sensing and Bayesian-based statistical approaches facilitate integrated risk modeling of S. japonicum, which in turn is of relevance for allocation of scarce resources for control of schistosomiasis japonica in Jiangsu province and elsewhere in China, where the disease remains of public health and economic significance.

Padrões espaço-temporais da mortalidade por câncer de pulmão no Sul do Brasil

As neoplasias representam a segunda causa mais comum de mortalidade no Brasil, juntamente com as chamadas causas externas. Dentre as neoplasias, o câncer de pulmão é um dos mais freqüentes, tanto em homens quanto em mulheres, e é também um dos que apresentam maior letalidade. Além disso, o risco atribuível do tabagismo como agente etiológico deste câncer é bastante alto, o que o torna potencialmente susceptível a medidas preventivas de saúde pública. O objetivo deste trabalho foi analisar os padrões espaço-temporais de câncer de pulmão em quatro Estados brasileiros (Rio Grande do Sul, Santa Catarina, Paraná e São Paulo), no período de 1996 a 2000. Os valores observados foram obtidos do Sistema de Informações de Mortalidade do Ministério da Saúde. Os valores esperados foram calculados utilizando-se a técnica de padronização indireta segundo sexo e faixa etária. As unidades geográficas utilizadas foram microrregiões definidas pelo IBGE. Foi utilizado um modelo bayesiano que permite interação espaço-temporal, ajustado através do software WinBUGS. Os resultados encontrados mostraram que no sul do Brasil existe um padrão em "U" nas razões de mortalidade por câncer de pulmão para homens, além de indicar áreas específicas que apresentaram riscos mais elevados e/ou maior ritmo de crescimento. A principal hipótese para este resultado seria diferentes incidências de tabagismo, mas a inexistência desta informação de abrangência regional impediu que esta variável fosse incluída na análise. Os resultados deste artigo podem ser utilizados para instruir políticas públicas voltadas para a redução do tabagismo e da mortalidade por câncer de pulmão.

Bayesian statistics for parasitologists

Bayesian statistical methods are increasingly being used in the analysis of parasitological data. Here, the basis of differences between the Bayesian method and the classical or frequentist approach to statistical inference is explained. This is illustrated with practical implications of Bayesian analyses using prevalence estimation of strongyloidiasis and onchocerciasis as two relevant examples. The strongyloidiasis example addresses the problem of parasitological diagnosis in the absence of a gold standard, whereas the onchocerciasis case focuses on the identification of villages warranting priority mass ivermectin treatment. The advantages and challenges faced by users of the Bayesian approach are also discussed and the readers pointed to further directions for a more in-depth exploration of the issues raised. We advocate collaboration between parasitologists and Bayesian statisticians as a fruitful and rewarding venture for advancing applied research in parasite epidemiology and the control of parasitic infections.

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.

Conglomerados de homicídios e o tráfico de drogas em Belo Horizonte, Minas Gerais, Brasil, de 1995 a 1999

Neste trabalho, apresentamos uma análise espacial dos homicídios ocorridos em Belo Horizonte e registrados pela Polícia Militar de Minas Gerais durante o período de 1995 até 1999. Utilizamos o programa SaTScan para identificar os conglomerados de risco de mortalidade mais elevado. Considerando todas as regiões da cidade de Belo Horizonte, apenas dez apresentam um risco maior de homicídios, quase todas concentradas em favelas. Como existem 85 favelas ao todo, concluímos que não são as condições sócio-econômicas per se as responsáveis pelos conglomerados de homicídios, mas o fato dessas regiões serem assoladas pelo trafico e violência associada ao comércio de drogas.