Detecting local risk factors for residual malaria in northern Ghana using Bayesian model averaging

Site description

Data were collected from the Bunkpurugu-Yunyoo district, Northern Region, which is in the Guinea savannah zone of northeastern Ghana and experiences recurring high levels of seasonal malaria transmission (Fig. 1). Two highly efficient malaria vectors predominate in this area, namely Anopheles gambiae sensu stricto (s.s.) and Anopheles funestus [42]. During the study period coverage of long-lasting insecticide-treated bed net (LLINs) was greater than 75%, having benefitted from two mass distribution campaigns in 2010 and 2012. Furthermore, annual IRS campaigns were conducted in 2011 and 2012 using alphacypermethrin 0.4% WP (ICON^®10CS, Syngenta, Basel Switzerland), with a second application of IRS provided in the dry season in the eastern portion of the district.

The district is composed of rural communities supported by small-scale farming and herding, and two modest urban centers: Bunkpurugu (population: 7436) and Nakpanduri (population: 5783). The major ethno-linguistic groups are the Bimoba (approximately 60%) and Konkomba (approximately 30%) with smaller populations of Mamprusi, Kusasis, Dagombas, Fulanis and others. The Bimoba tend to predominate in the higher ground of the north and east portions of the district, including the two urban areas, while the Konkomba are more prevalent in the lower lying area of the south and west, where they graze their cattle in the riverine plains. The Konkomba, who tend to be a geographically and economically marginalized group across northern Ghana, are recognized as more culturally conservative and in general tend to be less educated [43].

Data collection

The individual-level longitudinal dataset was collected in the course of operations research on IRS, which was conducted by the University of Ghana with the support of the President’s Malaria Initiative [44, 45]. The current study, which was carried out at the University of Florida in collaboration the University of Ghana, consisted fundamentally of enhancing that original dataset with remote-sensed variables and conducting follow-on analyses to address a different set of research objectives.

Correlations between all potential risk factors were calculated, and in cases of high correlations (R² > 0.49), a single representative covariate was selected (see Additional file 1). Selection of these covariates was based on the relevance of each covariate to malaria epidemiology and intervention strategies. The covariates dropped from all models were farming caretakers, indoor residual spraying (IRS) in past 7 months, average daytime land surface temperature, normalized difference vegetation index (NDVI), cumulative rainfall, and historical precipitation trends. Because BMA requires each individual to have information for all covariates, all individuals with at least one covariate with missing data were dropped from the analysis. As a consequence, all analyses were based on 10,029 children (84.0% of total dataset). These data were distributed across 80 communities in the first survey and 71 communities in each of the subsequent surveys. The number of individuals in each survey ranged from 1341 to 1788.

Statistical methods

Out-of-sample predictions

As illustrated in the preceding sections, allowance for greater model flexibility can be achieved through the additional of several derived covariates and their associated parameters. Specifically, the base model contained 29 covariates, adding interaction terms increased the number of covariates to 56, and adding linear splines expanded the model to include a total of 73 covariates. Increasing the number of parameters in a model can lead to overfitting, making variable selection an increasingly important task. To assess the out-of-sample performance of BMA, we performed predictions by training the model on data from a particular year and estimating malaria status for a future year. Due to high seasonality in malaria risk in the district, only same-season predictions were considered (i.e. rainy season predictions were based on a rainy season training dataset). These predictions were compared to standard logistic regression, as well as least absolute shrinkage and selection operator (Lasso) regression. Lasso is an alternative method for variable selection which has been shown to improve out-of-sample predictions [52]. To demonstrate how these models performed relative to the number of covariates, season-to-season predictions for the base model and the extended model which contained seasonal interactions and spline terms were performed. Out-of-sample predictive skill was evaluated based on the sum of the log likelihood, where the model with the largest log likelihood sum was considered to have the best predictive ability.

Descriptive analysis

There was a slight decreasing trend in malaria prevalence over the course study, however the distribution of seasonal community prevalence remained relatively consistent over the course of the study (see Additional file 1). Mean community prevalence (and interquartile ranges) in the three rainy season surveys were 0.57 (0.39–0.75), 0.52 (0.33–0.73), and 0.46 (0.27–0.61), whereas in the three dry season surveys these values were 0.35 (0.15–0.50), 0.31 (0.14–0.47), and 0.23 (0.10–0.33). The parasitaemia rate remained high during the final rainy season despite high coverage of ITNs and 2 years of IRS, highlighting the importance of devising complementary malaria control strategies based on the local risk factors.

Risk factor outcomes

Base model

The basic risk factor model with BMA variable selection detected that many expected, classic patterns of malaria risk factors are present amongst the early childhood populations in Bunkpurugu-Yunyoo (Fig. 2). The strongest risk factor associated with malaria infection was rainy season (mean regression coefficient equal to 0.647 with a credible interval (CI) of 0.565–0.728), as evident in the prevalence maps (Fig. 1). Age was also a significant risk factor (0.296, CI 0.268–0.324), as would be expected among young children (i.e. less than 5 years old) in an area of stable, holoendemic malaria. Among the distance measures, distance to nearest health facility (0.094, CI 0.056–0.131) and urban centers (0.183, CI 0.137–0.229) were significant risk factors, whereas distance to nearest road (0.014, CI 0.00–0.060) and water body (− 0.013, CI − 0.052 to 0.00) had little to no effect. The Konkomba communities experienced significantly higher malaria risk (0.233, CI 0.137–0.323), relative to the Bimoba, and generally had a high mean prevalence overall. Note that this represents the risk associated with ethnicity are adjusting for other covariates in the model, such as education, wealth, and elevation. Statistically significant protective factors were access to health insurance (− 0.463, CI − 0.530 to − 0.391) and mother’s education (− 0.220, CI − 0.300 to − 0.141). Elevation was a significant factor, however given the relatively narrow range in elevations (135–449 meters above sea level) this is likely a consequence of the two urban centers being in higher elevation, not because of high-altitude effects on local climate. IRS in the past year was also a significant protective factor (− 0.154, CI − 0.254 to − 0.050). The categorical variables for wealth quintiles did not have statistically significant effects individually, however as a group these variables indicated that the lower wealth quintile groups (below median and well below median) were positively associated with malaria prevalence.

Seasonal differences

Modelling malaria risk with seasonal interaction terms (see Additional file 1 for regression coefficients) suggested most risk factors did not exhibit prominent differences between the rainy and the dry seasons, with a few notable exceptions. Age was an important risk factor for malaria in both seasons, however the slope estimate for this parameter was significantly lower in the rainy season than in the dry season, as illustrated in Fig. 3. These patterns suggest that while all ages experience higher malaria burden in the rainy season, children in the upper end of the observed age range (50–59 months old) experienced nearly the same predicted prevalence in the dry season as they did in the rainy season (Fig. 3). Another important finding refers to ethnicity. All ethnic groups experienced increased malaria burden in the rainy season, however predicted mean prevalence based on seasonal-ethnicity interaction terms indicate that the increase in malaria prevalence during the rainy season was more intense for the Konkomba communities than for the other ethnic groups (Fig. 3). For example, the odds-ratio associated with the effect of Konkomba ethnicity compared to Bimoba ethnicity increased from 1.27 in the dry season to 1.60 in the rainy season. By comparison, the odds-ratio associated with the effect of Mamprusi ethnicity compared to Bimoba ethnicity were 1.09 and 1.15 in the dry and rainy seasons, respectively. Other marginal differences included health insurance, which was less significant of a protective factor in the rainy season, and personal medication use, which was a moderate risk factor in the dry season but had relatively no influence in the rainy season (see Additional file 1).

Nonlinear associations

The final model containing linear spline covariates revealed interesting nonlinear associations between malaria prevalence and distance to nearest urban centre, and distance to nearest health facility (Fig. 4). Distance to nearest urban centre was positively associated with malaria infection in a roughly linear pattern until about 12–14 kilometres (km), after which malaria risk began to plateau. Similarly, the implied malaria risk was greater for communities that were further away from the nearest health facilities, however there was a less steep relationship after approximately 2–4 km. These nonlinear patterns in malaria risk and proximity to urban centres and health facilities were consistent in the rainy and dry seasons.

Out-of-sample predictions

Based on the sum of the log-likelihood, BMA and Lasso regression both outperformed standard logistic regression for all predictions (Table 3). Both approaches improved the out-of-sample predications compared to standard logistic regression by shrinking the regression coefficient estimates towards zero (Fig. 5). A notable difference between these approaches is that BMA allows for near-zero parameter estimates, whereas Lasso will force marginal factors to zero. For the base set of covariates, BMA and Lasso had similar likelihood values, however BMA had higher likelihood values for all predictions based on the extended set of covariates, which included seasonal interactions and linear splines. In particular, note that the out-of-sample predictive skill of BMA increased slightly for the extended model relative to the base model whereas the predictive skill of the logistic regression model and the Lasso often (or always) decreased when comparing these models. These results suggest that BMA is noticeably more resistant to overfitting than Lasso or logistic regression as the number of parameters is substantially increased.

Training	Testing	Sum of log-likelihood
		Logistic	Lasso	BMA
Base model (p = 29)a
Rainy 2010	Rainy 2011	− 1072.27	− 1049.24	− 1028.24b
Rainy 2011	Rainy 2012	− 1055.39	− 1037.49	− 1032.57b
Rainy 2010	Rainy 2012	− 1153.62	− 1110.05	− 1057.07b
Dry 2011	Dry 2012	− 969.88	− 919.45b	− 921.54
Dry 2012	Dry 2013	− 915.95	− 897.03b	− 903.60
Dry 2011	Dry 2013	− 967.83	− 920.28	− 915.81b
	Average	− 1022.49	− 988.92	− 976.47
Model with interactions and splines (p = 73)a
Rainy 2010	Rainy 2011	− 1079.63	− 1042.02	− 1027.85b
Rainy 2011	Rainy 2012	− 1066.56	− 1035.44	− 1030.75b
Rainy 2010	Rainy 2012	− 1156.76	− 1092.52	− 1050.55b
Dry 2011	Dry 2012	− 1065.27	− 1029.66	− 921.05b
Dry 2012	Dry 2013	− 922.40	− 902.79	− 902.32b
Dry 2011	Dry 2013	− 1079.34	− 1059.24	− 917.82b
	Average	− 1061.66	− 1026.95	− 975.06

BMA Bayesian model average

^ap refers to the number of covariates in the model

^bIndicates the model with the best fit

Methodological findings

These findings lend strong support for the usefulness of Bayesian model averaging (BMA) as a statistical tool for detecting complex patterns in malaria risk factors. In order to promote reproducibility of these methods and findings, the code used to run this analysis has been provided in Additional file 1 and have placed the data and R scripts in a public repository (see “Availability of data and materials” section), and note that packages for similar model selection and averaging approaches using OpenBUGS and R are available [53, 54]. Moreover, BMA in this context demonstrated similar advantages over standard variable selection procedures found in simulation studies [30–32], and studies in other ecological contexts [32–37, 55], including epidemiological risk analysis [38, 39]. Unlike standard logistic and Lasso regression, increasing model complexity by including several additional covariates did not reduce the out-of-sample predictive performance when using BMA. Importantly, constructing confidence intervals for Lasso regression coefficients continues to be an ongoing area of research [56–58], whereas characterizing uncertainty via credible intervals in the Bayesian framework is straightforward. Credible intervals are also often a better approach for comparing the strength of associations when compared to other traditional metrics, such as p-values [59]. Reversible jump MCMC tends to be computational efficient and effective, and by integrating out the regression coefficients this Gibbs sampler avoided issues associated with poor mixing of chains that often plague these other variable selection approaches [32, 53]. Machine learning techniques, such as artificial neural networks and support vector machines, can also detect nonlinear and other relationships and often have better predictive performance than standard logistic regression, but it is typically difficult to make direct inferences about the role of individual covariates using these techniques [60]. BMA may be useful for specific applications to modelling malaria risk factors where both interpretability and predictive ability are important (such as designing locally targeted interventions).

The trade-off between interpretability and predictive skill, spatial and temporal scope, data accessibility, and computational limitations are important factors to consider when choosing a variable selection procedure. For example, Weiss et al. [23] describes an exhaustive analysis of variable selection for identifying environmental factors associated with Plasmodium falciparum prevalence across sub-Saharan Africa, containing over 50 million covariates. They then used a series of selection phases based on Akaike information criteria (AIC) to reduce the number of covariates. This procedure was able to distill a parameter space that would be computational impossible to explore using BMA, however it lacks interpretability and does not account for uncertainty in the selection process. These tradeoffs may not be significant for prediction applications, but are critical for the analysis in this study to appropriately generate inference on the significance of different predictor variables.

Inferences on malaria risk factors and control strategies

Another area for further analysis is utilizing the model interpretability characteristics of this framework for informing management applications. The BMA-based analysis described well-established patterns in malaria aetiology across sub-Saharan Africa, including the strong seasonal patterns in malaria transmission [40, 41] and age-related prevalence patterns [61]. Protective factors identified in our models, including access to health insurance and mother’s education, have also been described as important factors in similar settings [62, 63]. In addition to validating these data and the methodology, these findings may provide insight for guiding local intervention and control strategies. For instance, the protective effect of personal health insurance coverage, which was detectable in one of Ghana’s more remote corners, underscores the value of Ghana’s pioneering effort to institute and scale up a national health insurance scheme since 2006 [64].

The capacity to increase model complexity without sacrificing predictive performance is an important modelling characteristic, particularly when inference is used to inform management strategies [65]. The inclusion of seasonal interaction terms revealed seasonal differences in age- and ethnicity-related risk that may be useful for designing seasonal chemoprophylaxis interventions, which can be extremely effective method for reducing cost and maximizing impact depending on the local malaria dynamics [66–69]. The linear spline covariates allowed the model to describe the nonlinear protective buffer provided by the modest urban centers. The link between urbanicity and malaria transmission has been extensively discussed in the literature [70–73], but understanding the relative impact modest urban centers can have on health outcomes in rural regions can be challenging [74], particularly at small spatial scales. The revealed nonlinear relationship between malaria risk and distance to urban centers suggested that the risk associated with living far from the urban center eventually reaches a plateau around 12 km in Bunkpurugu-Yunyoo. This is an interesting finding considering that the increased housing density, reduced non-polluted water resources, and other urban characteristics resolved about 2–3 km from the centers of the towns, based on field observation and satellite imagery. In addition, IRS coverage was universal across the district and ITN use was the same or higher at the more remote locations. This implies that ecological and entomological factors are less likely to be driving this phenomenon, suggesting that socio-economic factors may be important.

Furthermore, this framework may be useful for projecting the impact of future management efforts. For example, the association between malaria risk and distance to nearest health facility became less pronounced after about 2–4 km. Comparable rate stabilization patterns at similar distances have been described in health facilities in rural regions of Kenya [75]. Distance to nearest health facility is known to be an important factor in treatment-seeking behaviour and health outcomes [76–78]. Access to healthcare is a guiding management principle in Ghana, as demonstrated by the expansion of access to health insurance and revitalization of the Community-Based Health Planning and Services (CHPS) programme. Future work with these data will build upon these findings to describe the impact of CHPS facilities on early childhood malaria in Bunkpurungu-Yunyoo, as well as project the potential impact of new CHPS facilities and optimize their locations.

Bayesian model selection approaches, like BMA, are likely to find its greatest value in forecasting applications, in which model interpretability, predictive performance, and uncertainty characterization are equally valued. Bayesian frameworks often require a deeper understanding in statistical theory and programming, can be computationally intensive, and may lack accessible tools/software, but offer many advantages for modelling epidemiological data, including high flexibility and intuitive expressions of inference and uncertainty [79]. Based on background literature review, this appears to be the first instance of using BMA for variable selection to model malaria risk factors. This methodology offers a flexible framework with many advantages over other methods for modelling disease risk factors.

Limitations

From a methodological perspective, the outcomes from this study provide promising support for BMA as a useful statistical tool for modelling highly dimensional data on malaria risk factors, however there are notable limitations. The analysis uses a single data set, and therefore further efforts are needed to corroborate these findings. It may be that at certain dimensionalities BMA less effective than the other methods tested in this article, and therefore this analyses should be applied to other data sets, particularly at different spatio-temporal scales. Other comparison criteria (such as area under the receiver operating curve) or other tests (such as cross-validation) could also be used to compare predictive performance. From an epidemiological perspective, while this study incorporates many potential risks for malaria there are additional variables that are not included. Most notably these data do not include vector-related variables. The data are also limited by the periodicity of sampling time (seasonal), rather than a continuous sampling approach.