Background
Malaria remains a leading cause of morbidity and mortality in tropical and subtropical regions of the world. There are an estimated three billion people at risk of this disease and more than half a billion episodes of clinical Plasmodium falciparum occur each year, killing over one million individuals annually 12. It has been estimated that the global burden of malaria exceeds 40 million disability-adjusted life years (DALYs) 23 and the disease drains the social and economic development of affected regions 45. High-risk groups are children under the age of five years and pregnant women, with sub-Saharan Africa particularly affected. Indeed, this part of the world accounts for a striking 90% of the global burden of malaria 67.
Predicting the abundance and spread of malaria in endemic settings, in order to develop locally-adopted malaria control strategies to lower the burden of the disease is a pressing public health issue. Recently, an audacious goal has been announced in Seattle, USA during a meeting led by the Bill and Melinda Gates Foundation, namely to eradicate malaria 8. This goal – so the claim – has become a realistic hope thanks to new scientific advances, including the development of novel antimalarial drugs, vaccines and integrated control efforts through insecticide-treated nets (ITNs), prophylactic treatment and indoor residual spraying (IRS), in the face of a growing political will and financial support for malaria control initiatives 8. A deeper understanding of the spatial distribution of malaria is pivotal so that appropriate local elimination efforts can be designed and rigorous monitoring implemented.
Advances made with geographical information system (GIS), remote sensing and geostatistical modelling to predict the spatial and temporal distribution of malaria and Anopheles vectors have opened new avenues in this field of research. In particular, modelling disease and disease-related data within a Bayesian framework allows fitting of complex models in quite a flexible way. Additionally, Bayesian approaches provide computational advantages over traditional frequentist approaches via implementation of Markov chain Monte Carlo (MCMC) simulation 91011. Recent studies made use of the advantages offered by Bayesian methods for spatially-explicit modelling of malaria 12131415161718.
In Côte d'Ivoire, malaria is one of the primary public health concerns. This is illustrated by a study carried out in the savannah zone that documented malaria being responsible for at least 60% of the consultations in hospitals and 46% in paediatric clinics 19. In 2005, Côte d'Ivoire ranked at position 13 among countries with the highest rates of under-five mortality and estimates at the time suggested that only 4% of children under five years of age slept under an ITN 20. In the present study, small-scale patterns and spatial risk factors of the prevalence of P. falciparum among schoolchildren in a rural part of western Côte d'Ivoire were explored, using Bayesian geostatistical models.
Methods
Study area, population and ethical clearance
The study area is the region of Man, located in western Côte d'Ivoire. It is a mountainous region with tropical climate, including rains during eight to nine months of the year, and a dry period between November and February. The landscape is characterized in the north by rounded mountains with altitudes ranging from 200 to 1,300 m above sea level and small valleys, whereas the southern part is a river-draining plain 21. The field work was carried out between October 2001 and February 2002.
The study protocol was approved by the institutional research commission of the Swiss Tropical Institute (Basel, Switzerland) and the Centre Suisse de Recherches Scientifiques (Abidjan, Côte d'Ivoire). The study was given ethical clearance from the Ministry of Health in Côte d'Ivoire. All children attending grades three to five from 57 schools in the rural parts of the study area were invited to participate.
School surveys
The education officers were contacted and the aims and procedures of the study were explained. After receipt of their approval, the education officers informed teachers who provided the research team with copies of the class lists, which included information of the children's name, sex and age. First, a questionnaire was administered and schoolchildren were interviewed for assets on ownership and household characteristics, and perceived symptoms and diseases with a recall period of one month. The questionnaire included 17 morbidity indicators (e.g. abdominal pain, fever, etc.) and 12 household assets (e.g. radio, TV, etc.). An asset-based approach was used to stratify schoolchildren into five socioeconomic groups 2223. An additional question was included to inquire whether children slept under a bed net.
Second, a cross-sectional survey was carried out, to collect finger prick blood samples from previously interviewed children. Two drops of blood were placed on a microscope slide and thin and thick blood films were prepared. Slides were air-dried, transferred to a laboratory in the town of Man and stained with Giemsa. The slides were then forwarded to a reference laboratory in Abidjan and analysed by experienced laboratory technicians for species-specific density of Plasmodium, assuming a standard white blood cell (WBC) count of 8,000 per μl of blood by light microscopy. A random sample of 10% of the slides were re-examined by the senior microscopist for quality control purposes. Since more than 95% of the cases were P. falciparum infections, subsequent spatial analyses was restricted on this malaria parasite.
Environmental data
Geographical coordinates of each school were collected using a hand-held Magellan 320 global positioning system (GPS; Thales Navigation; Santa Clara, CA, USA). Streets and rivers were digitized with the aid of readily available ground maps. Normalized difference vegetation index (NDVI) and land surface temperature (LST) were downloaded at 1 × 1 km spatial resolution from Moderate Resolution Imaging Spectroradiometer (MODIS) from the USGS EROS Data Centre. Rainfall estimate (RFE) data with an 8 × 8 km spatial resolution from Meteosat 7 satellite were obtained from the Africa Data Dissemination Service (ADDS). NDVI, LST and RFE were downloaded for the period of September, 2001 to August, 2002 and processed as detailed elsewhere 21. Distances from schools to the nearest healthcare facility and rivers were calculated.
Data management and statistical analysis
Data were entered twice and validated with EpiInfo version 6.4 (Centers for Disease Control and Prevention; Atlanta, GA, USA). Geographical data were displayed in ArcView GIS version 3.2 (Environmental Systems Research Institute, Inc.; Redlands, CA, USA). Schoolchildren were subdivided into two age groups; (i) six to 10 years, and (ii) 11 to 16 years.
All covariates were fitted into bivariate logistic regression models on the P. falciparum infection status variable using STATA version 9.2 (Stata Corporation; College Station, TX, USA). Covariates with a significance level <0.15 were built into (i) a stationary, and (ii) a non-stationary Bayesian logistic regression model for P. falciparum infection, using WinBUGS version 1.4 (Imperial College & Medical Research Council; London, UK). The stationary geostatistical model assumed that spatial correlation is a function of distance only, whereas the non-stationary geostatistical model assumed that spatial correlation is a function of the distance and location 1624. Spatial heterogeneity was taken into account by introducing location-specific random effects, which model a latent spatial process.
Model specification
Let Yij be the P. falciparum infection status of schoolchild j in school i. It is assumed that Yij arises from a Bernoulli distribution, Yij ~Be(Pij), with probability Pij. The covariates
ij and school-specific random effect φi were modelled on the logit(pij)=X¯ijTβ¯+φi
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGagiiBaWMaei4Ba8Maei4zaCMaemyAaKMaemiDaqNaeiikaGIaemiCaa3aaSbaaSqaaiabdMgaPjabdQgaQbqabaGccqGGPaqkcqGH9aqpdaadaaqaaiabdIfaybaadaqhaaWcbaGaemyAaKMaemOAaOgabaGaemivaqfaaOWaaWaaaeaacqaHYoGyaaGaey4kaSIaeqOXdy2aaSbaaSqaaiabdMgaPbqabaaaaa@450A@, that is log it (Pij), where is the vector of regression coefficients.
The spatial correlation was introduced on the φi's by assuming that
= (φ1, φ1, ... φN)T has a multivariate normal distribution, ~MVN(0, Σ), with variance-covariance matrix Σ. An isotropic spatial process, i.e. Σmn = σ2 exp (-udmn), was also assumed, where dmn is the Euclidean distance between schools m and n, σ2 is the geographic variability known as the sill, and u is a smoothing parameter that controls the rate of correlation decay with increasing distance. To take into account non-stationarity, the study area was partitioned in K subregions, assuming a locally stationary spatial process k in each subregion k = 1, ..., K, where k = (ωk1, ωk2, ..., ωkN)T. In order to separate the schools into approximately equal numbers, the study area was subdivided into two subregions on a diagonal from the north-western corner to the south-eastern corner. Spatial correlation in the study area was then viewed as a mixture of the different spatial processes and the spatial random effect φi at location i was modelled as a weighted average of the subregion-specific (independent) stationary processes as follows: φi=∑k=1Kaikωki
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcaaQaeqOXdyMcdaWgaaqcbaAaaiabdMgaPbqabaqcaaQaeyypa0JcdaaeWbqcaaAaaiabdggaHPWaaSbaaKqaGgaacqWGPbqAcqWGRbWAaeqaaKaaGkabeM8a3PWaaSbaaKqaGgaacqWGRbWAcqWGPbqAaeqaaaqaaiabdUgaRjabg2da9iabigdaXaqaaiabdUealbqcdaQaeyyeIuoaaaa@44F2@, with weights aik, which are decreasing functions of the distance between location i and the centroids of the subregions k 25. Assuming k ~ MVN(0, Σk) and (∑k)ij=σk2corr(dij;uk)
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcaaQaeiikaGIaeyyeIuUcdaWgaaWcbaGaem4AaSgabeaajaaOcqGGPaqkkmaaBaaaleaacqWGPbqAcqWGQbGAaeqaaKaaGkabg2da9iabeo8aZPWaa0baaSqaaiabdUgaRbqaaiabikdaYaaakiabdogaJjabd+gaVjabdkhaYjabdkhaYjabcIcaOiabdsgaKnaaBaaaleaacqWGPbqAcqWGQbGAaeqaaOGaei4oaSJaemyDau3aaSbaaSqaaiabdUgaRbqabaGccqGGPaqkaaa@4A8B@, one has φ¯=N(0¯,∑k=1KAkT∑kAk)
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcaaQafqOXdyMba0bacqGH9aqpcqWGobGtcqGGOaakcuaIWaamgaqhaiabcYcaSOWaaabCaeaacqWGbbqqdaqhaaWcbaGaem4AaSgabaGaemivaqfaaOGaeyyeIu+aaSbaaSqaaiabdUgaRbqabaGccqWGbbqqdaWgaaWcbaGaem4AaSgabeaakiabcMcaPaWcbaGaem4AaSMaeyypa0JaeGymaedabaGaem4saSeaniabggHiLdaaaa@4495@, where Ak = diag{a1k, a2k, ..., ank}. The range is defined as the minimum distance at which spatial correlation between locations is below 5%. For an exponential correlation function, it can be calculated as 3uk
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaqcfa4aaSGaaeaacqaIZaWmaeaacqWG1bqDdaWgaaqaaiabdUgaRbqabaaaaaaa@305C@ meters.
Following a Bayesian model specification, prior distributions were adopted for the model parameters. Vague Normal distributions for the
parameters with large variances (i.e. 10,000), inverse gamma priors for σk2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaeq4Wdm3aa0baaSqaaiabdUgaRbqaaiabikdaYaaaaaa@3016@ and uniform priors for uk, k = 1, ..., K were chosen. MCMC simulation was employed to estimate the model parameters 26. A single chain sampler with a burn-in of 5,000 iterations was run. Convergence was assessed by inspection of ergodic averages of selected model parameters.
Model performance
The deviance information criterion (DIC) was utilized to assess the model performance 27. For appraisal of the predictive ability of models, a training sample from the current database was used. From the 55 schools, 43 schools (78%) were randomly selected and fitted into the logistic regression models. The remaining 12 schools were utilized for validation purposes. 95%, 75%, 50%, 25% and 1–5% Bayesian credible intervals (BCIs) of the posterior predictive distribution of test locations were calculated. The model with the highest percentage of locations within the BCI with the smallest coverage was considered the best performing one.
Results
Study profile and operational results
In the school year 2001/2002, a total of 5,448 children were registered on the class lists of grades three to five of the 57 participating rural schools. Complete questionnaire and parasitological data were obtained from 3,962 schoolchildren (72.7%) in 55 schools (one school failed to return the questionnaires; no blood samples were collected in another school). All subsequent analyses are based on this final cohort (Figure 1).
<p>Figure 1</p>
Study profile and compliance.
Study profile and compliance.
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Plasmodium infections
Approximately two-thirds of the study population were infected with malaria parasites. P. falciparum was the predominant species (overall prevalence 64.9%), whereas infections with Plasmodium malariae and Plasmodium ovale were rare; the respective prevalences were 3.0% and 0.2%. At the unit of the school, the P. falciparum prevalence ranged from 34.0% to 91.9% (Figure 2).
<p>Figure 2</p>
Mean infection prevalence of P. falciparum in 55 rural schools in the Man region, western Côte d'Ivoire during the school year 2001/2002
Mean infection prevalence of P. falciparum in 55 rural schools in the Man region, western Côte d'Ivoire during the school year 2001/2002. NDVI is displayed in the background.
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Risk profiling and spatial patterns
Results of the bivariate non-spatial analyses considering demographic, socioeconomic and environmental covariates, distance to health care facilities and use of bed net are summarized in Table 1. While children aged six to 10 years were at a significantly higher risk of a P. falciparum infection than their older peers, no difference was found among boys and girls. Children from the third wealth quintile (poor) were at a significantly higher risk of having an infection with P. falciparum compared to the first wealth quintile (poorest group). Besides age and socioeconomic status, not sleeping under a bed net, distance to health care facilities, and three environmental factors (i.e. high NDVI, high RFE and attending schools located at a distance to rivers of 500 m to 1000 m) were risk factors for a P. falciparum infection.
<p>Table 1</p>
Results of the bivariate logistic regression model for P. falciparum infections among 3,962 children from 55 rural schools in the Man region, western Côte d'Ivoire.
Indicators
P. falciparum infection prevalence
ORa
95% CI
P-value (AICb)
Age (years)
6–10
1
11–16
0.70
0.61, 0.8
<0.001
Socioeconomic status
Most poor
1
Very poor
1.04
0.84, 1.28
Poor
1.24
1.01, 1.53
Less poor
0.95
0.77, 1.16
Least poor
0.86
0.70, 1.06
0.011
Sleeping under a bed net
0.79
0.65, 0.98
0.030
Distance to health care facility
1.17
1.09, 1.25
<0.001
NDVI
Mean Ic
0.96
0.91, 1.03
0.333
Mean IId
1.05
0.99, 1.12
0.131 (5139)
Mean IIIe
0.96
0.90, 1.03
0.228
Annual mean
1.20
1.12, 1.29
<0.001 (5110)
Mean of the transmission season
1.19
1.11, 1.27
<0.001 (5114)
RFE
Mean Ic
0.88
0.82, 0.94
<0.001 (5126)
Mean IId
1.04
0.97, 1.11
0.289
Mean IIIe
1.13
1.05, 1.20
<0.001 (5129)
Sum of annual rainfall
1.11
1.04, 1.18
0.003 (5132)
Mean of the transmission seasonf
1.14
1.07, 1.21
<0.001 (5125)
Maximum LST
1.03
0.96, 1.09
0.449
Distance to rivers (categorized)
<500 m
1
500–999 m
1.22
1.03, 1.46
= 1000 m
0.63
0.54, 0.74
<0.001
aOR: odds ratio
bAIC: Akaike information criterion. The smaller the AIC the better the model performance
cMean I: Mean value during the month prior to blood sample collection
dMean II: Mean value during the month of collection and the previous month
eMean III: Mean value during the month of collection and the two previous months
fThe main transmission season of malaria is from June to August
Spatial analyses
Results of the spatial analyses are summarized in Table 2. Only age was a significant risk factor for P. falciparum prevalence, both in the stationary and the non-stationary logistic regression model, whereas NDVI was 'borderline' significant. In general, for all indicators, odds ratios (ORs) were comparable between the stationary and the non-stationary logistic regression model. The range where spatial correlation became insignificant was similar between the stationary and the non-stationary model. The non-stationary model revealed that location only had a minor leverage on the range of spatial correlation. The geographical variability was 0.3 with the stationary model, whereas in the non-stationary model there was some difference in the geographical variability between the two subregions.
<p>Table 2</p>
Multivariate stationary and non-stationary spatial analyses results for P. falciparum infection prevalence for the Man region, western Côte d'Ivoire.
Indicator
Bayesian logistic regression models
Stationary
Non-stationary
ORa
95% BCIb
ORa
95% BCIb
Age (years)
6–10
1
1
11–16
0.75
0.65, 0.87
0.75
0.65, 0.87
Socioeconomic status
Most poor
1
1
Very poor
0.90
0.71, 1.13
0.90
0.71, 1.13
Poor
1.21
0.95, 1.51
1.21
0.95, 1.51
Less poor
0.91
0.90, 1.15
0.90
0.71, 1.14
Least poor
0.85
0.66, 1.08
0.84
0.65, 1.08
Sleeping under a bed net
0.92
0.72, 1.15
0.92
0.73, 1.15
Distance to health care facility
1.07
0.87, 1.29
1.04
0.82, 1.27
Annual mean NDVI
1.16
0.98, 1.38
1.17
0.98, 1.40
Mean RFE during transmission season
1.06
0.87, 1.27
1.06
0.87, 1.27
Distance to rivers
<500 m
1
1
500–999 m
1.32
0.87, 1.94
1.27
0.81, 1.89
= 1000 m
0.75
0.48, 1.14
0.72
0.47, 1.09
ρ
1
c
0.0014
0.0003, 0.002
0.0015
0.0003, 0.002
ρ
2
0.0014
0.0004, 0.002
σ
1
2d
0.30
0.17, 0.49
0.23
0.10, 0.48
σ
2
2
0.40
0.18, 0.79
DICe
4899.8
4900.1
aOR: odds ratio
bBCI: Bayesian credible interval
cρ: scalar parameter representing the rate of decline of correlation with distance between points
dσ2: estimate of geographic variability
eDIC: deviance information criterion; a composite measure of how well the model does, i.e. a compromise between fit and complexity, with smaller DICs indicating better performance of the model
Model performance
Comparison of DICs suggested that both the stationary and the non-stationary model were similar with regard to their performance. Since the DIC did not give any definite information on the best-fitting models, further exploration was necessary by data training. Table 3 shows the results of the model validation. The non-stationary logistic regression model predicted correctly 100% of the test locations compared to 93% with the stationary logistic regression model at a 95% BCI. Moreover, the non-stationary logistic regression model had the highest percentage of correctly predicted locations at the smallest BCI, and hence can be regarded as the best fitting model.
<p>Table 3</p>
Percentage of test locations with P. falciparum prevalence falling within selected BCIs. For the model validation 43 locations were used for model fitting and 12 for prediction.
BCI
Bayesian logistic regression model
Stationary
Non-stationary
95%
93%
100%
75%
80%
87%
50%
53%
60%
25%
27%
27%
5%
13%
27%
4%
7%
27%
3%
7%
27%
2%
7%
20%
1%
7%
13%
Discussion
The purpose of this study was to assess risk factors and small-scale spatial patterns of P. falciparum infection prevalence among schoolchildren in a highly endemic area of rural western Côte d'Ivoire. The following covariates were significantly associated with infection: age, socioeconomic status, sleeping under a bed net, distance to health care facilities and a number of environmental factors. However, after accounting for spatial correlation, only age remained a significant risk factor for P. falciparum prevalence, whereas NDVI showed only 'borderline' significance. The predictive ability of the spatial models was examined using a training sample of 78% of the schools, with the non-stationary model performing better than the stationary one.
There are a number of shortcomings worth discussing. First, only a single finger prick blood sample was collected from each child for microscopic examination. Hence it is conceivable that some infections, particularly those with a low parasitaemia, were missed 2829. Second, it should be noted that school-aged children in highly malaria-endemic areas are not at highest risk of disease-associated morbidity and mortality. The prevalence in children below the age of five years might have been even higher than the observed P. falciparum prevalence of 64.9% among six to 16-year-old children. Third, the parasitological survey was carried out over a period of several months due to the large number of schoolchildren subjected to interviews and finger prick blood sampling, which might have introduced a bias in the observed prevalence from one school to another due to seasonality. Fourth, in the absence of high-resolution data to compute distances to small standing water bodies that might serve as Anopheles breeding sites, information from digitized maps was used to obtain the distance to rivers as an indication for the distance to breeding sites. The most likely vector in this area is Anopheles gambiae and, to some extent, Anopheles funestus. The former vector species breeds in transient, sunlit and generally small pools, whereas the latter has been associated with larger, semipermanent bodies of water containing aquatic vegetation and algae 30.
The analysis presented here showed that schoolchildren from wealthier households were more likely to be infected with P. falciparum compared to schoolchildren from the poorest households. This result is surprising given that the common expectation would be that the poorest of the poor are at highest risk of malaria 31. Several studies have shown that the burden of malaria is elevated among the poorest population segments, probably because they are at a higher exposure to malaria vectors and have fewer means for personal protective measures. For example, a study carried out in a rural community in Cameroon found a significant relationship between malaria and low protective housing conditions, such as living in wooden plank houses 32. Surprisingly, no significant association between the risk of a P. falciparum infection and housing conditions was evident in the present study. It is conjectured that issues related to exposure were associated to socioeconomic status, which calls for further investigation. Previous research conducted in rural Tanzania, for example, found that lack of access to health care and preventive measures, including ITNs, was associated with people's socioeconomic status 31. Interestingly, the current study confirms that children from poorer households were less likely to sleep under a bed net. Furthermore, children who reported sleeping under a bed net were at a decreased risk of having a P. falciparum infection. Additionally, it was found that the risk of a P. falciparum infection was associated with distances to health care facilities. Nevertheless, after taking into account spatial correlation, the covariates socioeconomic status, distance to the nearest health care facility and sleeping under a bed net showed no significant association anymore, and hence other factor must explain the observed spatial heterogeneity of P. falciparum.
Several environmental factors, namely NDVI, RFE and distance to rivers, were significantly associated with a P. falciparum infection in the bivariate non-spatial models. These findings are in accordance with previous studies that showed significant associations between malaria and NDVI, rainfall and distance to rivers at a broader spatial scale 333435. It is conceivable that these environmental factors are related to the presence and abundance of malaria vectors, which is governed by suitable breeding and resting sites of Anopheles. An interesting observation in the present study was that children from schools that were located in close proximity to rivers (<500 m) were at a lower risk of a P. falciparum infection compared to more distant schools (between 500 m and 1000 m). Children from schools with distances <500 m were significantly more often reporting to sleep under a bed net, suggesting that the former observation might be partly confounded by a higher level of bed net coverage and usage due to nuisance from mosquitoes near rivers. Children enrolled in schools located at distances >1000 m of rivers were less likely to be infected with P. falciparum, which might be related to the flight range of mosquitoes, which is, on average, below 1 km 36. Interestingly, none of the environmental covariates showed a statistical significant association to P. falciparum prevalence after accounting for spatial correlation. Hence, the current results demonstrate the importance of accounting for spatial correlation when analysing malaria prevalence data at small spatial scales as reported here. Indeed, omission of spatial correlation would have underestimated the standard errors of the covariate coefficients 37. Furthermore, in contrast to previous work focussing on helminth infections in the same study area 11212438, no risk map and corresponding uncertainty map have been presented, since none of the environmental factors investigated was significant in the spatially-explicit model. The results therefore suggest that at small spatial scales, individual-level factors (e.g. age) determine the spatial distribution of the P. falciparum infections rather than coarser environmental factors. These observations suggest that environmental factors are particularly salient for malaria prediction at larger spatial scales.
In geostatistical modelling, the standard assumption is that there is a stationary spatial dependence in the data, which implies that the spatial correlation is a function of the distance between points and independent of the location. Bayesian non-stationary geostatistical models were employed before for the prediction of helminth infections in the same study area 2438. Gosoniu and colleagues were the first to use Bayesian non-stationary geostatistical models for malaria risk, in their recent research on Mali 16 and West Africa 39. The authors' underlying assumption was that local characteristics related to human behaviour and environment, including vector ecology, influenced spatial correlation differently at different locations over large areas, i.e. an entire country. The results presented here suggest that the use of non-stationary models may also be required at a smaller spatial scale (i.e. at the district level), since the non-stationary model performed better than the one assuming stationarity. The current work on P. falciparum can be integrated with our previous work on helminth infections for mapping P. falciparum-helminth co-infections using multinomial regression models for the simultaneous targeting of malaria and helminthic diseases 11. School-aged children are at the highest risk of such co-infections and data suggest that co-infections with P. falciparum and hookworm have an additive impact on anaemia, implying that those high-risk groups would greatly benefit from integrated malaria and helminth control 40.
Authors' contributions
KDS contributed to the conception and design of the study, collected the data, was responsible for quality control issues of malaria slide reading, assisted with the analysis of the data and editing of the manuscript, GR contributed to the conception and design of the study, collected the data, analysed and interpreted the data and drafted and edited the manuscript, AY was involved in the collection of the data and supervision of the field work, PV contributed to the analysis of the data and editing of the manuscript, MT contributed to the conception and design of the study, EKN and JU oversaw all aspects of the study, including conception, design, execution of the field work, interpretation of the data and editing of the manuscript. All authors read and approved the final version of the manuscript.