Disease maps can serve to display incidence rates geographically, to inform on public health provision about the success or failure of interventions, and to make hypothesis or to provide evidences concerning disease etiology. Poisson kriging was recently introduced to filter the noise attached to rates recorded over sparsely populated administrative units. Its benefit over simple population-weighted averages and empirical Bayesian smoothers was demonstrated by simulation studies using county-level cancer mortality rates. This paper presents the first application of Poisson kriging to the spatial interpolation of local disease rates, resulting in continuous maps of disease rate estimates and the associated prediction variance. The methodology is illustrated using cholera and dysentery data collected in a cholera endemic area (Matlab) of Bangladesh.
The spatial analysis was confined to patrilineally-related clusters of households, known as baris, located within 9 kilometers from the Matlab hospital to avoid underestimating the risk of disease incidence, since patients far away from the medical facilities are less likely to travel. Semivariogram models reveal a range of autocorrelation of 1.1 km for dysentery and 0.37 km for cholera. This result translates into a cholera risk map that is patchier than the dysentery map that shows a large zone of high incidence in the south-central part of the study area, which is quasi-urban. On both maps, lower risk values are found in the Northern part of the study area, which is also the most distant from the Matlab hospital. The weaker spatial continuity of cholera versus dysentery incidence rates resulted in larger kriging variance across the study area.
The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of incidence rates into the mapping of risk values and the quantification of the associated uncertainty. Differences in spatial patterns, in particular the range of spatial autocorrelation, reflect differences in the mode of transmission of cholera and dysentery. Our risk maps for cholera and dysentery incidences should help identifying putative factors of increased disease incidence, leading to more effective prevention and remedial actions in endemic areas.