Bayesian analysis of Gastric Cancer rate in Gilan Province by using the Auto-beta binomial model

Document Type : Original Paper

Authors

Departmant of Statistics, Shahrood University of Technology, Shahrood, Iran

Abstract

The climatic and environmental conditions in each region contribute to the outbreak of certain diseases. Therefore, providing a map of the event rate of a disease or mortality from various diseases on a geographic area is one issue of concern for physicians and health experts. Considering that gastric cancer is the most common cancer in Gilan province, Iran, in this paper, we study the impact of some risk factors on the rate of this cancer for the cities of Gilan province by using two auto-binomial and auto-beta-binomial Bayesian spatial models. The other purposes of this study are providing the gastric cancer rate prediction map and comparing the performance of the two proposed models. We used a dataset from the Razi Educational Center of Rasht in which the data were collected for sixteen cities of Gilan during the period of 2012-2017. We fitted the proposed models for these data by using an approximate Bayesian approach, called the integrated nested Laplace approximation (INLA). Based on the results, it was found that prediction of the rates of cancer in most of the cities of Gilan are similar by using of both models; in cities where there is a difference, the auto-binomial model predicts a higher rate than the auto-beta-binomial model. The reason for this is also that the auto-binomial model is over-fitted, which reduces its ability to predict.

Keywords

Main Subjects


[1] Rao, J. N. (2015). SmallArea Estimation. John Wiley and Sons, Ltd.
[2] Wilkinson, D., and Tanser, F. (1999). GIS/GPS to document increased access to community-based treatment for tuberculosis in Africa. The Lancet, 354(9176), 394-395.
[3] رمضانی، بهمن؛ حنیفی، اعظم (1387). شناخت پراکندگی جغرافیایی شیوع سرطان معـده در استان گیلان. فصلنامه علوم و تکنولوژی محیط‌زیست، دوره‌ی 13، شماره‌ی 2، ص92-79.
[4] رضوانی، محمود و همکاران 1374، طرح ثبت سرطان در استان گیلان، معاونت بهداشتی استان گیلان، ص 1.
[5] Ali, M., Rasool, S., Park, J. K., Saeed, S., Ochiai, R. L., Nizami, Q., and Bhutta, Z. (2004). Use of satellite imagery in constructing a household GIS database for health studies in Karachi, Pakistan. International Journal of Health Geographics, 3(1), 20.
[6] Cressie, N. (1993). Statistics for Spatial Data: Revised Edition. John Wiley and Sons.
[7] Snow, J. (1854). The cholera near Golden-square, and at Deptford. Medical Times and Gazette, 9, 321-322.
[8] Clayton, D., and Kaldor, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics, 43, 671-681.
[9] Kaiser, M. S., and Cressie, N. (1997). Modeling Poisson variables with positive spatial dependence. Statistics and Probability Letters, 35(4), 423-432.
[10] Lajaunie, C. (1991). Local risk estimation for a rare noncontagious disease based on observed frequencies. Note N-36/91/G, Centre de Géostatisque, Ecole des Mines de Paris.
[11] Oliver, M. A., Webster, R., Lajaunie, C., Muir, K. R., Parkes, S. E., Cameron, A. H., and Mann, J. R. (1998). Binomial cokriging for estimating and mapping the risk of childhood cancer. Mathematical Medicine and Biology: A Journal of the IMA, 15(3), 279-297.
[12] Monestiez, P., Dubroca, L., Bonnin, E., Durbec, J. P., and Guinet, C. (2006). Geostatistical modelling of spatial distribution of Balaenoptera physalus in the Northwestern Mediterranean Sea from sparse count data and heterogeneous observation efforts. Ecological Modelling, 193(3-4), 615-628.
[13] Goovaerts P. (2010). Geostatistical Analysis of County-Level Lung Cancer Mortality Rates in the Southeastern United States, Geographical analysis, 42(1), 32-52.
[14] Goovaerts, P. (2005). Geostatistical analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. International Journal of Health Geographics, 4(1), 31.
[15] Goovaerts, P. (2009). Medical geography: a promising field of application for geostatistics. Mathematical Geosciences, 41(3), 243.
[16] Shao, C., Mueller, U., and Cross, J. (2009). Area-to-point Poisson kriging analysis for lung cancer in Perth areas. Proceedings of the 18th World IMACS/MODSIM Congress, Jul 13-17, Caire, Australia.
[17] Kerry, R., Goovaerts, P., Smit, I., and Ingram, P. R. (2010). A Comparison of Indicator and Poisson Kriging of Herbivore Species Abundance in Kruger National Park. South Africa [Online].
[18] Bandyopadhyay, D., Reich, B. J., and Slate, E. H. (2011). A spatial beta-binomial model for clustered count data on dental caries. Statistical Methods in Medical Research20(2), 85-102.
[19] Harrison, X. A. (2015). A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology and evolution, PeerJ3, e1114.
[20] Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B (Methodology), 36(2), 192-236.
[21] Ferrari, S., and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics31(7), 799-815.
[22] Rue, H., Martino, S., and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society, Series B (Methodology), 71(2), 319-392.
[23] Rue, H., and Held, L. (2005). Gaussian Markov random fields: theory and applications, CRC press, London.
[24] Isaksson, A., Wallman, M., Göransson, H., and Gustafsson, M. G. (2008). Cross-validation and bootstrapping are unreliable in small sample classification. Pattern Recognition Letters29(14), 1960-1965.
[25] Varoquaux, G. (2017). Cross-validation failure: small sample sizes lead to large error bars. Neuroimage, 180, 68-77.