Non-stationary partition modeling of geostatistical data for malaria risk mapping

Abstract

The most common assumption in geostatistical modeling of malaria is stationarity, that is spatial correlation is a function of the separation vector between locations. However, local factors (environmental or human-related activities) may influence geographical dependence in malaria transmission differently at different locations, introducing non-stationarity. Ignoring this characteristic in malaria spatial modeling may lead to inaccurate estimates of the standard errors for both the covariate effects and the predictions. In this paper, a model based on random Voronoi tessellation that takes into account non-stationarity was developed. In particular, the spatial domain was partitioned into sub-regions (tiles), a stationary spatial process was assumed within each tile and between-tile correlation was taken into account. The number and configuration of the sub-regions are treated as random parameters in the model and inference is made using reversible jump Markov chain Monte Carlo simulation. This methodology was applied to analyze malaria survey data from Mali and to produce a country-level smooth map of malaria risk.

Keywords:

• Bayesian inference
• geostatistics
• kriging
• malaria risk
• prevalence data
• non-stationarity
• reversible jump Markov chain Monte Carlo
• Voronoi tessellation

Acknowledgements

The authors would like to thank the MARA collaboration for making the malaria data available. This work was supported by the Swiss National Foundation grant Nr. 3252B0-102136/1.