Spatiotemporal Analysis and Mapping of Oral Cancer Risk in Changhua County (Taiwan): An Application of Generalized Bayesian Maximum Entropy Method
Introduction
Knowledge of the spatiotemporal distribution of disease-specific incidence rates and its associated reliability is essential in the understanding of the underlying disease risk and the potential “environmental hazards-disease” causal associations 1, 2. The crude or adjusted incidence rates of a rare event (e.g., cancer) based on small populations may exhibit high variance and are, thus, less reliable 3, 4. This small population effect can yield unreliable and uncertain incidence rate data for spatiotemporal disease mapping purposes (5). To remove the small population effect in incidence rate estimation, large spatial units (e.g. counties and states) or small area aggregation are commonly used to stabilize the rates 6, 7. A similar concept is used to calculate temporal average incidence (during several years) that can yield a more stable spatial rate distribution. However, aggregated rates over a larger geographical area or a longer time period may cause the loss of detailed information about geographical and temporal rate variations that is valuable in disease risk assessment (5).
A variety of Poisson models have achieved considerable popularity in disease rate estimation 8, 9, 10, 11. Most of these models, however, often do not provide an adequate representation of the spatial dependence structure of incidence rates 5, 12, 13, 14. In a parallel development, geostatistics techniques have been used with increased frequency recently to analyze disease data distributed across space and time 15, 16, 17. However, most mainstream geostatistics techniques (such as the various forms of Kriging) are based on assumptions of rate homogeneity/stationarity patterns and linear disease estimators, which may not provide a meaningful representation of a disease pattern with heterogeneous space-time characteristics (18). In several other cases, nonlinear space-time disease estimators may provide more accurate disease assessment than linear or linearized Kriging estimators (19). Moreover, the small population effect can cause a significant increase of the incidence rate variance that clearly violates the homogeneity/stationary assumption.
There have been certain attempts to account for the spatial heterogeneity of disease rate variances: (a) One group of techniques (say, Group A) focuses on the underlying characteristics of the rate counting process and integrates the Poisson model into geostatistics analysis. Poisson model has been implemented as the estimator of either meantrend (16) or semivariogram (20) of spatial random processes. Among them, Kriging with a Poisson embedded semivariogram has been called Poisson Kriging (PK) 17, 20. PK has shown an improved performance over previous techniques in rare event simulation studies (17). (b) Alternatively, instead of working directly with the counting process, another group of techniques (say, Group B) chooses to transform the original site-specific data into a space-time homogeneous/stationary dataset 21, 22, 23.
In view of the above considerations, this study proposed to use the generalized Bayesian Maximum Entropy approach in the spatiotemporal mapping of rare disease incidence rates (24). GBME can, without assumptions of linearity and normality, synthesize various kinds of knowledge in a rigorous and general framework and provides a sound space-time image characterization in terms of the complete predictive probability density function at every point. Insight will be gained by applying GBME in the spatiotemporal mapping of oral cancer incidence rates over 26 townships in Changhua County (Taiwan) during the time period 1993-2002.
Section snippets
Study area
Changhua County, located in the geographic middle of Taiwan, has 26 townships, a total area of about 1074 km2 and a population of over 1.3 million; 38% of the residents are farmers, Fig. 1. (25). In recent years, oral cancer mortality in Taiwan has been promptly rising. Su et al. (26) showed that the oral cancer incidence rate in Changhua, at the rate of 45.07 per 10,000 males per year, was among the highest in the world, and was also the highest among the 23 counties of Taiwan during 2001 (
Results and Discussion
The GBME method (in which the Poisson-based semivariogram model constituted part of its G-KB) was applied in the spatiotemporal estimation of annual oral cancer incidence rate over the Changhua County during the period 1993-2002. Incidence rate uncertainty due to the small population effect was considered part of the S-KB and was accounted for in terms of Eq. (3), where a hyperbolic function expressed the “incidence rate variance-population size” relationship. Fig. 6 displays a summary of
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