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Acta Tropica 132 (2014) 57–63

Contents lists available at ScienceDirect

Acta Tropica

jo ur nal home p age: www.elsev ier .com/ locate /ac ta t ropica

redictive risk mapping of schistosomiasis in Brazil using Bayesianeostatistical models

onaldo G.C. Scholtea,b,c, Laura Gosoniua,b, John B. Maloned, Frédérique Chammartina,b,ürg Utzingera,b, Penelope Vounatsoua,b,∗

Department of Epidemiology and Public Health, Swiss Tropical and Public Health Institute, P.O. Box, CH-4002 Basel, SwitzerlandUniversity of Basel, P.O. Box, CH-4003 Basel, SwitzerlandCoordenac ão Geral de Hanseníase e Doenc as em Eliminac ão, Secretaria de Vigilância em Saúde—MS, SCS Qd 4 Bloco A Ed. Principal 3◦ andar,EP:70304-000 Brasília, DF, BrazilPathobiological Sciences, School of Veterinary Medicine, Louisiana State University, Baton Rouge, LA 70803, USA

r t i c l e i n f o

rticle history:eceived 5 September 2012eceived in revised form 16 October 2013ccepted 8 December 2013vailable online 19 December 2013

eywords:ayesian modellingeostatistics

a b s t r a c t

Schistosomiasis is one of the most common parasitic diseases in tropical and subtropical areas, includingBrazil. A national control programme was initiated in Brazil in the mid-1970s and proved successful interms of morbidity control, as the number of cases with hepato-splenic involvement was reduced sig-nificantly. To consolidate control and move towards elimination, there is a need for reliable maps on thespatial distribution of schistosomiasis, so that interventions can target communities at highest risk. Thepurpose of this study was to map the distribution of Schistosoma mansoni in Brazil. We utilized readilyavailable prevalence data from the national schistosomiasis control programme for the years 2005–2009,derived remotely sensed climatic and environmental data and obtained socioeconomic data from various

redictive risk mappingchistosoma mansonichistosomiasisrazil

sources. Data were collated into a geographical information system and Bayesian geostatistical mod-els were developed. Model-based maps identified important risk factors related to the transmission ofS. mansoni and confirmed that environmental variables are closely associated with indices of poverty. Oursmoothed predictive risk map, including uncertainty, highlights priority areas for intervention, namelythe northern parts of North and Southeast regions and the eastern part of Northeast region. Our predictiverisk map provides a useful tool for to strengthen existing surveillance-response mechanisms.

. Introduction

Schistosomiasis remains one of the most common parasitic dis-ases in tropical and subtropical areas. Indeed, more than 200illion people are infected among the almost 800 million people

t risk of schistosomiasis (Steinmann et al., 2006). The disease isntimately connected with conditions of poverty, poor sanitationnd lack of clean water, and schistosomiasis is emerging in areasndergoing major water resources development and managementSouthgate, 1997; Steinmann et al., 2006; King, 2010; Utzinger et al.,011).

In Brazil, schistosomiasis is a largely neglected disease, although

t is of considerable public health relevance, especially in the poo-est regions of the country (Katz and Peixoto, 2000). During theast decades, the distribution of schistosomiasis has changed as

∗ Corresponding author at: Department of Epidemiology and Public Health, Swissropical and Public Health Institute, P.O. Box, CH-4002 Basel, Switzerland.el.: +41 61 284 8109; fax: +41 61 284 8105.

E-mail address: penelope.vounatsou@unibas.ch (P. Vounatsou).

001-706X/$ – see front matter © 2014 Published by Elsevier B.V.ttp://dx.doi.org/10.1016/j.actatropica.2013.12.007

© 2014 Published by Elsevier B.V.

a result of demographic and ecological transformations, such asthe expansion of rural areas to the outskirts of large urban cen-tres. Due to the lack of adequate sanitation, sewage released intofreshwater bodies and re-use of wastewater in agriculture, schisto-somiasis persists as a public health problem (Graeff-Teixeira et al.,1999; Leal Neto et al., 2012). In the mid-1970s, Brazil established anational control programme (NCP) against schistosomiasis, led bythe Ministry of Health (MoH). At the onset of this programme, thekey strategy was morbidity control using the antischistosomal drugoxamniquine (Katz, 2008). By 2003, more than 12 million treat-ments were administered. At the beginning, the programme wascentralized at the MoH in Brasilia. Over time, the municipalitiestook leadership in surveys and control efforts. The NCP was suc-cessful in reducing the prevalence of Schistosoma mansoni infectionand the number of cases with hepato-splenic involvement (Amaralet al., 2006). However, it did not prevent the occurrence of newoutbreaks (Carvalho et al., 1997; Graeff-Teixeira et al., 1999; Katz

and Almeida, 2003).

The control of schistosomiasis and other poverty-related dis-eases requires reliable risk maps, so that interventions can focus onhigh-risk communities, which in turn enhance cost-effectiveness

5 ta Tropica 132 (2014) 57–63

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Brooker et al., 2009; Carvalho et al., 2010; Guimarães et al.,010a; Hürlimann et al., 2011; Leal Neto et al., 2012). Recenttudies determined the spatial distribution of S. mansoni in sev-ral states of Brazil. For example, the risk of schistosomiasis haseen associated with environmental variables and/or social deter-inants in the states of Bahia, Pernambuco and Minas Gerais,

nd regions designated for ecotourism, e.g. “Estrada Real” (Baviat al., 2001; Guimarães et al., 2006, 2008, 2010a, 2010b; Carvalhot al., 2010; Galvão et al., 2010; Paredes et al., 2010; Leal Netot al., 2012). However, a country-wide risk map of schistosomia-is does not exist. Studies carried out thus far used data from theCP and employed ecological niche modelling or biology-drivennd standard statistical models for risk profiling, assuming spa-ial independence of the data. Survey data, however, are spatiallyorrelated because neighbouring geographical areas share similarnvironmental exposures, thus influencing disease risk in a similaray. Ignoring spatial correlation could lead to incorrect estimates

f the significance of the risk factors and model-based predictions.ayesian geostatistical models have been successfully applied tochistosoma spp. prevalence data in different parts of Africa andsia to generate predictive risk maps and to identify underlyingisk factors that govern the spatial distribution of schistosomiasisRaso et al., 2005; Clements et al., 2006, 2008; Beck-Wörner et al.,007; Koroma et al., 2010; Peng et al., 2010; Schur et al., 2011,013).

In the current study, we analyzed S. mansoni prevalence datarom the NCP in Brazil that were obtained between 2005 and 2009.

e obtained climatic, environmental and socioeconomic data fromarious sources, established a geographical information system andsed Bayesian statistical models to generate a smoothed predictiveisk map of schistosomiasis in Brazil.

. Materials and methods

.1. Schistosoma mansoni prevalence data

Our prevalence data of S. mansoni were obtained from004 municipalities in Brazil surveyed in the years 2005–2009ithin the frame of the NCP (http://tabnet.datasus.gov.br/

gi/tabcgi.exe?sinan/pce/cnv/pce.def, accessed 8 March 2010). Sur-eyed municipalities, together with observed prevalence data haveeen plotted using ArcGIS version 9.3 (ESRI, Redlands, CA, USA) andre presented in Fig. 1. Of note, the NCP was primarily implementedn known schistosome-endemic areas with entire communitieseing surveyed. The Kato–Katz technique with single stool sam-les subjected to duplicate Kato–Katz thick smears was utilized forhe diagnosis of S. mansoni infection (Katz et al., 1972), as recom-

ended by the World Health Organization (WHO) (1994).

.2. Climatic and environmental data

Climatic and environmental proxies were considered in ournalyses since these are the main predictors for the distribution ofntermediate host snails that play a central role in the life cycle ofchistosomiasis (Appleton, 1978; Stensgaard et al., 2013). Climaticata were extracted from Worldclim Global Climate Data (Hijmanst al., 2005). These data consist of 19 bioclimatic variables (Table 1),hich are generated through interpolation of average monthly cli-ate data from weather stations for a 50-year period (1950–2000)

t a spatial resolution of 1 km.Environmental data were obtained from different freely accessi-

le remote sensing sources, as summarized in Table 1. Land surfaceemperature (LST) data were utilized as proxy for day and nightemperature, the normalized difference vegetation index (NDVI)nd enhanced vegetation index (EVI) as proxies for moisture and

Fig. 1. Observed prevalence of schistosomiasis in Brazil from 2005 to 2009 (NCP).

vegetation, respectively, whilst a digital elevation model (DEM) wasemployed for extracting altitude estimates.

2.3. Socioeconomic data

Socioeconomic indicators were included to enable evaluation ofthe influence of poverty on the risk of schistosomiasis (Table 2).Data were gathered, as recent as possible, from different opensources, such as: (i) population data from 2010, human devel-opment index (HDI) from 2000 and rural population from 2000(census data) provided by the Instituto Brasileiro de Geografia eEstatística (IBGE); (ii) unsatisfied basic needs (UBN) from 2000 pro-vided by the Pan American Health Organization (PAHO); and (iii)infant mortality rate (IMR) from 2000 and human influence index(HII) from 2005 provided by the Center for International Earth Sci-ence Information Network (CIESIN).

2.4. Snail data

Scholte et al. (2012) recently presented maps of the distributionof schistosomiasis intermediate host snails in Brazil. Based on thesemaps, the probability of the presence of intermediate host snails atspecific locations was determined and considered as an additionalcovariate in the present study. The raw data were obtained frompeer-reviewed publications and from a database held at the Labo-ratory of Medical Malacology and Helmintology in Fiocruz, MinasGerais, Brazil. The probability of the presence of the intermediatehost snails was determined using a maximum entropy (MaxEnt)approach.

2.5. Statistical analysis

We established a geographical information system with

S. mansoni infection prevalence utilized as outcome variable. Thecovariates considered for the spatially explicit analysis were socio-economic (household assets ownership, HDI, HII, IMR and UBNindicators), climatic and environmental proxies from Worldclim

R.G.C. Scholte et al. / Acta Tropica 132 (2014) 57–63 59

Table 1Data sources and properties of the climatic and other environmental covariates used in our Bayesian geostatistical model (1 km spatial resolution).

Source Data type Data period Temporal resolution

Shuttle Radar Topography Mission Data (SRTM) Digital elevation model (DEM) 2000 OnceModerate Resolution ImagingSpectroradiometer (MODIS)/Terra

Land surface temperature (LST) for day and night 2005–2009 8 daysNormalized difference vegetation index (NDVI) 2005–2009 16 days

Worldclim Global Climate Data BIO1 (annual mean temperature) 1950–2000 OnceBIO2 (mean diurnal range (mean of monthly (min. and max. temperature)) 1950–2000 OnceBIO3 (isothermality (BIO2/BIO7) (×100)) 1950–2000 OnceBIO4 (temperature seasonality (standard deviation × 100)) 1950–2000 OnceBIO5 (max. temperature of warmest month) 1950–2000 OnceBIO6 (min. temperature of coldest month) 1950–2000 OnceBIO7 (temperature annual range (BIO5–BIO6)) 1950–2000 OnceBIO8 (mean temperature of wettest quarter) 1950–2000 OnceBIO9 (mean temperature of driest quarter) 1950–2000 OnceBIO10 (mean temperature of warmest quarter) 1950–2000 OnceBIO11 (mean temperature of coldest quarter) 1950–2000 OnceBIO12 (annual precipitation) 1950–2000 OnceBIO13 (precipitation of wettest month) 1950–2000 OnceBIO14 (precipitation of driest month) 1950–2000 OnceBIO15 (precipitation seasonality (coefficient of variation)) 1950–2000 OnceBIO16 (precipitation of wettest quarter) 1950–2000 OnceBIO17 (precipitation of driest quarter) 1950–2000 Once

est qust qua

GLt(ypgcsgelc

praam

TD

BIO18 (precipitation of warmBIO19 (precipitation of colde

lobal Climate Data (bioclimatic parameters) and MODIS (LST day,ST night, NDVI and EVI). Relationships between S. mansoni infec-ion prevalence and different functional forms of the predictorslinear and categorical) were assessed on the basis of bivariate anal-ses. The best functional form was chosen by visual examination oflots of the log it of the prevalence versus predictor and by investi-ating model goodness-of-fit according to the Akaike’s informationriterion. In case of high correlation among the predictors (Pear-on’s correlation coefficient >0.9), only those presenting the bestoodness-of-fit were considered in the geostatistical analysis. Lin-ar predictors were standardized prior to any analysis. Stepwiseogistic regression models were employed to select the subset ofovariates which gave the best fit to the data.

To account for spatial correlation in S. mansoni infectionrevalence, Bayesian geostatistical models with location-specificandom effects were fitted. Spatial correlation was modelled by

ssuming that the random effects are distributed according to

multivariate normal distribution with the variance–covarianceatrix related to an exponential correlation function between all

able 2ata sources and properties of the socioeconomic covariates used in our Bayesian geosta

Source Data

Instituto Brasileiro de Geografia eEstatística (IBGE) (census data)

PopulHumaRural

Pan American Health Organization(unsatisfied basic needs) (census data)

Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Bras0Infan

Center for International Earth Science Information Network (CIESIN) Huma

arter) 1950–2000 Oncerter) 1950–2000 Once

pairs of municipalities. Our application includes a large number ofmunicipalities (n = 1004) giving rise to a large covariance matrix.Large matrix computations which are required for model fit areunfeasible. To overcome this issue, we employed a methodologythat is adapted to such large geostatistical data (Banerjee et al.,2008; Chammartin et al., 2013; Schur et al., 2013), which estimatethe spatial correlation from a subset of locations. Modelling detailsare given in Appendix A.

Markov chain Monte Carlo (MCMC) simulation techniques wereutilized to fit the models, providing estimates of the parame-ters and their precision. The posterior estimates were furtheremployed to predict the risk of S. mansoni at non-sampled loca-tions. Predictions were obtained via Bayesian kriging (Diggle et al.,1998) at 8 km spatial resolution, covering around 283,700 pixelsfor the whole of Brazil. The geostatistical models were validatedin terms of their predictive performance by calculating the per-

centage of locations that were predicted within a 95% Bayesiancredible interval (BCI). The analysis was implemented in FORTRAN95 (Compaq Visual FORTRAN Professional 6.6.0) with codes written

tistical model (by municipality).

type Data period

ation data 2010n development index (HDI) 2000

population 2000 3 (% of pupils enrolled in primary school) 2000 4 (% of pupils completing primary school) 2000 5 (rate literacy in 15–24-year-olds) 2000 6 (girls and boys primary school) 20007 (girls and boys high school) 2000

8 (girls and boys undergraduate school) 2000 9 (relation literacy women and men aged 15–24 years) 2000 10 (proportion women work nonfarming activities) 2000 11 (rate people with potable water at house) 2000 12 (rate people with sanitation at house) 2000 13 (rate people with energy at house) 2000 14 (proportion of houses owned × rented) 2000 15 (index secure tenure house) 2000 16 (unemployment rate) 2000 17 (proportion of houses with phone) 200018 (proportion of house with computer) 2000

t mortality rate (IMR) 2000n influence index (HII) 2005

60 R.G.C. Scholte et al. / Acta Tro

Table 3Parameter estimates of non-spatial (bivariate and multivariate) and Bayesian geo-statistical logistic regression models relating S. mansoni risk in Brazil with climatic,environmental and socioeconomic predictors.

Variable Bivariate non-spatial model Geostatistical model

OR 95% CI OR 95% BCI

Bras0 3 0.73 (0.73, 0.74) 0.99 (0.98, 0.99)Bras0 11 0.77 (0.76, 0.77) 0.87 (0.86, 0.88)Bras0 18 0.69 (0.69, 0.70) 0.97 (0.97, 0.98)HDI 0.67 (0.67, 0.68) 0.60 (0.59, 0.60)Rural 1.14 (1.14, 1.15) 0.95 (0.94, 0.95)HII 0.93 (0.92, 0.93) 1.06 (1.05, 1.06)Altitude 0.87 (0.86, 0.87) 0.73 (0.72, 0.73)LST day 0.85 (0.85, 0.86) 0.49 (0.47, 0.49)NDVI 1.15 (1.14, 1.15) 1.01 (1.00, 1.01)Bioclim2 0.86 (0.85, 0.86) 1.42 (1.40, 1.42)Bioclim10 1.10 (1.10, 1.11) 0.84 (0.83, 0.84)Bioclim11 1.13 (1.12, 1.13) 1.85 (1.83, 1.87)Bioclim12 1.06 (1.05, 1.06) 0.60 (0.59, 0.60)Bioclim18 0.85 (0.85, 0.86) 1.52 (1.50, 1.52)Bioclim19 1.16 (1.15, 1.16) 1.63 (1.61, 1.63)Snail 1.43 (1.42, 1.44) 1.87 (1.84, 1.87)�2 0.56 (0.17, 3.47)Range (km) 1.58 (1.47, 2.24)

Bras0 3: proportion of children enrolled in primary school; Bras0 11: rate of peo-ple with potable water at home; Bras0 18: proportion of houses with computer;HDI: human development index; rural: proportion of people living in rural areas;HII: human influence index; LST night/day: average night and day land surface tem-perature during 2005–2009; NDVI: average normalized difference vegetation indexduring 2005–2009; Bioclim2: mean diurnal range; Bioclim10: mean temperatureof the warmest quarter; Bioclim11: mean temperature of the coldest quarter; Bio-clim12: annual precipitation; Bioclim18: precipitation warmest quarter; Bioclim19:pOB

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recipitation coldest quarter; Snail: probability of snail presence.R: odds ratio; 95% CI: lower and upper bound of a 95% confidence interval; BCI:ayesian credible interval.

y the authors using standard numerical libraries (NAG, Numericallgorithm Group Ltd.). Data management was done using STATAersion 10.1 (StataCorp LP, College Station, TX, USA) and the finalaps plotted using ArcGIS version 9.3 (ESRI, Redlands, CA, USA).

. Results

The pooled data at the unit of the municipality, as obtainedrom the schistosomiasis NCP in the years 2005–2009, revealedhat the prevalence of S. mansoni ranged from nil to 70% with a

ean prevalence of 5.3% (median prevalence 3.4%, standard devi-tion (SD) 7.1%). Approximately 42% of the observed locations hadrevalence estimates below 2.5%.

The covariates included in the final geostatistical model areummarized in Table 3. All considered covariates were significantlyssociated with the risk of S. mansoni in the bivariate non-spatialogistic regressions. Socioeconomic status (as proxied by HDI), pro-ortion of children enrolled in primary school (Bras0 3), rate ofeople with potable water at home (Bras0 11), proportion of housesith computer (Bras0 18) and proportion of population living in

ural areas were all negatively associated with the risk of S. mansoni.oreover, negative associations were found between S. mansoni

nd altitude, HII, day LST, mean diurnal range and precipitation inhe warmest quarter of the year. NDVI, night LST, mean tempera-ure of the warmest and coldest quarter, annual precipitation andrecipitation of the coldest quarter were all positively associatedith the prevalence of S. mansoni. The probability of the presence

f intermediate host snails showed a statistically significant asso-iation with the risk of S. mansoni, suggesting that the higher therobability of Biomphalaria snail presence, the higher the risk of

chistosomiasis.

Multivariate geostatistical analysis indicated that all covariatesere significantly associated with the transmission of S. mansoni.owever although some of the predictors had a different effect

pica 132 (2014) 57–63

direction compared to the one estimated by the correspondingnon-spatial bivariate logistic regression model (Table 3). In partic-ular, when the effect of the other predictors was considered andthe spatial correlation was taken into account, night LST, meantemperature in the warmest quarter, annual precipitation and theproportion of population living in rural areas became negativelyassociated with the risk of schistosomiasis, whereas mean diur-nal range, precipitation of the warmest quarter and HII showed asignificant positive effect.

The posterior estimates of the spatial parameters are also pre-sented in Table 3. The estimates of the decay parameter suggestthat, considering the exponential correlation function chosen, theminimum distance for which the spatial correlation becomes neg-ligible is 1.58 km (95% BCI: 1.47, 2.24 km). The amount of spatialvariance was estimated at 0.56 (95% BCI: 0.17, 3.47).

The spatial distribution of S. mansoni risk in Brazil is shownin Fig. 2A. Areas at highest risk of infection are located in thenorthern part of the North region, the eastern part of the Northeastregion and the northern part of the Southeast region. Low riskareas are mainly concentrated in the Amazon, Center and Southregions. Fig. 2B shows the corresponding prediction uncertaintymap, as indicated by the SD of model prediction errors. Modelvalidation showed that the predictive ability of the geostatisticalmodel was 31.5%, indicating that the model was able to correctlypredict the prevalence of S. mansoni in only about one third of themunicipalities.

4. Discussion

We present a smoothed predictive schistosomiasis risk mapfor Brazil, including uncertainty. Our models were constructed byrelating geolocated parasite prevalence data with climatic, envi-ronmental, socioeconomic and intermediate host snail data. Therelative low predictive ability of our model suggests that a sin-gle model is not able to capture the disease-environment andsocioeconomic relations across different ecological zones. Indeed,Guimarães et al. (2010a) showed that the regionalization improvedthe predictability of S. mansoni risk estimates in Minas Gerais.

Our geostatistical modelling approach also allowed identi-fication of key risk factors that govern the transmission ofS. mansoni. Our results confirm that socioeconomic, environmen-tal and climatic data are important drivers that explain the spatialdistribution of schistosomiasis. Moreover, our results corroborateearlier work, which showed that these variables proved usefulfor investigating the spatial epidemiology and the importancefor the control of major human helminthiases (Beck et al., 2000;Brooker and Michael, 2000; Bavia et al., 2001; Brooker, 2002;Guimarães et al., 2006, 2008; Raso et al., 2006; Carvalho et al., 2010).Due to the lack of reliable information about sewage and watersupply sources across Brazil (i.e. each state has its own sewageand water company), these factors were not considered in theanalysis.

Our maps indicate areas with sparse or no information ondisease transmission. In fact, non-endemic areas such as Acre, Ama-zonas, Roraima, Amapa and Tocantins are subjected to compulsorynotification of schistosomiasis cases to the ‘Information System forNotifiable Diseases’ (SINAN) and are not enrolled within the NCP.As can be seen in Fig. 2A, the estimated prevalence of S. mansoniwas below 5% in the Amazon region. Since we do not haveS. mansoni prevalence data for this part of Brazil, the prediction hasbeen driven by the high vegetation index, which has been shown

as an important environmental covariate governing the distribu-tion of schistosomiasis (Brooker and Michael, 2000; Bavia et al.,2001; Brooker, 2002; Guimarães et al., 2006, 2008; Carvalho et al.,2010). Our model indicates climatic suitability for the parasite in

R.G.C. Scholte et al. / Acta Tropica 132 (2014) 57–63 61

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Fig. 2. Estimates of the spatial distribution of Schistosoma mansoni infec

he Amazon. The remoteness of this area might contribute to thender-reporting to the SINAN.

The highest prevalence of S. mansoni was found in the Northnd Northeast regions, probably explained by suitable areas forntermediate host snail proliferation. The lowest prevalence rates

ere predicted in Center-West, South and part of the Southeastegions (except Minas Gerais state). The later are the most devel-ped areas in Brazil according to the HDI. It is important to notehat schistosomiasis usually shows a focal distribution (Lengelert al., 2002). Since the S. mansoni prevalence data analyzed herere highly aggregated, more detailed investigations are necessary toetermine small-scale within-municipality variation. The availableata are reported at municipality level, and hence, we are unableo accurately estimate small-scale heterogeneity.

Some important issues related to the nature and precision ofur model predictions need to be considered when interpretinghe results. First, the geographical information is available at the

unicipality although the surveys were performed at specific loca-ions (villages and towns) within the municipality. Second, theow spatial resolution of the S. mansoni prevalence data coulderturbate the relation between the disease and the predictors.ost municipalities with survey data were located in the north-

rn, northeastern and southeastern parts of Brazil (mainly Minaserais and Espírito Santo states). It is conceivable that the lack ofata over large areas in Brazil compromises the prediction accuracy

n these areas. These issues might have affected and masked the cor-elations of the prevalence data with explanatory variables. Third,e assumed stationarity of the spatial process. However, given the

arge size of Brazil and the fact that its geographical extent encom-asses a wide range of ecological zones, it is conceivable that thepatial process is non-stationary. It would therefore be interestingo construct separate models for specific ecological zones and theno assemble them into a single map. Unfortunately, the scarcityf data for certain ecozones precludes such an approach. Fourth,ith regard to the diagnosis of S. mansoni, the WHO-recommendedato-Katz technique was employed with duplicate Kato–Katz thickmears. It must be noted, however that the Kato–Katz technique

as a low sensitivity, particularly for light infection intensities (Enkt al., 2008; Utzinger et al., 2011). It follows that our predictiveisk maps likely underestimate the true infection risk. Anotherimitation of our study is the nature of the data. The NCP aims to

revalence across Brazil (A) and corresponding prediction error map (B).

screen the entire population rather than selecting a representa-tive sample. However, only few municipalities reach this objective.Statistical methods allow to infer on the population from a sample.Hence, it is not necessary to collect data from the whole popula-tion. Nonetheless, bias could be introduced in the analysis in casethe screened individuals are not representative of the overall pop-ulation.

Amaral et al. (2006) analyzed the impact of the national sch-istosomiasis control programme in Brazil since inception in themid-1970s until 2003. The current investigation is part of a largerproject with the overarching goal to assess the geographicaldistribution of selected neglected diseases, including schistoso-miasis. Only the most recent available data were considered (i.e.2005–2009), which allowed comparison among diseases studied.It was not our aim to analyse the temporal pattern of S. mansoniinfection risk. However, in a next step, it will be interesting to adda temporal component to deepen the understanding of the risk ofS. mansoni in Brazil—both in space and over time.

In order to further improve model accuracy for more preciseestimates and its application to identify priority areas for interven-tion on a large scale, we recommend that a national, geo-referencedprevalence survey, coupled with malacological data collection, beconducted in those municipalities where data are insufficient orcurrently lacking. The predictive risk map of the spatial distri-bution of schistosomiasis presented here identified areas wherecontrol interventions are needed. Hence, it provides an opportu-nity for more efficient control, and can guide the establishmentof innovative surveillance-response mechanisms (e.g. identifica-tion of transmission hot spots and public health responses readilyadapted to these settings), including environmental education,health awareness programmes, and perhaps targeted intermediatehost snail control.

Acknowledgements

ican Health Organization (PAHO). The authors would like to thankStephen K. Ault, Ruben S. Nicholls, of PAHO, Washington DC forexpertise and guidance during these studies (the work presenteddoes not necessarily reflect the position of PAHO).

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ppendix A.

.1. Bayesian geostatistical modelling

The S. mansoni data were derived from surveys carried out atarious locations. These are typical binomial data and modelledia logistic regression. Let Ni be the number of people tested atocation Si, = 1, . . ., n, Yi, be the number of those found positive and¯ i =

(X1

i, . . ., Xp

i

)Tbe the vector of p associated predictors observed

t location Si. We assume that Yi arises from a Binomial distribution,hat is Yi∼Bin (Ni, pi), where parameter Pi is the disease risk. Theelation between the S. mansoni prevalence and the covariates isodelled via the logistic regression log it (pi) = b0 +

∑pk=1bkXk

i,

here b = (b0, b1, . . . bp)T is the vector of regression coefficients.S. mansoni data have a spatial structure because individuals in

lose proximity are exposed to common risk factors. Hence, it ismportant to take into account the spatial dependence. At each loca-ion, a new parameter �i called random effect was introduced to

odel the unexplained spatial correlation. The terms �i are allowedo vary continuously through space and are assumed to derive from

stationary Gaussian process with mean 0, variance �2 and corre-ation function dij, �, where dij is the Euclidean distance betweenocations Si and Sj. An exponential correlation function is assumed,hat is corr

(dij.�

)= exp

(−� × dij

). The parameter �2, called also

he partial sill, represents the spatial variation and it arises due topatial heterogeneity in predictors of S. mansoni transmission notncluded as covariates in the model. The decay parameter � controlshe rate at which the correlation approaches the minimum withncreasing the distance between locations. For the correlation func-ion chosen, the minimum distance for which spatial correlationetween locations is below 5% is 3/� (range).

These types of hierarchical models are usually fitted within aayesian framework that allows flexible modelling and inferencend avoids the computational problems encountered by likelihood-ased fittings. The trade-off for the flexibility of a fully Bayesianpproach is the complexity of the model fit. This step is carriedut via the implementation of MCMC methods. To complete thepecification of the Bayesian hierarchical model, prior distributionseed to be assigned to the model parameters b, �2 and �. Further,ayesian inference is based on the posterior distribution that ishe conditional distribution over parameters given observed data.on-informative Normal prior distributions were specified for the

ntercept and the regression coefficients, p(bk) = N(0, 100), k = 1,.., p. The spatial correlation parameters �2 and � were assignedn inverse gamma and a gamma prior distribution, respectively,(

�2)

= IG (a1, b1) and p (�) = G (a2, b2). The values of the param-ters a1, b1, a2 and b2 were chosen such that the mean of theorresponding distribution is 1 and the variance is 100.

.2. Geostatistical model for very large data

Estimation of the location-specific random effects and of thepatial parameters requires repeated inversions of the covarianceatrix

∑at each iteration during the fitting and prediction pro-

ess. Due to the large number of locations in our dataset (n = 1004),atrix inversion is computationally intensive and even infeasible.

o overcome the computational burden, the spatial process waspproximated by a subset of locations (knots)

{si∗, i = 1, . . ., m

}

m � n) with latent observations ϕ∗ = (ϕ∗1, ..., ϕ∗

m)T . ϕ* is consid-red to arise from the same spatial process ϕ* and thus ϕ* ∼ MVN(0,*), where ˙* is the m × m covariance matrix of the sub-process.

he latent observations of the original process can be approximatedy the “predictions” of the sub-process via the conditional meanT˙*−1ϕ*, where Q = Cov(ϕ*, ϕ) is an m × n matrix of the covari-nce functions between the m knots and the observed n locations

pica 132 (2014) 57–63

(Seeger, 2003; Banerjee et al., 2008). The dimension of the matrixto be inverted is reduced to the knots sample size m × m, thereforethe computational speed is significantly increased. We have usedthe balanced sampling method (Deville and Tillé, 2004) to selecta sample of knots which preserved the characteristics (e.g. covari-ates) of the population. This method has been proved to be efficientand computationally inexpensive for very large data (Chammartinet al., 2013). The authors showed that using the variance of theoutcome as the inclusion probability, a minimum sample of 100data points is enough to correctly estimate the model parameters.For the current analysis a sample of 150 knots was chosen. We run200,000 iterations with a burn-in of 10,000 iterations and assessedthe convergence by examining the ergodic averages of selectedparameters. The analysis was implemented in FORTRAN 95 (Com-paq Visual FORTRAN Professional 6.6.0) with codes written by theauthors using standard numerical libraries (NAG, The NumericalAlgorithm Group Ltd.).

A.3. Prediction model (Bayesian kriging)

Bayesian kriging (Diggle et al., 1998) was used to predict theS. mansoni risk at locations where disease data were not available.This approach treats the disease risk at a non-sampled location asrandom and calculates its predictive posterior distribution, whichprovides not only a single estimate, but a whole range of likelyvalues together with their probabilities to be the true values at aspecific location. This makes it possible to estimate the predictionerror, a substantial advantage over the classical kriging methods.

A.4. Model validation

To validate the geostatistical models, the disease dataset wassplit in two, a training set containing 85% of the data and a test-ing set comprising the remaining 15% of the data points. Model fitwas carried out on the training set using Bayesian kriging. Bayesiancredible intervals of the posterior predictive distribution at the testlocations with probability coverage equal to 95% were calculatedand the percentages of test locations with observed disease risk orrate falling in these intervals were computed (Gosoniu et al., 2006).

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