A heterogeneity measure for cluster identification with application to disease mapping

Abstract

Mapping of disease incidence has long been of importance to epidemiology and public health. In this paper, we consider identification of clusters of spatial units with elevated disease rates and develop a new approach that estimates the relative disease risk in association with potential risk factors and simultaneously identifies clusters corresponding to elevated risks. A heterogeneity measure is proposed to enable the comparison of a candidate cluster and its complement under a pair of complementary models. A quasi‐likelihood procedure is developed for estimating the model parameters and identifying the clusters. An advantage of our approach over traditional spatial clustering methods is the identification of clusters that can have arbitrary shapes due to abrupt or noncontiguous changes while accounting for risk factors and spatial correlation. Asymptotic properties of the proposed methodology are established and a simulation study shows empirically sound finite‐sample properties. The mapping and clustering of enterovirus 71 infections in Taiwan are carried out for illustration.

Identification of geographic clusters for temporal heterogeneity with application to dengue surveillance

“…The proposed approach, on the other hand, can be used to explore different routes of epidemic propagation from a common source of an infectious disease, as we illustrated in the data analysis for the dengue infection. Although Lin and Zhu 11 developed a method that also can connect spatial clustering and classification approaches, their work focuses on dealing with spatial heterogeneity.…”

“…We use the spatial-temporal estimating Equation ( 6) to estimate 𝝃 k for each cluster G k . The test statistic U k,k ′ in (11) is then computed to measure heterogeneity between ξk and ξk ′ . Let 𝜒 2 52,0.95 denote a 95th percentile of the chi-squared distribution with 52 degrees of freedom.…”

“…A central limit theorem thus gives the desired result. (11): Since V can be approximated by a spatially block-diagonal matrix by the discussion for Assumption 1, we have…”

Iterative estimating equations for disease mapping with spatial zero‐inflated Poisson data

“…However, positive counts in disease diffusion data could exhibit geographical clustering effects, which would indicate the existence of spatial correlation among positive responses. One way to address this issue is to combine a disease mapping model (e.g., Lin & Zhu, 2020) with a ZIP model for the analysis of count data with spatial correlation and zero inflation. In this paper, we propose a new estimation method for a spatial ZIP model that accommodates excessive zeros, spatial correlation and covariates.…”

“…In this paper, we combine a frequentist disease mapping model (e.g., Lin & Zhu, 2020) with a ZIP model to address the Wombling problem for spatial count data with excessive zeros. In the frequentist disease mapping model associated with a system of estimating equations that involve second‐order moments, spatial correlation can play a role to smooth out abrupt changes of responses.…”