Geostatistical analysis and mapping of malaria risk in children under 5 using point-referenced prevalence data in Ghana

Ghana is located between latitudes \(4^{\circ }\) and \(12^{\circ }\)N and longitudes \(4^{\circ }\)W and \(2^{\circ }\)E, see Fig. 1. Geographically, Ghana is closer to the centre of the world than any other country, and the Greenwich Meridian passes through the country. Ghana has a total land area of 238,538 km\({^2}\); with 840 km distance from South to North and 554 km from East to West. Ghana shares border with Togo to the East, Cote d’Ivoire to the West, Burkina Faso to the North and has a coastline in the South along the Gulf of Guinea. There are 10 administrative regions in Ghana [6].

In this study, data from the Ghana malaria indicator survey (MIS) were used; malaria indicator surveys are conducted as part of the demographic and health surveys (DHS) and are well known [6, 39, 40]. The 2016 Ghana DHS was conducted through the malaria indicator survey (MIS) implemented by the Ghana Statistical Service (GSS), in collaboration with the Ghana NMCP and the national public health reference laboratory (NPHRL) of the GHS [6]. The 2016 Ghana MIS collected information that complements routine administrative data which are used to inform strategic planning and evaluation of Ghana’s malaria control programme [6]. Information on malaria prevention, treatment and prevalence were obtained during the survey. Specifically, data were collected on key malaria indicators such as the proportion of the ownership and use of ITNs, assessment of the coverage of IPT to protect pregnant women against malaria, estimated prevalence of malaria and anaemia among children aged 6–59 months, IRS coverage, wealth index of households, region where the survey took place, area of residence, gender, children’s age in months, mother’s education and others [6]. The response variable is the outcome of malaria test.

The 2016 Ghana MIS was designed and conducted to provide estimates of key malaria indicators for the whole country, for urban and rural areas separately, and for each of the ten administrative regions [6]. The administrative regions are Ashanti, Brong Ahafo, Central, Eastern, Greater Accra, Northern, Upper East, Upper West, Volta and Western. The sample frame used was the 2010 population and housing census (PHC), using a complete list of enumeration areas (EA). In this two-stage design, the first stage was to select 200 EAs with probability proportional to EA size. In the second stage, a fixed number of 30 households were then sampled from each of the selected EAs, giving a nationally representative sample of 6000 households.

Ghana MIS collected data via both the computer-assisted personal interviewing (CAPI) system on tablet computers and paper-based questionnaires. The three main questionnaire types used were the household questionnaire, the woman’s questionnaire and the biomarker questionnaire [6]. Blood samples for malaria testing were collected by finger- or heel-prick from children aged 6–59 months, and then tested for malaria with SD bioline malaria Ag P.f./pan rapid diagnostic test (RDT). Malaria RDT results were recorded in the biomarker questionnaire and the result shared with the child’s parent or guardian [6]. Additionally, microscopy results were read in the laboratory. Children who tested positive or showed signs and symptoms for malaria were either offered a full course of medication according to standard treatment protocol in Ghana or were referred to a health facility [6]. In the current analysis, only RDT tests results were used.

The formulation of the geostatistical model in the current study follows from the standard geostatistical model for prevalence surveys in Diggle et al. [41]. Consider a field team that visit communities at different locations \(x_i\) in a study region say \(G \subset \mathbb {R}^2\), and sample \(m_i: i = 1,\dots ,n\) individuals at risk in each community, as well as taking the records of whether each individual tests positive or negative for the disease under study. Let \(Y_i\) denote the number of positive malaria RDT outcomes out of \(m_i\) individuals tested at locations \(x_i\) in a region of interest \(G \subset \mathbb {R}^2\), and a vector of associated covariates \(\varvec{d(x_i)} \in \mathbb {R}^p\). The standard geostatistical model then assumes that \(Y_i \sim \textit{Binomial} (m_i, p(x_i))\), where \(p(x_i)\) measures the disease prevalence at locations \(x_i\). Adopting the logistic link function, the model further assumes that:where \(\alpha\) is the intercept parameter, S(x) is an unobservable random effect which is Gaussian process with zero-mean and a constant variance \(\sigma ^2\); \(d(\cdot )\) represents a vector of observed spatial explanatory variables associated with the response Y,  and \(\varvec{\beta }\) is a vector of spatial regression coefficients for the covariates. The empirical logit transform is defined as follows:and the underlining assumption is that:where \(Z_i\) are mutually independent zero-mean Gaussian random variables with variance \(\tau ^2\). The index i represents the household and the index j represents an individual within the household. The transformation in Eq. (2) was preferred here as it allows for a computationally simpler non-hierarchical approximate model fitting [42], this is especially advantageous where computational resources are limited.

Throughout the analysis, a Matérn parametric family of correlation functions for the process S(x) is assumed, to enable the definition of a legitimate class of covariance functions for the data. The Matérn correlation function is positive definite and sufficiently flexible [30]. The process S(x) is assumed to have mean of zero, stationary and isotropic Gaussian process, that is, with invariant distribution under translation and rotation [43]. The Matérn correlation function [44] for stationary Gaussian processes is a two-parameter family given by:in which u denotes the distance between two locations x and \(x^{\prime }\), \(\phi > 0\) is a scale parameter that determines the rate at which correlation decays to 0 as the distance increases, and \(\kappa > 0\), is a shape parameter which determines the analytic smoothness of the underlying process S(x). Also, \(\Gamma (\kappa )\) denotes the smallest integer greater than or equal to \(\kappa\), and \(K_{\kappa }(\cdot )\) denotes a modified Bessel function of order \(\kappa > 0\) [30].

A non-spatial generalized linear model (GLM) was fitted in the first step. For variable selection in the GLM, ordinary binomial logistic regression model was used, retaining covariates with nominal p-values less than 0.05. The resulting covariates are presented in Table 2 with terms for residence, age, indoor residual spray use, wealth index and mother’s education. In the second step, a spatial model was fitted. The Matérn shape parameter \(\kappa\) and relative variance parameters \(\tau ^2\) were fixed at 1.5 and 0, respectively.

In the spatial analysis, estimates of the model parameters were obtained and used to make spatial predictions over a fine grid of 5 \(\times\) 5 km, over the whole of Ghana. Under a predefined control scenario, malaria risk of children aged 24–36 months, middle household wealth status, middle mothers’ education level, with no indoor residual status and assumed rural residence for all the unsampled locations, was mapped. All the analysis and mapping were carried out using the R statistical software environment version 3.5.0 [45].

One of the objectives of the current study is to identify “hotspots” (here defined as areas that are above a prevalence threshold, say t). In prevalence estimation analyses, it is worthy noting that the resulting estimates p(x) at a location x have uncertainty that needs to be taken into account. It has been shown that classifying areas into different endemic levels purely based on estimates of p(x) at location x can lead to unwarranted policy decisions [31]. To overcome this issue, the geostatistical model developed in the statistical analysis section above, was used to derive a distribution of the most likely values that p(x) can take. This distribution was then used to quantify how likely p(x) is to be above a threshold t through the so-called exceedance probability (EP), formally expressed as:where t is the prevalence threshold, set to 20% in the current analysis. In other words, EP expresses how likely prevalence is to be above the threshold t based on the available survey data. An EP close to 100% indicates that prevalence is highly likely to be above the threshold t; if close to 0%, prevalence is highly likely to be below the threshold t; finally, if close to 50%, prevalence, is equally likely to be above or below the threshold t, hence this corresponds to the highest level of uncertainty. This is important when defining the level of certainty that a locality is above 20% and might be considered suitable for targeted interventions or proves that an area is highly intractable to interventions applied in that area to-date. It is desirable to be \(\ge\) 80% or \(\ge\) 90% certain that this is a real value based on the available data. If a locality does not reach the required level of certainty, additional sampling effort or surveys are required in order to classify that into the appropriate endemic level.

In some cases, the interest may be in delineating areas where p(x) is less than the threshold t, that is, areas that are below a prevalence threshold, through non-exceedance probability (NEPs), formally expressed as:NEP expresses how likely p(x) is below the threshold t based on the available survey data. A NEP close to 100% indicates that p(x) is highly likely to be below the threshold t; if close to 0%, p(x) is highly likely to be above the threshold t; finally, if close to 50%, p(x) is equally likely to be above or below the threshold t, hence this corresponds to the highest level of uncertainty. Here, areas that have 20% or less malaria prevalence based on the available 2016 GDHS data are shown, with 80% and 90% certainty. The 20% threshold was chosen based on the prevailing malaria prevalence in Ghana, which was 21% as per the MIS in 2016 [6]

In order to justify the need for modeling using the spatial geostatistical model applied here, evidence against the residual spatial correlation in the data was tested using the following 5-step variogram-based validation algorithm [31, 46].To conclude that there is no evidence against the adopted spatial model correlation, the empirical semi-variogram from the original data must fall within the generated 95% confidence intervals.

The response variable for each child was the binary outcome of the test for presence/absence of malaria from a finger- or heel-prick blood sample. Results from a GLM model are presented in Table 2. The binomial logistic model in Eq. (1) was fitted to obtain the Monte Carlo maximum likelihood [49] estimates of the parameters and associated 95% confidence intervals, as shown in Table 2. The \(\sigma ^2\) and \(\phi\) are variance of the Gaussian process and scale of the spatial correlation, respectively.

The validity of the adopted spatial structure used in the modeling exercise was tested using steps outlined in the model validation sub-section above. This is important especially when identifying areas where prevalence lies below (i.e. NEP) or above (i.e. EP) pre-defined thresholds. The results of this process are shown in Fig. 2. Since the empirical semi-variogram (solid line) falls within the 95% confidence intervals (dashed lines), then the adopted covariance model is compatible with the malaria parasite prevalence data implying that the results of NEPs, EP and the model overall are valid.

From Table 2, residing in the rural areas and child’s age are associated with an increase in probability of a positive malaria outcome in children. Household wealth status and mother’s education are negatively associated with the probability of a positive outcome, whereas IRS shows a negative, but non-significant association.

The 5 \(\times\) 5 km resolution maps for malaria prevalence in children under 5 years are presented. Overall, prevalence is low at national level, with an average of 22% but characterized by areas that are above average prevalence. Hotspots were observed to be mainly localized in the Northern, Upper West, Western, Eastern and Central regions. The region with the highest prevalence (deep orange) is the Northern region, particularly the communities surrounding the Mo and Oti rivers. The map of predicted malaria prevalence is shown in Fig. 3.

Figure 4 presents maps of malaria exceedance and non-exceedance probabilities, showing areas where \(p(x) \ge 0.2 \mid data\) as well as areas where \(p(x) < 0.2 \mid data\), with 80% and 90% certainty in both cases. Several regions, including, South western, Central, Upper West, Western, Eastern, Northern, and Ashanti have locations with predicted prevalence above 20%. The dark red areas show locations where prevalence is above 20%, at 90% certainty and light red are all areas where prevalence is above 20% at 80% certainty. In the same Fig. 4, non-exceedance probabilities are presented, showing areas where prevalence is less than 20% with 80% and 90% certainty. The following regions: Upper East, Greater Accra, Volta and Brong Ahafo have locations where predicted malaria prevalence in children under 5 years is less than 20%.