Multivariate Poisson cokriging: A geostatistical model for health count data.

Multivariate disease mapping is important for public health research, as it provides insights into spatial patterns of health outcomes. Geostatistical methods that are widely used for mapping spatially correlated health data encounter challenges when dealing with spatial count data. These include heterogeneity, zero-inflated distributions and unreliable estimation, and lead to difficulties when estimating spatial dependence and poor predictions. Variability in population sizes further complicates risk estimation from the counts. This study introduces multivariate Poisson cokriging for predicting and filtering out disease risk. Pairwise correlations between the target variable and multiple ancillary variables are included. By means of a simulation experiment and an application to human immunodeficiency virus incidence and sexually transmitted diseases data in Pennsylvania, we demonstrate accurate disease risk estimation that captures fine-scale variation. This method is compared with ordinary Poisson kriging in prediction and smoothing. Results of the simulation study show a reduction in the mean square prediction error when utilizing auxiliary correlated variables, with mean square prediction error values decreasing by up to 50%. This gain is further evident in the real data analysis, where Poisson cokriging yields a 74% drop in mean square prediction error relative to Poisson kriging, underscoring the value of incorporating secondary information. The findings of this work stress on the potential of Poisson cokriging in disease mapping and surveillance, offering richer risk predictions, better representation of spatial interdependencies, and identification of high-risk and low-risk areas.