Conventional geostatistical methodology solves the problem of predicting the realized value of a linear functional of a Gaussian spatial stochastic process Sx) based on observations Y i Sx i Z i at sampling locations x i , where the Z i are mutually independent, zero-mean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The ®rst concerns the assessment of residual contamination from nuclear weapons testing on a South Paci®c island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity; we conclude that a conventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of north Lancashire and south Cumbria. For this application, we treat the data as binomial counts at unit postcode locations, conditionally on an unobserved relative risk surface which we estimate. The theoretical framework for our extension of geostatistical methods is that, conditionally on the unobserved process Sx, observations at sample locations x i form a generalized linear model with the corresponding values of Sx i appearing as an offset term in the linear predictor. We use a Bayesian inferential framework, implemented via the Markov chain Monte Carlo method, to solve the prediction problem for non-linear functionals of Sx, making a proper allowance for the uncertainty in the estimation of any model parameters.

BackgroundTransmission intensity affects almost all aspects of malaria epidemiology and the impact of malaria on human populations. Maps of transmission intensity are necessary to identify populations at different levels of risk and to evaluate objectively options for disease control. To remain relevant operationally, such maps must be updated frequently. Following the first global effort to map Plasmodium falciparum malaria endemicity in 2007, this paper describes the generation of a new world map for the year 2010. This analysis is extended to provide the first global estimates of two other metrics of transmission intensity for P. falciparum that underpin contemporary questions in malaria control: the entomological inoculation rate (PfEIR) and the basic reproductive number (PfR).MethodsAnnual parasite incidence data for 13,449 administrative units in 43 endemic countries were sourced to define the spatial limits of P. falciparum transmission in 2010 and 22,212 P. falciparum parasite rate (PfPR) surveys were used in a model-based geostatistical (MBG) prediction to create a continuous contemporary surface of malaria endemicity within these limits. A suite of transmission models were developed that link PfPR to PfEIR and PfR and these were fitted to field data. These models were combined with the PfPR map to create new global predictions of PfEIR and PfR. All output maps included measured uncertainty.ResultsAn estimated 1.13 and 1.44 billion people worldwide were at risk of unstable and stable P. falciparum malaria, respectively. The majority of the endemic world was predicted with a median PfEIR of less than one and a median PfRc of less than two. Values of either metric exceeding 10 were almost exclusive to Africa. The uncertainty described in both PfEIR and PfR was substantial in regions of intense transmission.ConclusionsThe year 2010 has a particular significance as an evaluation milestone for malaria global health policy. The maps presented here contribute to a rational basis for control and elimination decisions and can serve as a baseline assessment as the global health community looks ahead to the next series of milestones targeted at 2015.

BackgroundEfficient allocation of resources to intervene against malaria requires a detailed understanding of the contemporary spatial distribution of malaria risk. It is exactly 40 y since the last global map of malaria endemicity was published. This paper describes the generation of a new world map of Plasmodium falciparum malaria endemicity for the year 2007.Methods and FindingsA total of 8,938 P. falciparum parasite rate (PfPR) surveys were identified using a variety of exhaustive search strategies. Of these, 7,953 passed strict data fidelity tests for inclusion into a global database of PfPR data, age-standardized to 2–10 y for endemicity mapping. A model-based geostatistical procedure was used to create a continuous surface of malaria endemicity within previously defined stable spatial limits of P. falciparum transmission. These procedures were implemented within a Bayesian statistical framework so that the uncertainty of these predictions could be evaluated robustly. The uncertainty was expressed as the probability of predicting correctly one of three endemicity classes; previously stratified to be an informative guide for malaria control. Population at risk estimates, adjusted for the transmission modifying effects of urbanization in Africa, were then derived with reference to human population surfaces in 2007. Of the 1.38 billion people at risk of stable P. falciparum malaria, 0.69 billion were found in Central and South East Asia (CSE Asia), 0.66 billion in Africa, Yemen, and Saudi Arabia (Africa+), and 0.04 billion in the Americas. All those exposed to stable risk in the Americas were in the lowest endemicity class (PfPR2−10 ≤ 5%). The vast majority (88%) of those living under stable risk in CSE Asia were also in this low endemicity class; a small remainder (11%) were in the intermediate endemicity class (PfPR2−10 > 5 to < 40%); and the remaining fraction (1%) in high endemicity (PfPR2−10 ≥ 40%) areas. High endemicity was widespread in the Africa+ region, where 0.35 billion people are at this level of risk. Most of the rest live at intermediate risk (0.20 billion), with a smaller number (0.11 billion) at low stable risk.ConclusionsHigh levels of P. falciparum malaria endemicity are common in Africa. Uniformly low endemic levels are found in the Americas. Low endemicity is also widespread in CSE Asia, but pockets of intermediate and very rarely high transmission remain. There are therefore significant opportunities for malaria control in Africa and for malaria elimination elsewhere. This 2007 global P. falciparum malaria endemicity map is the first of a series with which it will be possible to monitor and evaluate the progress of this intervention process.

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SUMMARYTechniques for analysing three-dimensional spatial point patterns are demonstrated on data from a confocal microscope recording the locations of cells in three dimensions. New computational techniques are proposed for edge corrections and empty space measurement. A novel feature of the data is replication and nesting in a sampling design: multiple spatial patterns were observed from each of several animals. For this we develop a ratio regression approach.