Re-examining environmental correlates of Plasmodium falciparum malaria endemicity: a data-intensive variable selection approach

Abstract

Background: Malaria risk maps play an increasingly important role in disease control planning, implementation, and evaluation. The construction of these maps using modern geospatial techniques relies on covariate grids: continuous surfaces quantifying environmental factors that partially explain spatial heterogeneity in malaria endemicity. Although crucial, past variable selection processes for this purpose have often been subjective and ad-hoc, with many covariates used in modeling with little quantitative justification.

Methods: This research consists of an extensive covariate construction and selection process for predicting Plasmodium falciparum parasite rates (PfPR) in Africa for years 2000-2012. First, a literature review was conducted to establish a comprehensive list of covariates used for malaria mapping. Second, a library of covariate data was assembled to reflect this list, a process that included the construction of multiple, temporally dynamic datasets. Third, the resulting set of covariates was leveraged to create more than 50 million possible covariate terms via factorial combinations of different spatial and temporal aggregations, transformations, and pairwise interactions. Fourth, the expanded set of covariates was reduced via successive selection criteria to yield a robust covariate subset that was assessed using an out-of-sample validation approach.

Results: The final covariate subset included predominately dynamic covariates and it substantially out-performed earlier sets used by the Malaria Atlas Project (MAP) for creating global malaria risk maps, with the pseudo-R(2) value for the out-of-sample validation increasing from 0.43 to 0.52. Dynamic covariates improved the model, with 17 of the 20 new covariates consisting of monthly or annual products, but the selected covariates were typically interaction terms that included both dynamic and synoptic datasets. Thus the interplay between normal (i.e., long-term averages) and immediate conditions may be key for characterizing environmental controls on parasite rate.

Conclusions: This analysis represents the first effort to systematically audit covariate utility for malaria mapping and then derive an objective, empirically based set of environmental covariates for modeling PfPR. The new covariates produce more reliable representations of malaria risk patterns and how they are changing through time, and these covariates will be used to characterize spatially and temporally varying environmental conditions affecting PfPR within a geostatistical-modeling framework, thus building upon previous research by MAP that produced global malaria maps for 2007 and 2010.

Figure 1

Covariate use in malaria mapping. Summarized results from research from 113 published studies.

Figure 2

Map of household clusters by year. These survey points constitute the dependent variable for this research, with the training points used to parameterize the model, and the reserve points used for out-of-sample model validation.

Figure 3

Spatial summarization conceptual model. Multiple finer-resolution raster cells are summarized to create a variety outputs that characterize intra-cell properties at the coarser-resolution.

Figure 4

Temporal summarization conceptual overview. Summary statistics are derived from multiple rasters that are used directly as covariates and indirectly in the production of the anomaly covariates.

Figure 5

The number of covariates relative to the phase of analysis. The light grey points represent increasing covariates resulting from leveraging procedures, while the dark grey points represent the reduction in covariates by processing phase.

Figure 6

Comparisons of model performance when using the old vs new covariate sets. The panels A-E depict five different test metrics to illustrate the model improvement relative to the number of terms in the model.

Figure 7

Map of the Pf PR residual values associated with clusters within the reserve dataset. The residuals were calculated for each reserve cluster (n = 3000) as the measured PfPR minus the modeled PfPR.

Figure 8

The histogram of Pf PR residual values for clusters in the reserve dataset. Each cluster point was weighted by the number of individuals residing in the cluster to reflect the results of a model based upon binomial GLMs.