Modeling Schistosoma japonicum Infection under Pure Specification Bias: Impact of Environmental Drivers of Infection

Abstract

Keywords: schistosomiasis; pure specification bias; uncertainty; Bayesian statistics; convolution model

Full text

International Journal of
Environmental Research
and Public Health
Article
Modeling Schistosoma japonicum Infection under
Pure Specification Bias: Impact of Environmental
Drivers of Infection
Andrea L. Araujo Navas 1, *, Frank Osei 1, Lydia R. Leonardo 2, Ricardo J. Soares Magalhães 3,4
and Alfred Stein 1
1Faculty of Geo-information Science and Earth Observation (ITC), University of Twente, PO Box 217,
7500 AE Enschede, The Netherlands; f.b.osei@utwente.nl (F.O.); a.stein@utwente.nl (A.S.)
2
Institute of Biology, College of Science, University of the Philippines Diliman, UP Diliman 1101 Quezon City,
Philippines; lrleonardo@up.edu.ph
3UQ Spatial Epidemiology Laboratory, School of Veterinary Science, The University of Queensland,
Gatton 4343 QLD, Australia; r.magalhaes@uq.edu.au
4Child Health and Environment Program, Child Health Research Centre, The University of Queensland,
South Brisbane 4101 QLD, Australia
*Correspondence: a.l.araujonavas@utwente.nl; Tel.: +31-534-893-599
Received: 14 November 2018; Accepted: 3 January 2019; Published: 9 January 2019


Abstract:
Uncertainties in spatial modeling studies of schistosomiasis (SCH) are relevant for the
reliable identification of at-risk populations. Ecological fallacy occurs when ecological or group-level
analyses, such as spatial aggregations at a specific administrative level, are carried out for an
individual-level inference. This could lead to the unreliable identification of at-risk populations, and
consequently to fallacies in the drugs’ allocation strategies and their cost-effectiveness. A specific
form of ecological fallacy is pure specification bias. The present research aims to quantify its effect on
the parameter estimates of various environmental covariates used as drivers for SCH infection. This
is done by (i) using a spatial convolution model that removes pure specification bias, (ii) estimating
group and individual-level covariate regression parameters, and (iii) quantifying the difference
between the parameter estimates and the predicted disease outcomes from the convolution and
ecological models. We modeled the prevalence of Schistosoma japonicum using group-level health
outcome data, and city-level environmental data as a proxy for individual-level exposure. We
included environmental data such as water and vegetation indexes, distance to water bodies, day
and night land surface temperature, and elevation. We estimated and compared the convolution
and ecological model parameter estimates using Bayesian statistics. Covariate parameter estimates
from the convolution and ecological models differed between 0.03 for the nearest distance to water
bodies (NDWB), and 0.28 for the normalized difference water index (NDWI). The convolution model
presented lower uncertainties in most of the parameter estimates, except for NDWB. High differences
in uncertainty were found in night land surface temperature (0.23) and elevation (0.13). No significant
differences were found between the predicted values and their uncertainties from both models. The
proposed convolution model is able to correct for a pure specification bias by presenting less uncertain
parameter estimates. It shows a good predictive performance for the mean prevalence values and
for a positive number of infected people. Further research is needed to better understand the spatial
extent and support of analysis to reliably explore the role of environmental variables.
Keywords:
schistosomiasis; pure specification bias; uncertainty; Bayesian statistics;
convolution model
Int. J. Environ. Res. Public Health 2019,16, 176; doi:10.3390/ijerph16020176 www.mdpi.com/journal/ijerph

Int. J. Environ. Res. Public Health 2019,16, 176 2 of 17
1. Introduction
Schistosomiasis (SCH) is a water-borne infection caused by parasitic worms known as
schistosomes. People get infected by skin penetration of the infective stage of the parasite. Three
schistosomes species cause the infection: Schistosoma mansoni,Schistosoma japonicum, and Schistosoma
haematobium. Among these, S. japonicum is the hardest one to control due to its zoonotic life cycle [
1
],
which includes the infection of an amphibious snail from the species Oncomelania hupensis quadrasi as
the intermediate host, and humans and other mammals as definitive hosts [
2
,
3
]. Schistosomiasis is a
disease of public health significance [
4
,
5
] since it affects more than 252 million people worldwide [
6
].
This especially concerns communities in tropical and subtropical areas, where access to clean water
and sanitation is limited. Schistosomiasis leads to malnutrition, which causes anemia and stunted
growth in school-aged children [7,8].
Schistosomiasis risk mapping has enabled the identification of at-risk populations to target mass
drug administration campaigns for disease control [
9
]. Mapping SCH involves the use of geographic
information systems, remote sensing, and global positioning systems (GPS). These help to allocate
data about infection and the physical and biological environmental variables in space. Environmental
variables together with various statistical methods have been combined to model the distribution of
the disease [10–13] and to quantify the role of the environmental exposure factors on SCH risk [14].
Spatial epidemiological studies are susceptible to uncertainties, which are inherent in spatial
information [
14
–
16
]. Most of these uncertainties are caused by positional measurement errors
due to GPS inaccuracies, multiple addresses, geocoding errors, misalignments between covariates
and disease outcomes, and disease outcome or covariate aggregations [
14
]. Particularly, disease
outcome and covariate aggregations at a specific administrative level could be incorrectly obtained
for individual-level inference [
17
]. Health data are often available at a specific administrative level
(i.e., group-level) while environmental data consists of a set of recorded values aggregated at monitor
sites or gridded data derived from remote sensing images [
18
]. Spatial aggregation occurs due to the
lack of geolocated information at the individual level, caused by the scarcity of sampling resources,
availability of associated data or the need to protect confidentiality [14].
Disease outcome and covariate aggregations cause an ecological bias or ecological fallacy. This
represents an important source of uncertainty [
14
,
15
,
17
–
19
] because any direct link between exposure
and health outcomes is imperfectly measured [
17
]. For instance, Wakefield and Lyons [
20
] mention
that the fundamental problem of this kind of spatial aggregations is the loss of information. Thus,
the function used in the regression modeling does not represent the real relationship between the
affected population and their exposure. This type of ecological fallacy is also called pure specification
bias and arises due to the loss of information when a non-linear model changes its form under
aggregation [20,21]. It is called ‘pure’ because it specifically addresses a model specification bias [21].
Several efforts have been made to address pure specification bias resulting in disaggregation
methods. For instance, Prentice and Sheppard [
22
] suggest an ‘aggregated data’ method to create
models based on exposure information available for a subset of individuals. Richardson et al. [
23
]
assume parametric distributions for within-area exposures to derive accurate risk functions. Wakefield
and Shaddick [
18
] propose a convolution model and derive an appropriate likelihood function for a
scenario where health outcome data are aggregated at the district level, and exposure information is
known at monitoring sites. Wang et al. [
24
] address pure specification bias in the least informative data
scenario for aggregated disease counts with associated counts of the population at-risk, and a separate
set of point level exposures from monitoring stations. They propose a conceptual probability of the
incidence surface over the entire study region as a function of an exposure surface. This probability
surface was then used to simulate individual disease outcomes and to obtain individual-level
parameter estimates.
For a tropical disease such as SCH, the availability of individual-level infection data obtained from
schools or health care centers is common [
25
–
29
]. Nevertheless, there are several SCH epidemiological
studies [
9
,
30
–
33
] that limit their modeling to the outcome and covariate data aggregated at a specific

Int. J. Environ. Res. Public Health 2019,16, 176 3 of 17
administrative level (i.e., ward, municipal, province, county, district, barangays, among others) without
taking pure specification bias into consideration. Moreover, there are no up-to-date studies that have
quantified the effect of the covariate information on the parameter estimates when accounting for pure
specification bias in SCH modeling.
The objective of this study is to quantify the effect of pure specification bias on the parameter
estimates of various environmental covariates used as drivers for SCH infection. To achieve this
objective we aim to: (i) use a spatial convolution model that removes pure specification bias by using
group-level health outcome data and individual-level environmental covariate data, (ii) estimate group
and individual-level covariate regression parameters, and (iii) quantify the difference between the
parameter estimates and predicted disease outcomes from the convolution and ecological models.
2. Materials and Methods
2.1. Data on Human Schistosoma japonicum Infection, Study Area, and Sampling Design
We use S. japonicum infection data collected as part of the 2008 Nationwide Schistosomiasis
Survey in The Philippines [
34
]. In this case, S. japonicum is endemic in 28 of its 81 provinces [
35
], with
approximately 1.8 million estimated infected people [
36
]. The disease affects children, adolescents,
and individuals with high-risk occupations, such as farmers and fishermen [36,37].
A two-stage systematic cluster sampling was used in the sampling design. Stratification was done
by a prevalence level (high, medium, and low), obtained from the 1994 World Bank-assisted Philippine
Health Development Program. Provinces and barangays were the primary and secondary sampling
units respectively. A barangay is the smallest administrative division in the Philippines, numbering
about 22–50 in a single municipality. Provinces with high and moderate prevalence rates were included,
while the random selection was done among the low-prevalence provinces and non-endemic provinces.
Within the selected provinces, high prevalence barangays were also selected. We decided to work in
the Mindanao region due to the good spatial coverage of the sampling over the whole region (Figure 1),
and the high response rate of 70 percent [
9
,
34
,
38
]. In total, 22 provinces were surveyed, and between 2
and 10 barangays were surveyed per province. In total, 108 out of 10,021 barangays were surveyed
in Mindanao.
Data from 19,763 individuals were recorded in the survey but not georeferenced. Information
regarding the corresponding barangay and province were recorded for each individual. For this reason,
individual-level survey data were aggregated and geo-located to the centroids of 108 barangays in
Mindanao. We used a probability of infection pin barangay kas our disease outcome variable.
Kato-Katz thick smear examination [
39
] was used to diagnose S. japonicum infection based on
two-sample stool collection. Each sample was read using a microscope and the presence of S. japonicum
eggs indicated active infection. Due to inconsistencies in the submission of the second stool sample,
however, only the results of the first stool sample were available [
9
] from people aged two years and
above. Information such as gender and age were recorded for each individual. More details about the
sampling design can be found in Leonardo et al. [34,38].

Int. J. Environ. Res. Public Health 2019,16, 176 4 of 17
Int. J. Environ. Res. Public Health 2019, 16, x FOR PEER REVIEW 4 of 17
Figure 1. Study area.
2.2. Environmental and Geographical Data
Six environmental variables were included in the analysis: the nearest distance to water bodies
(NDWB), normalized difference vegetation index (NDVI), normalized difference water index
(NDWI), day (LSTD) and night (LSTN) land surface temperature, and elevation (E). The nearest
distance to water bodies was calculated using the closest facility network analysis tool in ArcGIS
version 10 [40]. We used rivers and lakes as water bodies. As input for the network, we used the river
and road networks, and the location of cities and hamlets. We first calculated the NDWB for each city
point and then interpolated the distance values for all the surveyed barangays. Interpolation was
performed using Ordinary Kriging. The nearest distance to water bodies shows the accessibility of
people to water bodies since they represent the main infection foci. We used NDVI obtained from the
Modis MOD13Q1 product. The normalized difference vegetation index served as an indicator of
vegetation presence and greenness, particularly the presence of flooded agricultural land such as
paddy fields, which is an important factor for Asian schistosomiasis [41]. We included NDWI from
the Google Earth Engine as an annual Landsat 7 composite for the year 2008. The normalized
difference water index was used as a proxy indicator of flooding [42‐43]. The day land surface
temperature was also included and obtained from the Modis MOD11A2_LST product. The day land
surface temperature is determinant for the survival of larval stages of snails [44‐46] and is used as a
proxy for water temperature given that the thermal condition of shallow waters usually reflects the
ambient temperature of the air [9]. Elevation was also included and obtained from ASTER GDEM
version 2 from United States Geological Survey (USGS) [47]. In the Philippines, the presence of snails
is also driven by the local topography [48‐50]. At lower altitudes, the risk of finding snails increases.
Table 1 summarizes the information about environmental information and their sources.
Figure 1. Study area.
2.2. Environmental and Geographical Data
Six environmental variables were included in the analysis: the nearest distance to water bodies
(NDWB), normalized difference vegetation index (NDVI), normalized difference water index (NDWI),
day (LSTD) and night (LSTN) land surface temperature, and elevation (E). The nearest distance to
water bodies was calculated using the closest facility network analysis tool in ArcGIS version 10 [
40
].
We used rivers and lakes as water bodies. As input for the network, we used the river and road
networks, and the location of cities and hamlets. We first calculated the NDWB for each city point and
then interpolated the distance values for all the surveyed barangays. Interpolation was performed
using Ordinary Kriging. The nearest distance to water bodies shows the accessibility of people to water
bodies since they represent the main infection foci. We used NDVI obtained from the Modis MOD13Q1
product. The normalized difference vegetation index served as an indicator of vegetation presence
and greenness, particularly the presence of flooded agricultural land such as paddy fields, which is an
important factor for Asian schistosomiasis [
41
]. We included NDWI from the Google Earth Engine as
an annual Landsat 7 composite for the year 2008. The normalized difference water index was used as a
proxy indicator of flooding [
42
,
43
]. The day land surface temperature was also included and obtained
from the Modis MOD11A2_LST product. The day land surface temperature is determinant for the
survival of larval stages of snails [
44
–
46
] and is used as a proxy for water temperature given that the
thermal condition of shallow waters usually reflects the ambient temperature of the air [
9
]. Elevation
was also included and obtained from ASTER GDEM version 2 from United States Geological Survey
(USGS) [
47
]. In the Philippines, the presence of snails is also driven by the local topography [
48
–
50
].
At lower altitudes, the risk of finding snails increases. Table 1summarizes the information about
environmental information and their sources.

Int. J. Environ. Res. Public Health 2019,16, 176 5 of 17
Table 1. Environmental variables description.
Environmental
Variable
Spatial
Resolution
Temporal
Resolution
Data
Type
Original
Coordinate
System
Data Source
Elevation 30 m NA Raster EPSG:4326 Aster GDEM V2 from USGS
NDVI 250 m 2008 Raster EPSG:4326 MOD13Q1
NDWI 500 m 2008 Raster EPSG:32651 Landsat 7, one-year composite
LST 1 km 2008 Raster EPSG:4326 MOD11A2
NDWB 250 m 2010 Raster EPSG:32651
Derived from closest facility
network using roads, urban areas,
river network, and water bodies
NDVI: Normalized difference vegetation index; NDWI: normalized difference water index; LST: day land surface
temperature; NDWB: nearest distance to water bodies; USGS: United States Geological Survey.
2.3. Convolution Model (Individual-Level Model)
An individual is considered infected if at least one parasite egg is found. S. japonicum infection
data
y
are available at individual-level
i
recorded within a barangay
k
. Various
n
environmental
variables
x
are available for each image pixel. Because the exact response locations of the
yik
are
unknown, individual-level data are aggregated to their corresponding barangay centroid and are, thus,
denoted by yk. A naive group-level model is given by Equation (1).
yk|xk,γ∼Binomial(Nk,ˆ
pk)(1)
where
Nk
and
pk
are the number of sampled individuals and the probability of infection in barangay
k
,
respectively, and
xk
is the observed mean exposure within barangay
k
. The probability
ˆ
pk
is modelled
based on Equation (2) using environmental variables as predictors, where
γ
are the group-level
covariate coefficients.
logit(ˆ
pk) = γ0+γ1·x1k+γ2·x2k+. . . +γn·xnk(2)
We suppose that, for an individual
i
in area
k
,
yik
follows a Bernoulli distribution (Equation (3)).
Then an individual level model is presented in Equation (4), where the parameters
β
are the
individual-level coefficients. However, this model assumes that we know the individual level locations.
yik |xik,β∼Bernoulli(pik)(3)
logit(pik ) = β0+β1·x1ik +β2·x2ik +. . . +βn·xnik (4)
Pure specification bias will result in
γ6=β
, where the relationship between aggregated disease
risk and exposure on areal units differs from the relationship between the individual disease risk and
the associated exposure. In a non-linear model, as in our case, this difference is produced by a loss of
information due to aggregation known as pure specification bias. Pure specification bias is reduced in
size since the ‘within area’ exposure is more homogenous [
20
]. This could be obtained by having a
finer partition of space in which exposure measurements are available [18,20].
As we know the individual-level responses
yik
but not their locations, we minimized the pure
specification bias by extracting covariate information from cities within the barangays. We selected
cities since they were the finest units we found available by taking them as a proxy for exposure
locations at an individual level. Cities were extracted from the 2010 build-up data base from the
National Mapping and Resource Information Authority from The Philippines [
51
]. Cities were not
available for all the surveyed barangays. Therefore, we digitalized them using Google Earth images.
We used the aggregate data method proposed by Prentice and Sheppard, 2001 [
22
]. Let exposure
or covariate data
xjk
be measured at locations
sjk j=
1,
. . .
,
mk≤Nk
, for a subset of individuals. Then,
we estimated the average risk of the individuals in area
k
, and the individual level coefficients
β
. This

Int. J. Environ. Res. Public Health 2019,16, 176 6 of 17
was done by calculating the mean of the risk function (Equation (5)) instead of evaluating the risk
function at the mean exposure (Equation (2)). In this way, the average
ˆ
ˆ
pk
of the function over the
exposures corrects for the pure specification bias and differs from the function evaluated at the average
exposure (ˆ
pk). Thus, ˆ
ˆ
pkis the estimated average probability of infection of the individuals in area k.
ˆ
ˆ
pk=1
mk
·
mk
∑
j=1
1
1+exp−β0+β1·x1jk +β2·x2jk +. . . +βn·xnjk (5)
In our study, covariate data were obtained at a finer level of analysis than the barangay. Therefore,
we assumed that averaged covariate values at city level
j
represent individual covariate values (i.e.,
xjk =xik
). We then know
xjk
but not the geographical linkage with individuals. One way to account
for this is to allocate
Njk
individuals to measurement
xjk
by equally dividing the population. Therefore,
Njk =Nk/mk, is a simple version of the convolution model.
The spatial convolution model is represented in Equation (6), where the risk function also accounts
for the spatial variability by including spatial (sk) structured random effects.
ˆ
ˆ
pk=1
mk
·
mk
∑
j=1
1
1+exp−β0+β1·x1jk +β2·x2jk +. . . +βn·xnjk +sk (6)
The implemented convolution model that corrects for the ecological fallacy is of the form.
yk|xjk,β∼BinomialNk,ˆ
ˆ
pk(7)
The model includes an intercept (
β0
), averaged city-level environmental variables (
xjk =
NDV I
,
NDW I
,
LST D
,
LST N
,
E
,
NDWB
), and their corresponding individual-level coefficients
β
, and
a spatial random effect (
sk
) as described in Equation (6). All covariates were standardized to have
mean = 0 and standard deviation = 1. Collinearity between covariates was assessed with the Pearson
correlation coefficient.
Prior information for the intercept
β0
was given as a proper uniform distribution with wide
bounds (
−
100, 100). The other
β
parameters were given non-informative normal distributions with
mean = 0 and precision 1/
σ2
, with
σ
uniformly distributed on a wide range (0, 100). These distributions
are recommended in order to avoid overestimations on the parameters [
52
]. These parametrizations
allow a good mixing of the sequences used for Marcov Chain Monte Carlo simulations and contribute
to their faster convergence [53].
Spatial dependence was modelled using a spatially structured random effects distribution based
upon a geo-statistical model. This model can be used as a sampling distribution for continuous spatial
data [
54
]. The vector of random variables
s
associated with point locations (
xk
,
yk
),
k=
1,
. . .
,
K
,
was modelled with a multivariate normal distribution
s∼MVNK(µ,Σab )
with mean
µ
= 0 and a
covariance matrix
Σab
defined by a powered exponential spatial correlation function from Equation (8).
Σab =σ2·exp−(φ·dab )κ(8)
The covariance matrix is specified as a function of the distances
dab
between barangay centroids
a
and
b
, the rate of decline of spatial correlation per unit of distance
φ
, the scalar parameter representing
the overall variance
σ2
, and the scalar parameter
κ
controlling the amount of spatial smoothing. Since
it is often difficult to learn much about the
κ
parameter, and large values of
κ
could lead to smoothing,
we used
κ=
1. The prior distribution for
φ
was set uniform with lower and upper bounds at 2
×
10
−7
and 3
×
10
−3
, respectively. These values give a diffuse but plausible prior range of correlations between
0.1 and 0.99 at the minimum distance between points (575 m) and between 0 and 0.3 at the maximum
distance between points (<552 km), which assists identification [
55
]. The variance parameter was

Int. J. Environ. Res. Public Health 2019,16, 176 7 of 17
given a half-normal distribution with mean = 0 and variance = 1. Half-normal was selected in order to
restrict our prior to positive values and avoid problems with convergence [52,56].
The model was run using three sequences or chains with 50,000 iterations that ensured simulations
representative of target distributions [
53
] and a good stability for convergence [
53
]. A burn-in of 25,000
iterations was used, discarding the first half of each sequence that is used to diminish the influence
of starting values [
53
]. We monitored convergence visually and statistically, first by inspecting at the
trace plots and then by checking the
ˆ
R
statistic [
57
,
58
], which are also called a potential scale reduction
factor. This assesses sequences mixing by comparing the between and within variation.
ˆ
R
values < 1.1
indicate evidence that sequences had converged [
57
], while high values suggest that an increase in
the number of simulations may improve our inferences [
53
]. Data were structured in a rectangular
format, where the columns are headed by the array name. The survey data and the codes in bugs for
the convolution and ecological models are provided in the supplementary files 1 and 2, respectively.
2.4. Ecological Model (Group-Level Model)
As a comparison, we estimated the group-level covariate regression parameters
γ
by using
Equations (1) and (2). We used
ˆ
pk
as a function of the same covariate information,
xk=
NDV I
,
NDW I
,
LST D
,
LST N
,
E
,
NDWB
, but averaged for each surveyed barangay, and added the
spatial random effects term
sk
(Equation (9)). Prior distributions for
γ
and
sk
were the same as the ones
given for the βparameters and the geo-statistical spatial term.
ˆ
pk=
K
∑
k=1
1
1+exp(−(γ0+γ1·x1k+γ2·x2k+. . . +γn·xnk+sk))(9)
We compared estimated covariate regression coefficients and their credible intervals from both
models, and also the data generated from the posterior predictive distribution to the observed data.
Posterior predictive distributions were generated using simulations. Residuals were calculated by
subtracting the simulated values from the observed values. We created correlation and residual plots for
convolution and ecological models for three different simulations. Lastly, we compared the predicted
prevalence values for both models and their corresponding credible intervals for each barangay.
2.5. Model Validation
In order to assess the model fit, we compared the deviance information criterion (DIC) values
between simple and spatial models from the convolution and ecological models. Convolution
and ecological models were validated using two methods. First, we used the posterior predictive
distribution to check our model assumptions by comparing the data generated from the simulations
of the predictive distribution to the observed data using a test statistic. The test statistic generates a
posterior predictive p-value (ppp-value) by calculating the proportion of the predicted values that are
more extreme for the test statistic than the observed value for that statistic. If the data violated our
model assumptions, the observed test statistic should differ from most of the replicated test statistics
from our model (i.e., ppp-value close to 0 or 1). If the model fits the data, a ppp-value around 0.5 is
expected. Test statistics and ppp-values were created for maximum, minimum, and mean values for
both, convolution, and ecological models.
Second, we used the area under the curve (AUC) of the receiving operating characteristics (ROC)
for applying a threshold of 0.5%, which is the prevalence mean in the Mindanao region. Thus, we
would like to know the ability of the model to discriminate the mean prevalence level in the study
area. We also investigated the ability of the models to discriminate the number of positive cases. Thus,
a threshold of 1 was used, which indicates the presence of at least one positive case. An AUC value of
70% was taken to indicate acceptable predictive performance [9,59].

Int. J. Environ. Res. Public Health 2019,16, 176 8 of 17
2.6. Software and Data Sources
Barangay centroids were obtained from an up-to-date barangay shape file from a DIVA geographic
information system [
60
]. River and road networks were obtained from the Open Street Map Project in
the Philippines [
61
]. Locations of cities and hamlets were extracted from the National Mapping and
Resource Information Authority from The Philippines [62] from 2010.
The model was implemented in the software OpenBUGS 3.2.3 [
63
,
64
] (Medical Research Council,
Cambridge, UK and Imperial College London, UK). The software is available for free at [
65
]. We
used the package R2OpenBUGS [
66
] to call OpenBUGS from R. The spatial models were coded using
functions from GeoBUGS [
55
], which is an add-on module to OpenBUGS that provides an interface to
work with conditional autoregressive and geo-statistical models. Data pre-processing and Ordinary
Kriging was performed in R [67].
2.7. Ethics Approval
The data used in this study was collected in 2005 when there was no requirement for ethical
review and clearance. This study used aggregated (barangay-level) survey data, which enabled full
de-identification of individuals involved in the survey.
3. Results
3.1. Convolution Model
Posterior means and credible intervals resulting from the simple version of the convolution model
(Equation (5)) are given in Table 2. The credible intervals did not include zero values, which shows that
all covariates have a strong effect in the observed outcomes except NDVI. We decided to discard NDVI
from the spatial convolution and ecological model (Equation (6)). Deviance information criterion
values for the simple and spatial models were 419.8 and 64.13, respectively. This shows that the spatial
model performs better than the simple model. This is also supported by the residual spatial variation
of the survey data presented in Mindanao [
9
]. Table 2shows the resulting parameter estimates and
credible intervals for the spatial convolution model.
Table 2. Estimated regression coefficients (mean and 95% credible intervals).
Estimated
Parameters
Posterior Mean (95% Crl) Standard Deviation Credible Intervals Width
(Uncertainty)
Convolution Model Ecological Model Convolution
Model
Ecological
Model
Convolution
Model
Ecological
Model
Intercept −5.79 (−6.11,−5.5) −5.67 (−5.93,−5.41) 0.16 0.13 0.62 0.53
NDWI −0.74 (−0.96,−0.55) −1.02 (−1.24,−0.80) 0.11 0.11 0.44 0.44
LSTD −0.63 (−0.92,−0.38) −0.79 (−1.08,−0.49) 0.14 0.15 0.56 0.59
LSTN −0.84 (−1.13,−0.55) −0.65 (−1.05,−0.24) 0.15 0.21 0.59 0.82
Elevation −1.05 (−1.4,−0.71) −1.13 (−1.53,−0.70) 0.18 0.22 0.71 0.84
NDWB −0.28 (−0.51,−0.05) −0.24 (−0.43,−0.05) 0.13 0.09 0.48 0.38
φ4×10−5(−0.004,0.004)
2
×
10
−5
(
−
0.0004,0.0004)
2.00 ×10−41.00 ×10−56.80 ×10−53.50 ×10−5
Variance of
spatial
random effect
2.58 (1.7,3.6) 2.6 (1.8,3.61) 0.48 0.47 1.9 1.82
Crl: Credible interval.
3.2. Ecological Model
As in the convolution model, credible intervals resulting from the simple version of the ecological
model (Equation (2)) showed that all covariates have a strong effect in the observed outcomes except
NDVI. The normalized difference vegetation index was also discarded from the spatial ecological
model (Equation (9)). Deviance information criterion values for the simple and spatial models were
388.1 and 126.4, respectively. This shows that the spatial model is more adequate. Table 2shows the
resulting parameter estimates and credible intervals for the spatial ecological model.

Int. J. Environ. Res. Public Health 2019,16, 176 9 of 17
3.3. Convolution Versus Ecological Model
Figure 2shows the resulting density plots from the regression parameter estimates derived from
the ecological and convolution models. For the intercept parameter (Figure 2a), the convolution model
estimated a lower mean value (difference = 0.11) (Table 2) with a higher uncertainty, or credible interval
width, than the ecological model (Table 2). The regression parameter estimate for NDWI from the
convolution model shows a higher mean value than the one from the ecological model (Table 2and
Figure 2b). The difference between these estimates is around 0.28 with the same uncertainty for both
models (Table 2). In the case of LSTD (Figure 2c), the estimated mean values from the convolution
model are higher but with a slightly lower uncertainty than the ecological model. Difference between
estimates are around 0.16 (Table 2). For the LSTN parameter (Table 2) and Figure 2d, the convolution
model estimated a lower mean value with lower uncertainty than the ecological model (Table 2).
The difference between these estimates is approximately 0.2. In the case of the elevation parameter
(Figure 2e), estimated mean values from the convolution model are slightly higher than estimates from
the ecological model (difference = 0.08) (Table 2) and have lower uncertainty than the ecological model
estimates (Table 2). The estimated parameter value for NDWB (Figure 2f) is lower in the convolution
than in the ecological model (Table 2). The difference in this value is relatively small at around 0.03.
Nevertheless, uncertainty is higher in the convolution than in the ecological model (Table 2).
Int. J. Environ. Res. Public Health 2019, 16, x FOR PEER REVIEW 9 of 17
Figure 2. Covariate regression coefficients density plots for the convolution and ecological models.
(a) Intercept, (b) Normalized Difference Water Index, (c) Day Land Surface Temperature, (d) Night
Land Surface Temperature, (e) Elevation, and (f) Nearest Distance to Water Bodies.
Table 2. Estimated regression coefficients (mean and 95% credible intervals).
Estimated
Parameters
Posterior Mean (95% Crl) Standard Deviation Credible Intervals Width
(Uncertainty)
Convolution Model Ecological Model
Convolution
Model
Ecological
Model
Convolution
Model
Ecological
Model
Intercept
−5.79 (−6.11,−5.5)
−5.67 (−5.93,−5.41)
0.16
0.13
0.62
0.53
NDWI −0.74 (−0.96,−0.55) −1.02 (−1.24,−0.80) 0.11 0.11 0.44 0.44
LSTD
−0.63 (−0.92,−0.38)
−0.79 (−1.08,−0.49)
0.14
0.15
0.56
0.59
LSTN −0.84 (−1.13,−0.55) −0.65 (−1.05,−0.24) 0.15 0.21 0.59 0.82
Elevation −1.05 (−1.4,−0.71) −1.13 (−1.53,−0.70) 0.18 0.22 0.71 0.84
NDWB
−0.28 (−0.51,−0.05)
−0.24 (−0.43,−0.05)
0.13
0.09
0.48
0.38
ϕ 4 × 10−5 (−0.004,0.004)
2 × 10−5 (−0.0004,0.0004)
2.00 × 10−4 1.00 × 10−5 6.80 × 10−5 3.50 × 10−5
Variance of
spatial
random
effect
2.58 (1.7,3.6) 2.6 (1.8,3.61) 0.48 0.47 1.9 1.82
Crl: Credible interval.
Differences between observed and predicted prevalence values are similar for both models (
= 0.9). For the convolution and ecological model, the maximum difference between the predicted and
the observed prevalence values is around 1% (Figure 3a and Figure 3b). Figure 3a and Figure 3b show
that, for fitted prevalence values higher than 2%, both models underestimate the prevalence of
infection, while, for fitted prevalence values lower than 2%, both overestimation and underestimation
Figure 2.
Covariate regression coefficients density plots for the convolution and ecological models. (
a
)
Intercept, (b) Normalized Difference Water Index, (c) Day Land Surface Temperature, (d) Night Land
Surface Temperature, (e) Elevation, and (f) Nearest Distance to Water Bodies.
Differences between observed and predicted prevalence values are similar for both models
(
R2= 0.9
). For the convolution and ecological model, the maximum difference between the predicted
and the observed prevalence values is around 1% (Figure 3a,b). Figure 3a,b show that, for fitted

Int. J. Environ. Res. Public Health 2019,16, 176 10 of 17
prevalence values higher than 2%, both models underestimate the prevalence of infection, while, for
fitted prevalence values lower than 2%, both overestimation and underestimation occur. Both models
show similar predicted values with a maximum difference of 0.3%. The uncertainty in the predictions
from both models is the same in 88 barangays. The ecological model presents a higher uncertainty
than the convolution model in 9 barangays, while the convolution model shows higher uncertainty
than the ecological model in 11 barangays.
Int. J. Environ. Res. Public Health 2019, 16, x FOR PEER REVIEW 10 of 17
occur. Both models show similar predicted values with a maximum difference of 0.3%. The
uncertainty in the predictions from both models is the same in 88 barangays. The ecological model
presents a higher uncertainty than the convolution model in 9 barangays, while the convolution
model shows higher uncertainty than the ecological model in 11 barangays.
Figure 3. Residual plots for the (a) convolution and (b) ecological models.
3.4. Model Validation
The maximum and minimum observed prevalence values are 0.085 and 0, respectively. For the
convolution model, the ppp‐values for the maximum and minimum observed values are 0.65 and 1,
respectively. This shows that it is likely to see the maximum and minimum prevalence values from
the observed data in the predicted data. The highest ppp‐value of 1 assures that 100% of our predicted
data contain the minimum observed value. This could be due to an over fit to the data for small
prevalence values. For the ecological model, the maximum and minimum ppp‐values are 0.67 and 1,
respectively. Like the convolution model, it is likely to see the maximum and minimum observed
prevalence values in our predicted data and there might be an over fit to the data for small prevalence
values.
Results from the second validation method show the high ability of both models to predict
prevalence values with an AUC equal to 93% and 94% for the convolution and ecological models,
respectively. The AUC values with respect to predictive ability of the number of cases are 81% and
94% for the convolution and ecological models, respectively. Both models can discriminate the
Figure 3. Residual plots for the (a) convolution and (b) ecological models.
3.4. Model Validation
The maximum and minimum observed prevalence values are 0.085 and 0, respectively. For the
convolution model, the ppp-values for the maximum and minimum observed values are 0.65 and 1,
respectively. This shows that it is likely to see the maximum and minimum prevalence values from the
observed data in the predicted data. The highest ppp-value of 1 assures that 100% of our predicted data
contain the minimum observed value. This could be due to an over fit to the data for small prevalence
values. For the ecological model, the maximum and minimum ppp-values are 0.67 and 1, respectively.
Like the convolution model, it is likely to see the maximum and minimum observed prevalence values
in our predicted data and there might be an over fit to the data for small prevalence values.
Results from the second validation method show the high ability of both models to predict
prevalence values with an AUC equal to 93% and 94% for the convolution and ecological models,
respectively. The AUC values with respect to predictive ability of the number of cases are 81% and

Int. J. Environ. Res. Public Health 2019,16, 176 11 of 17
94% for the convolution and ecological models, respectively. Both models can discriminate the number
of positive cases of schistosomiasis and mean prevalence values. Nevertheless, as we can see, the
ecological model might over fit the data as compared to the convolution model with respect to the
number of positive cases.
4. Discussion
Several studies have modelled SCH disease risk using surveyed and environmental aggregated
information at an administrative-level [
9
,
30
–
33
]. These studies so far ignored the pure specification
bias caused by the use of ecological or group-level estimates as individual-level estimates. Only a few
studies [
18
,
24
] have quantified the influence of pure specification bias on the regression parameter
estimates and all studies on SCH ignored the influence of pure specification bias on disease predictions.
In our paper, we quantified the effect of pure specification bias on assessing the parameters for
environmental covariates that are used for the mapping of S. japonicum infection risk. Our contribution
is both methodological and practical.
Our starting point was that NDVI, NDWI, LSTD, LSTN, elevation, and NDWB are relevant for
SCH transmission [
68
–
70
]. For instance, NDVI is an indicator of flooded vegetation [
9
], specifically
rice paddy fields, and environmental moisture [
42
,
71
]. In both models, all variables have a strong
effect in the observed range of outcomes, except NDVI. An explanation could be the effect of spatial
support of this variable at 250 m. The International Rice Research Institute (IRRI) estimated an area
substantially smaller than 25 ha for rice paddy fields [
72
]. The area covered by an NDVI pixel equals
6.25 ha. This shows that a spatial support of 250 m is still too coarse to reliably represent paddy fields.
It could be relevant to use a higher spatial support to reliably assess the role of NDVI. For instance,
Walz et al. [
42
] have successfully delineated paddy fields by using NDVI from RapidEye imagery at a
higher spatial support of 5 m.
In the case of NDWI, the convolution model estimates a higher NDWI parameter value than the
ecological model, but closer to zero (Figure 2b). Hence, it may not have a strong effect on the observed
range of outcomes. The difference between convolution and ecological models when estimating the
NDWI parameter is high (0.28) as compared to the differences for other variables. This could be due to
(i) the decrease of the spatial extent of analysis from barangay to a city-level for covariate extraction,
and (ii) the coarse spatial support of the variable at 500 m. A correspondence between a decrease in
the extent of analysis and the within cities variability of NDWI values would change the average value
used for parameter estimation. This could yield the high differences in the estimates and, together with
the coarse support of the variable, could lead to a weaker effect of NDWI in SCH prevalence. Hence,
NDWI pixels of 0.25 km
2
are too coarse to reliably define flooded zones in city areas that range from
0.02 to 3 km
2
. The uncertainty in NDWI parameter estimate is similar for both models, as shown by
the credible interval with of 0.44 (Figure 2b and Table 2). A possible explanation is that NDWI values
are similar between and within cities, and between and within barangays. For instance, NDWI values
between cities and between barangays range from 0.095 to 0.51 and from 0.099–0.51, respectively. The
average NDWI value within a specific barangay is 0.3, while NDVI values range from 0.29–0.31 for the
cities it contains.
For LSTD, a higher estimated value in the convolution model was observed than in the ecological
model (Figure 2c). As for NDWI, this could be (i) due to the decrease in the within cities variability
corresponding to a decrease in spatial extent for covariate values extraction, and (ii) the coarse LSTD
spatial support of 1 km. The day land surface temperature, area pixels of 1 km
2
are too coarse to reliably
define low and high-temperature zones in city areas ranging from 0.02 to 3 km
2
. The uncertainty is
slightly lower in the convolution model than in the ecological model possibly due to the similarity
of the LSTD variability between and within cities and between and within barangays. For instance,
similar LSTD values ranging from 25 to 35.7
◦
C and from 21.7 to 36
◦
C were found for the convolution
and ecological models, respectively.

Int. J. Environ. Res. Public Health 2019,16, 176 12 of 17
A different pattern is observed for the estimate of the LSTN parameter. In contrast to LSTD, the
estimate and uncertainty from the convolution model are lower than for the ecological one (Figure 2d).
This could be explained by the difference between the LSTN variability within cities and within
barangays. For instance, we selected a barangay bigger in size than the cities it contains. We compared
LSTN values from the cities and from the barangay and found differences from 4 to 7
◦
C, although the
spatial support of LSTN is coarse at 1 km. These differences are small, but could be determinant for
the parasite presence, as the distribution of SCH is driven by water temperatures from 15 to 20
◦
C [
73
].
This means that we could find the parasite in the barangay with an average LSTN value of 20
◦
C, but
we could not find it in the cities inside the barangay, with LSTN values ranging from 22–24
◦
C. Thus,
there is a clear loss of information produced by a pure specification bias.
Elevation presents an estimate closer to zero in the convolution model as compared to the
ecological model (Figure 2e). This is possibly related to the decrease in the within cities elevation
variability as a result of the decrease in the spatial extent of covariate extraction, from barangays to
cities. Although its spatial support is relatively high, i.e., 30 m, within cities variability decreases
because the Mindanao region does not contain steep slopes or sharp changes in elevation. Changes in
elevation are gradual, which means that a city can share a single elevation value. The uncertainty in
the convolution model is lower than in the ecological model. The reason could be the large difference
in the between and within cities and barangays variability. For instance, elevation values between the
cities ranged from 0 to 0.9 km, while elevation values between barangays ranged from 0 to 1.3 km. We
also compared the elevation values averaged in a specific barangay and the range of values from the
cities within the barangay. The averaged barangay value was around 1.3 km, while the city values
within the barangay ranged from 0.87 to 0.89 km. These differences are high and give an idea of the
large amount of information that could be lost when estimating individual parameters at ecological
levels of analysis.
Lastly, for NDWB, the convolution model estimates a lower parameter value but with a higher
uncertainty (Figure 2f). This could be explained by the discrepancy between the within barangay and
city variability. For instance, for a specific barangay, the averaged NDWB value was approximately
3.75 km, while NDWB values for the cities within this barangay ranged from 0.4 to 6.4 km. In addition,
the NDWB values between the cities ranged from 0.17 to 26.2 km, while the NDWB values between
the barangays ranged from 0.26 to 15.5 km. The higher uncertainty in the convolution model could be
explained by the use of ordinary Kriging in the NDWB calculation. The use of interpolation increases
the variance in the estimates in a somewhat unrealistic way since it uses a constant mean [
54
] while, in
reality, the different cities and barangays have different means.
The present research shows that the ecological and convolution models present similar prediction
results. However, the proposed convolution model is preferred based on the lower uncertainties found
in most of its parameter estimates, which shows that it corrects for pure specification bias. Moreover,
according to our validation results, the convolution model has a high predictive ability to detect a
positive number of cases (81%) and mean prevalence values (93%). From a public health perspective,
the provision of regression coefficients that are less uncertain and better approach the individual-level
estimates is a step forward to the desired uncertainty analysis in a schistosomiasis-modelling
framework. This could be used as a decision support tool for helminth control programs. Moreover,
less uncertain models and maps would avoid erroneous conclusions and decisions about the spatial
distribution of schistosomiasis. Lastly, information on uncertainty regarding pure specification bias
could guide mass drug administration campaigns by enhancing the assessment of the infection risk
and understand potential impacts on human health [15,74].
Suggestions
Spatial extent and support of analysis are relevant drivers for the model parameter estimates and
their associated uncertainties. The choice of support may affect the pattern identified from the data
and the relationship between environmental variables and SCH prevalence [
75
,
76
]. We recommend

Int. J. Environ. Res. Public Health 2019,16, 176 13 of 17
bringing all covariates to a common spatial support prior to analysis. A suggestion would be to start
at e.g., 30 m and examine larger supports to more precisely quantify the role of an environmental
variable in the disease modelling process [13,77].
The trend in the residual plots from both models (Figure 3) points to a dependence between the
residuals and the fitted prevalence values. This dependence could be due to heteroscedasticity [
78
],
which means that similar interactions between the variables could lead to different prevalence values.
This does not represent a problem in the model parameter estimates but is an indicator that the model
can be improved [
79
,
80
]. Although our aim is not about model fit, we could possibly improve our
predictions by exploring other disease driven factors and include them in the model or explore the
model specification. Perhaps fitting a zero-inflated binomial (ZIB) model could help improve the
predictions given that our data show a high number of barangays with zero prevalence (~77%).
5. Conclusions
The present study proposes a convolution model that removes pure specification bias by using
ecological, group-level, health outcome data and city-level, individual-level, environmental data. For
most covariates, the uncertainties in the convolution model are lower than those in the ecological model.
The spatial extent of the covariates values and the spatial support or resolution of these covariates
are relevant for the parameter estimates and their uncertainties. The spatial extent and support also
influence the role of the covariates in SCH modelling. Why this happens should be further explored.
Additionally, between-covariate and within-covariate variability resulted in similar uncertainties
in both models. Conversely, differences in between and within covariate variability explain the
loss of information produced by a pure specification bias, which leads to lower uncertainties in the
convolution model.
Lastly, this study shows no significant differences in the predicted values from both models.
Predicted values from the convolution model are as uncertain as the predicted values from the
ecological model in the majority of surveyed barangays (81.5%). The convolution model, however,
shows a good predictive performance for the mean prevalence values and a positive number of
infected people.
Author Contributions:
Conceptualization, A.L.A.N., F.O., and R.J.S.M. Formal analysis, A.L.A.N. Investigation,
A.L.A.N. Methodology, A.L.A.N. and F.O. Resources, L.R.L. and R.J.S.M. Software, A.L.A.N. Supervision, F.O.,
R.J.S.M., and A.S. Validation, A.L.A.N. Visualization, A.L.A.N. Writing—original draft, A.L.A.N. Writing—review
& editing, A.L.A.N., F.O., L.R.L., R.J.S.M., and A.S.
Funding:
The research team acknowledges the World Health Organization funds provided to conduct the surveys.
This research received no external funding. ALAN’s doctoral research is funded by the University of Twente.
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of
the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Jia, T.W.; Zhou, X.N.; Wang, X.H.; Utzinger, J.; Steinmann, P.; Wu, X.H. Assessment of the age-specific
disability weight of chronic schistosomiasis japonica. Bull. World Health Organ.
2007
,85, 458–465. [CrossRef]
[PubMed]
2.
Tarafder, M.R.; Balolong, E.; Carabin, H.; Belisle, P.; Tallo, V.; Joseph, L.; Alday, P.; Gonzales, R.O.; Riley, S.;
Olveda, R.; et al. A cross-sectional study of the prevalence of intensity of infection with Schistosoma
japonicum in 50 irrigated and rain-fed villages in Samar Province, the Philippines. BMC Public Health
2006
,
6, 10. [CrossRef] [PubMed]
3. Yang, K.; Wang, X.H.; Yang, G.J.; Wu, X.H.; Qi, Y.L.; Li, H.J.; Zhou, X.N. An integrated approach to identify
distribution of Oncomelania hupensis, the intermediate host of Schistosoma japonicum, in a mountainous
region in China. Int. J. Parasitol. 2008,38, 1007–1016. [CrossRef] [PubMed]
4.
King, C.H.; Dickman, K.; Tisch, D.J. Reassessment of the cost of chronic helmintic infection: A meta-analysis
of disability-related outcomes in endemic schistosomiasis. Lancet 2005,365, 1561–1569. [CrossRef]

Int. J. Environ. Res. Public Health 2019,16, 176 14 of 17
5.
Walz, Y.; Wegmann, M.; Dech, S.; Vounatsou, P.; Poda, J.-N.; N’Goran, E.K.; Utzinger, J.; Raso, G. Modeling
and Validation of Environmental Suitability for Schistosomiasis Transmission Using Remote Sensing.
PLoS Negl. Trop. Dis. 2015,9, e0004217. [CrossRef] [PubMed]
6.
Hotez, P.J.; Alvarado, M.; Basanez, M.G.; Bolliger, I.; Bourne, R.; Boussinesq, M.; Brooker, S.J.; Brown, A.S.;
Buckle, G.; Budke, C.M.; et al. The Global Burden of Disease Study 2010: Interpretation and Implications for
the Neglected Tropical Diseases. PLoS Negl. Trop. Dis. 2014,8, e2865. [CrossRef] [PubMed]
7.
Leenstra, T.; Acosta, L.P.; Langdon, G.C.; Manalo, D.L.; Su, L.; Olveda, R.M.; McGarvey, S.T.; Kurtis, J.D.;
Friedman, J.F. Schistosomiasis japonica, anemia, and iron status in children, adolescents, and young adults
in Leyte, Philippines. Am. J. Clin. Nutr. 2006,83, 371–379. [CrossRef]
8.
Coutinho, H.M.; McGarvey, S.T.; Acosta, L.P.; Manalo, D.L.; Langdon, G.C.; Leenstra, T.; Kanzaria, H.K.;
Solomon, J.; Wu, H.W.; Olveda, R.M.; et al. Nutritional status and serum cytokine profiles in children,
adolescents, and young adults with Schistosoma japonicum-associated hepatic fibrosis, in Leyte, Philippines.
J. Infect. Dis. 2005,192, 528–536. [CrossRef]
9.
Soares Magalhães, R.J.; Salamat, M.S.; Leonardo, L.; Gray, D.J.; Carabin, H.; Halton, K.; McManus, D.P.;
Williams, G.M.; Rivera, P.; Saniel, O.; et al. Geographical distribution of human Schistosoma japonicum
infection in The Philippines: Tools to support disease control and further elimination. Int. J. Parasitol.
2014
,
44, 977–984. [CrossRef]
10.
Herbreteau, V.; Salem, G.; Souris, M.; Hugot, J.-P.; Gonzalez, J.-P. Thirty years of use and improvement of
remote sensing, applied to epidemiology: From early promises to lasting frustration. Health Place
2007
,13,
400–403. [CrossRef]
11.
Hay, S.I.; Packer, M.; Rogers, D. Review article The impact of remote sensing on the study and control of
invertebrate intermediate hosts and vectors for disease. Int. J. Remote Sens. 1997,18, 2899–2930. [CrossRef]
12.
Kalluri, S.; Gilruth, P.; Rogers, D.; Szczur, M. Surveillance of arthropod vector-borne infectious diseases
using remote sensing techniques: A review. PLoS Pathog. 2007,3, e116. [CrossRef] [PubMed]
13.
Hamm, N.A.S.; Soares Magalhães, R.J.; Clements, A.C.A. Earth Observation, Spatial Data Quality, and
Neglected Tropical Diseases. PLoS Negl. Trop. Dis. 2015,9, e0004164. [CrossRef] [PubMed]
14.
Zhang, Z.J.; Manjourides, J.; Cohen, T.; Hu, Y.; Jiang, Q.W. Spatial measurement errors in the field of spatial
epidemiology. Int. J. Health Geogr. 2016,15, 12. [CrossRef] [PubMed]
15.
Araujo Navas, A.L.; Hamm, N.A.S.; Soares Magalhães, R.J.; Stein, A. Mapping Soil Transmitted Helminths
and Schistosomiasis under Uncertainty: A Systematic Review and Critical Appraisal of Evidence. PLoS Negl.
Trop. Dis. 2016,10, e0005208. [CrossRef] [PubMed]
16.
Zhang, J.; Goodchild, M.F. Uncertainty in Geographical Information; Taylor & Francis Group: London, UK,
2002; ISBN 0-415-27723-X.
17.
Richardson, S.; Monfort, C. Ecological Correlation Studies. In Spatial Epidemiology: Methods and Applications;
Elliot, P.W., Wakefield, J.C., Best, N.G., Briggs, D.J., Eds.; Oxford University Press: Oxford, UK, 2000;
pp. 205–220, ISBN 0192629417.
18.
Wakefield, J.; Shaddick, G. Health-exposure modeling and the ecological fallacy. Biostatistics
2006
,7, 438–455.
[CrossRef] [PubMed]
19.
King, G. A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data;
Princeton University Press: Princeton, NJ, USA, 2013; ISBN 1400849209.
20.
Wakefield, J.; Lyons, H. Spatial Aggregation and the Ecological Fallacy. In Handbook of Modern Statisticcal
Methods; Hall/CRC, C., Ed.; CRC Press: Boca Raton, FL, USA, 2010; pp. 541–558, ISBN 9781420072877.
21.
Gelfand, A.E.; Diggle, P.; Guttorp, P.; Fuentes, M. Handbook of Spatial Statistics; Taylor & Francis Group: Boca
Raton, FL, USA, 2010; p. 619, ISBN 9781420072877.
22.
Prentice, R.L.; Sheppard, L. Aggregate data studies of disease risk factors. Biometrika
1995
,82, 113–125.
[CrossRef]
23.
Richardson, S.; Stucker, I.; Hemon, D. Comparison of relative risks obtained in ecological and individual
studies: Some methodological considerations. Int. J. Epidemiol. 1987,16, 111–120. [CrossRef]
24.
Wang, F.F.; Wang, J.; Gelfand, A.; Li, F. Accommodating the ecological fallacy in disease mapping in the
absence of individual exposures. Stat. Med. 2017,36, 4930–4942. [CrossRef]
25.
Raso, G.; Matthys, B.; N’goran, E.; Tanner, M.; Vounatsou, P.; Utzinger, J. Spatial risk prediction and mapping
of Schistosoma mansoni infections among schoolchildren living in western Côte d’Ivoire. Parasitology
2005
,
131, 97–108. [CrossRef]

Int. J. Environ. Res. Public Health 2019,16, 176 15 of 17
26.
Chammartin, F.; Houngbedji, C.A.; Huerlimann, E.; Yapi, R.B.; Silue, K.D.; Soro, G.; Kouame, F.N.;
N’Goran, E.K.; Utzinger, J.; Raso, G.; et al. Bayesian Risk Mapping and Model-Based Estimation of
Schistosoma haematobium-Schistosoma mansoni Co-distribution in Cote d’Ivoire. PLoS Negl. Trop. Dis.
2014,8, e3407. [CrossRef] [PubMed]
27.
Woodhall, D.M.; Wiegand, R.E.; Wellman, M.; Matey, E.; Abudho, B.; Karanja, D.M.S.; Mwinzi, P.M.N.;
Montgomery, S.P.; Secor, W.E. Use of Geospatial Modeling to Predict Schistosoma mansoni Prevalence in
Nyanza Province, Kenya. PLoS ONE 2013,8, e71635. [CrossRef]
28.
Sturrock, H.J.W.; Pullan, R.L.; Kihara, J.H.; Mwandawiro, C.; Brooker, S.J. The Use of Bivariate Spatial
Modeling of Questionnaire and Parasitology Data to Predict the Distribution of Schistosoma haematobium
in Coastal Kenya. PLoS Negl. Trop. Dis. 2013,7, e2016. [CrossRef] [PubMed]
29.
Hu, Y.; Bergquist, R.; Lynn, H.; Gao, F.; Wang, Q.; Zhang, S.; Li, R.; Sun, L.; Xia, C.; Xiong, C.; et al. Sandwich
mapping of schistosomiasis risk in Anhui Province, China. Geospat. Health
2015
,10, 111–116. [CrossRef]
[PubMed]
30.
Souza Guimaraes, R.J.d.P.; Freitas, C.C.; Dutra, L.V.; Carvalho Scholte, R.G.; Martins-Bede, F.T.; Fonseca, F.R.;
Amaral, R.S.; Drummonds, S.C.; Felgueiras, C.A.; Oliveira, G.C.; et al. A geoprocessing approach for
studying and controlling schistosomiasis in the state of Minas Gerais, Brazil. Mem. Inst. Oswaldo Cruz
2010
,
105, 524–531. [CrossRef]
31.
Scholte, R.G.C.; Gosoniu, L.; Malone, J.B.; Chammartin, F.; Utzinger, J.; Vounatsou, P. Predictive risk mapping
of schistosomiasis in Brazil using Bayesian geostatistical models. Acta Trop.
2014
,132, 57–63. [CrossRef]
[PubMed]
32.
Soares Magalhães, R.J.; Salamat, M.S.; Leonardo, L.; Gray, D.J.; Carabin, H.; Halton, K.; McManus, D.P.;
Williams, G.M.; Rivera, P.; Saniel, O.; et al. Mapping the Risk of Soil-Transmitted Helminthic Infections in
the Philippines. PLoS Negl. Trop. Dis. 2015,9, e0003915. [CrossRef]
33.
Clements, A.C.A.; Brooker, S.; Nyandindi, U.; Fenwick, A.; Blair, L. Bayesian spatial analysis of a national
urinary schistosomiasis questionnaire to assist geographic targeting of schistosomiasis control in Tanzania,
East Africa. Int. J. Parasitol. 2008,38, 401–415. [CrossRef]
34.
Leonardo, L.; Rivera, P.; Saniel, O.; Villacorte, E.; Lebanan, M.A.; Crisostomo, B.; Hernandez, L.; Baquilod, M.;
Erce, E.; Martinez, R. A national baseline prevalence survey of schistosomiasis in the Philippines using
stratified two-step systematic cluster sampling design. J. Trop. Med. 2012,2012, 8. [CrossRef]
35.
Leonardo, L.; Rivera, P.; Saniel, O.; Solon, J.A.; Chigusa, Y.; Villacorte, E.; Chua, J.C.; Moendeg, K.; Manalo, D.;
Crisostomo, B.; et al. New endemic foci of schistosomiasis infections in the Philippines. Acta Trop.
2015
,141,
354–360. [CrossRef]
36.
Leonardo, L.; Acosta, L.P.; Olveda, R.M.; Aligui, G.D.L. Difficulties and strategies in the control of
schistosomiasis in the Philippines. Acta Trop. 2002,82, 295–299. [CrossRef]
37.
Zhou, X.N.; Bergquist, R.; Leonardo, L.; Yang, G.J.; Yang, K.; Sudomo, M.; Olveda, R. Schistosomiasis
Japonica: Control and Research Needs. In Important Helminth Infections in Southeast Asia: Diversity and
Potential for Control and Elimination, Peart A; Zhou, X.N., Bergquist, R., Olveda, R., Utzinger, J., Eds.; Elsevier
Academic Press Inc.: San Diego, CA, USA, 2010; Volume 72, pp. 145–178, ISBN 978-0-12-381513-2.
38.
Leonardo, L.R.; Rivera, P.; Saniel, O.; Villacorte, E.; Crisostomo, B.; Hernandez, L.; Baquilod, M.; Erce, E.;
Martinez, R.; Velayudhan, R. Prevalence survey of schistosomiasis in Mindanao and the Visayas, The
Philippines. Parasitol. Int. 2008,57, 246–251. [CrossRef] [PubMed]
39.
Santos, F.L.N.; Cerqueira, E.J.L.; Soares, N.M. Comparison of the thick smear and Kato-Katz techniques for
diagnosis of intestinal helminth infections. Rev. Soc. Bras. Med. Trop.
2005
,38, 196–198. [CrossRef] [PubMed]
40. ESRI. ArcGIS Desktop, 10; Environmental Systems Research Institute: Redlands, CA, USA, 2011.
41.
Zhou, Y.B.; Liang, S.; Jiang, Q.W. Factors impacting on progress towards elimination of transmission of
schistosomiasis japonica in China. Parasit. Vectors 2012,5, 7. [CrossRef] [PubMed]
42.
Walz, Y.; Wegmann, M.; Dech, S.; Raso, G.; Utzinger, J. Risk profiling of schistosomiasis using remote sensing:
Approaches, challenges and outlook. Parasit. Vectors 2015,8, 16. [CrossRef] [PubMed]
43.
Xu, H. Modification of normalised difference water index (NDWI) to enhance open water features in remotely
sensed imagery. Int. J. Remote Sens. 2006,27, 3025–3033. [CrossRef]
44.
Prah, S.; James, C. The influence of physical factors on the survival and infectivity of miracidia of Schistosoma
mansoni and S. haematobium I. Effect of temperature and ultra-violet light. J. Helminthol.
1977
,51, 73–85.
[CrossRef]

Int. J. Environ. Res. Public Health 2019,16, 176 16 of 17
45.
Woolhouse, M.; Chandiwana, S. Population dynamics model for Bulinus globosus, intermediate host for
Schistosoma haematobium, in river habitats. Acta Trop. 1990,47, 151–160. [CrossRef]
46.
Pietrock, M.; Marcogliese, D.J. Free-living endohelminth stages: At the mercy of environmental conditions.
Trends Parasitol. 2003,19, 293–299. [CrossRef]
47. Geological Survey, U.S. Global Data Explorer. Available online: https://gdex.cr.usgs.gov/gdex/ (accessed
on 15 August 2017).
48.
Pesigan, T.P.; Hairston, N.G.; Jauregui, J.J.; Garcia, E.G.; Santos, A.T.; Santos, B.C.; Besa, A.A. Studies on
Schistosoma japonicum infection in the Philippines 2. The molluscan host. Bull. World Health Organ.
1958
,
18, 481–578.
49.
Stensgaard, A.S.; Jorgensen, A.; Kabatereine, N.B.; Rahbek, C.; Kristensen, T.K. Modeling freshwater snail
habitat suitability and areas of potential snail-borne disease transmission in Uganda. Geospat. Health
2006
,1,
93–104. [CrossRef] [PubMed]
50.
Stensgaard, A.S.; Utzinger, J.; Vounatsou, P.; Hurlimann, E.; Schur, N.; Saarnak, C.F.L.; Simoonga, C.;
Mubita, P.; Kabatereine, N.B.; Tchuente, L.A.T.; et al. Large-scale determinants of intestinal schistosomiasis
and intermediate host snail distribution across Africa: Does climate matter? Acta Trop.
2013
,128, 378–390.
[CrossRef] [PubMed]
51.
National Mapping and Resource Information Authority. Available online: http://www.namria.gov.ph/
(accessed on 15 February 2018).
52.
Gelman, A. Prior distributions for variance parameters in hierarchical models (Comment on an Article by
Browne and Draper). Bayesian Anal. 2006,1, 515–533. [CrossRef]
53.
Gelman, A.; Carlin, J.B.; Stern, H.S.; Rubin, D.B. Bayesian Data Analysis; Chapman and Hall/CRC: Boca
Raton, FL, USA, 1995; ISBN 1135439419.
54.
Diggle, P.J.; Tawn, J.; Moyeed, R. Model-based geostatistics. J. R. Stat. Soc. Ser. C Appl. Stat.
2002
,47, 299–350.
[CrossRef]
55.
Thomas, A.; Best, N.; Lunn, D.; Arnold, R.; Spiegelhalter, D. GeoBugs User Manual; MRC Biostatistics Unit:
Cambridge, UK, 2004.
56.
Lunn, D.; Jackson, C.; Best, N.; Thomas, A.; Spiegelhalter, D. The BUGS Book: A Practical Introduction to
Bayesian Analysis; CRC Press: Boca Raton, FL, USA, 2012; ISBN 1584888490.
57.
Brooks, S.P.; Gelman, A. General methods for monitoring convergence of iterative simulations. J. Comput.
Graph. Stat. 1998,7, 434–455. [CrossRef]
58.
Gelman, A.; Rubin, D.B. Inference from iterative simulation using multiple sequences. Stat. Sci.
1992
,7,
457–472. [CrossRef]
59.
Brooker, S.; Hay, S.I.; Bundy, D.A.P. Tools from ecology: Useful for evaluating infection risk models?
Trends Parasitol. 2002,18, 70–74. [CrossRef]
60.
Hijmans, R.; Rojas, E.; Cruz, M.; O’Brien, R.; Barrantes, I. DIVA-GIS free, simple and effective. Available
online: http://www.diva-gis.org/Data (accessed on 8 April 2018).
61. Project, O.S.M. Planet OSM; Open Street Map Project: Cambridge, UK, 2017.
62.
OCHA Humanitarian Data Exchange v1.25.3. Available online: https://data.humdata.org/search?groups=
phl&q=&ext_page_size=25 (accessed on 10 April 2018).
63.
Spiegelhalter, D.; Thomas, A.; Best, N.; Lunn, D. OpenBUGS User Manual; Version 3.0.2.; MRC Biostatistics
Unit: Cambridge, UK, 2007.
64.
Spiegelhalter, D.; Thomas, A.; Best, N.; Lunn, D. WinBUGS User Manual; MRC Biostatistics Unit: Cambridge,
UK, 2003.
65.
Lunn, D.; Spiegelhalter, D.; Thomas, A.; Best, N. OpenBUGS license. Available online: http://www.
openbugs.net/w/Downloads (accessed on 25 June 2018).
66.
Sturtz, S.; Ligges, U.; Gelman, A. R2OpenBUGS: A Package for Running OpenBUGS from R.; Journal of Statistical
Software: Innsbruck, Austria, 2010.
67.
Team, R.D.C. R: A Language and Environment for Statistical Computing; The R Foundation for Statistical
Computing: Vienna, Austria, 2013.
68.
Brooker, S.; Hay, S.; Issae, W.; Hall, A.; Kihamia, C.; Lawambo, N.; Wint, W.; Rogers, D.; Bundy, D. Predicting
the distribution of urinary schistosomiasis in Tanzania using satellite sensor data. Trop. Med. Int. Health
2001
,
6, 998–1007. [CrossRef]

Int. J. Environ. Res. Public Health 2019,16, 176 17 of 17
69.
Kristensen, T.; Malone, J.; McCarroll, J. Use of satellite remote sensing and geographic information systems
to model the distribution and abundance of snail intermediate hosts in Africa: A preliminary model for
Biomphalaria pfeifferi in Ethiopia. Acta Trop. 2001,79, 73–78. [CrossRef]
70.
Brooker, S.; Hay, S.I.; Tchuente, L.-A.T.; Ratard, R. Using NOAA-AVHRR data to model human helminth
distributions in planning disease control in Cameroon, West Africa. Photogramm. Eng. Remote Sens.
2002
,68,
175–179.
71.
Malone, J.B.; Yilma, J.M.; McCarroll, J.C.; Erko, B.; Mukaratirwa, S.; Zhou, X.Y. Satellite climatology and the
environmental risk of Schistosoma mansoni in Ethiopia and east Africa. Acta Trop.
2001
,79, 59–72. [CrossRef]
72.
Rice Science for a Better World. Available online: http://irri.org/our-work/research/policy-and- markets/
mapping-rice-in-the- philippines-where (accessed on 18 October 2018).
73.
Stensgaard, A.; Jorgensen, A.; Kabatareine, N.; Malone, J.; Kristensen, T. Modeling the distribution of
Schistosoma mansoni and host snails in Uganda using satellite sensor data and Geographical Information
Systems. Parassitologia 2005,47, 115–125. [PubMed]
74.
Burns, C.J.; Wright, M.; Pierson, J.B.; Bateson, T.F.; Burstyn, I.; Goldstein, D.A.; Klaunig, J.E.; Luben, T.J.;
Mihlan, G.; Ritter, L.; et al. Evaluating Uncertainty to Strengthen Epidemiologic Data for Use in Human
Health Risk Assessments. Environ. Health Perspect. 2014,122, 1160–1165. [CrossRef]
75.
Schur, N.; Hurlimann, E.; Garba, A.; Traore, M.S.; Ndir, O.; Ratard, R.C.; Tchuente, L.A.T.; Kristensen, T.K.;
Utzinger, J.; Vounatsou, P. Geostatistical Model-Based Estimates of Schistosomiasis Prevalence among
Individuals Aged <= 20 Years in West Africa. PLoS Negl. Trop. Dis. 2011,5, e1194. [CrossRef] [PubMed]
76.
Schur, N.; Hurlimann, E.; Stensgaard, A.S.; Chimfwembe, K.; Mushinge, G.; Simoonga, C.; Kabatereine, N.B.;
Kristensen, T.K.; Utzinger, J.; Vounatsou, P. Spatially explicit Schistosoma infection risk in eastern Africa
using Bayesian geostatistical modelling. Acta Trop. 2013,128, 365–377. [CrossRef] [PubMed]
77.
Simoonga, C.; Utzinger, J.; Brooker, S.; Vounatsou, P.; Appleton, C.C.; Stensgaard, A.S.; Olsen, A.;
Kristensen, T.K. Remote sensing, geographical information system and spatial analysis for schistosomiasis
epidemiology and ecology in Africa. Parasitology 2009,136, 1683–1693. [CrossRef] [PubMed]
78.
White, H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.
Econometrica 1980, 817–838. [CrossRef]
79.
Fox, J. Applied Regression Analysis, Linear Models, and Related Methods; Sage Publications, Inc.: Thousand Oaks,
CA, USA, 1997; ISBN 080394540X.
80. Mankiw, N.G. A Quick Refresher Course in Macroeconomics. J. Econ. Lit. 1990,28, 1645–1660.
©
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).