Kleinschmidt I, Bagayoko M, Clarke G P, Craig M, Le Sueur D
Medical Research Council (South Africa), Congella, Durban.
Int J Epidemiol. 2000 Apr;29(2):355-61. doi: 10.1093/ije/29.2.355.
Good maps of malaria risk have long been recognized as an important tool for malaria control. The production of such maps relies on modelling to predict the risk for most of the map, with actual observations of malaria prevalence usually only known at a limited number of specific locations. Estimation is complicated by the fact that there is often local variation of risk that cannot be accounted for by the known covariates and because data points of measured malaria prevalence are not evenly or randomly spread across the area to be mapped.
We describe, by way of an example, a simple two-stage procedure for producing maps of predicted risk: we use logistic regression modelling to determine approximate risk on a larger scale and we employ geo-statistical ('kriging') approaches to improve prediction at a local level. Malaria prevalence in children under 10 was modelled using climatic, population and topographic variables as potential predictors. After the regression analysis, spatial dependence of the model residuals was investigated. Kriging on the residuals was used to model local variation in malaria risk over and above that which is predicted by the regression model.
The method is illustrated by a map showing the improvement of risk prediction brought about by the second stage. The advantages and shortcomings of this approach are discussed in the context of the need for further development of methodology and software.
长期以来，优质的疟疾风险地图一直被视为疟疾防控的重要工具。此类地图的制作依赖于建模来预测地图大部分区域的风险，而疟疾流行率的实际观测通常仅在有限数量的特定地点已知。由于存在往往无法由已知协变量解释的局部风险差异，且测量的疟疾流行率数据点在待绘制区域并非均匀或随机分布，估计变得复杂。
我们通过一个例子描述一种制作预测风险地图的简单两阶段程序：我们使用逻辑回归建模在更大尺度上确定近似风险，并采用地理统计（“克里金法”）方法在局部层面改进预测。以气候、人口和地形变量作为潜在预测因子，对10岁以下儿童的疟疾流行率进行建模。回归分析后，研究模型残差的空间依赖性。对残差进行克里金法建模，以模拟回归模型预测之外的疟疾风险局部差异。
一张地图展示了第二阶段带来的风险预测改进，以此说明该方法。在需要进一步开发方法和软件的背景下，讨论了这种方法的优缺点。
