Quantifying Aggregated Uncertainty in Plasmodium falciparum Malaria Prevalence and Populations at Risk via Efficient Space-Time Geostatistical Joint Simulation

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Abstract
Risk maps estimating the spatial distribution of infectious diseases are required to guide public health policy from local to global scales. The advent of model-based geostatistics (MBG) has allowed these maps to be generated in a formal statistical framework, providing robust metrics of map uncertainty that enhances their utility for decision-makers. In many settings, decision-makers require spatially aggregated measures over large regions such as the mean prevalence within a country or administrative region, or national populations living under different levels of risk. Existing MBG mapping approaches provide suitable metrics of local uncertainty—the fidelity of predictions at each mapped pixel—but have not been adapted for measuring uncertainty over large areas, due largely to a series of fundamental computational constraints. Here the authors present a new efficient approximating algorithm that can generate for the first time the necessary joint simulation of prevalence values across the very large prediction spaces needed for global scale mapping. This new approach is implemented in conjunction with an established model for P. falciparum allowing robust estimates of mean prevalence at any specified level of spatial aggregation. The model is used to provide estimates of national populations at risk under three policy-relevant prevalence thresholds, along with accompanying model-based measures of uncertainty. By overcoming previously unchallenged computational barriers, this study illustrates how MBG approaches, already at the forefront of infectious disease mapping, can be extended to provide large-scale aggregate measures appropriate for decision-makers. Reliable disease maps can support rational decision making. These maps are often made by interpolation: taking disease data from field studies and predicting values for the gaps between the data to make a complete map. Such maps always contain uncertainty, however, and measuring this uncertainty is vital so that the reliability of risk maps can be determined. A modern approach called model-based geostatistics (MBG) has led to increasingly sophisticated ways of mapping disease and measuring spatial uncertainty. Many health management decisions are made for administrative areas (e.g., districts, provinces, countries) and disease maps can support these decisions by averaging their values over the regions of interest. Carrying out this aggregation in conjunction with MBG techniques has not previously been possible for very large maps, however, due largely to the computational constraints involved. This study has addressed this problem by developing a new algorithm and allows aggregation of a global MBG disease map over very large areas. It is used to estimate Plasmodium falciparum malaria prevalence and corresponding populations at risk worldwide, aggregated across regions of different sizes. These estimates are a cornerstone for disease burden estimation and are provided in full to facilitate that process.