糖尿病為台灣常見的慢性代謝疾病，而糖尿病引發的心血管疾病併發症為患者死亡的主要原因。美國心臟學會於2010年公布第二版的共識與建議中，表示空氣汙染是心血管疾病的風險因子，而空氣汙染又跟地理環境息息相關，患者暴露在不同的地理位置所接觸到的空氣汙染量不盡相同，因此患者的發病時間可能會因其所在的地理位置而產生空間相關，這樣的資料稱為空間存活資料。
本研究旨在考慮空間相關之下，透過空間參數比例風險模型(spatial parametric proportional hazards model)的建立，來分析第II型糖尿病高風險患者心血管疾病的發作時間，與空氣汙染物和其他臨床風險因子之間的關係，並以貝氏統計(Bayesian statistics)的方式來進行參數估計，同時也會使用沒有考慮空間相關的韋伯模型(Weibull model)、Cox等比例風險模型(Cox proportional hazards model)與之進行比較。分析結果顯示PM2.5僅在有考慮空間相關下有顯著，且風險比為1.0399；SO2在三種模型下皆有顯著，但在有考慮空間相關下得到的風險比估計值為1.8859，相比沒有考慮空間相關下得到的風險比估計值來得高。
本研究把患者的經緯度資訊考慮進去模型，透過患者距離的遠近來決定相關性的大小，相比其他研究僅以區域的經緯度來衡量相關性，以個人層面來看待空間影響包含更多的資訊。我們僅透過實例應用建議後續的研究者在存活分析中，若欲考慮與地理位置有關之空氣汙染物等當作解釋變數時，應優先使用有考慮空間相關的空間參數比例風險模型，才能合理估計出空氣汙染物的效果。

Type 2 diabetes mellitus (T2DM) is a common chronic disease predisposing to cardiovascular disease (CVD), which is one of the principal causes of death among diabetic patients. Epidemiological studies have shown that air pollution might be a risk factor for CVD while the exposure of air pollution of each patient may vary spatially due to geographic locations. Consequently, there might exist a spatial correlation between the time of onset of CVD and different air pollutants.
To investigate the associations between survival time and the risk factors while taking the spatial correlation into account, a spatial parametric proportional hazards model is applied, in which the spatially correlated frailties are modeled by a log-Gaussian stochastic process. Bayesian approach is used for the estimation of parameters. Based on the results, both PM2.5 and SO2 increase the risk of CVD. The hazard ratio (HR) of PM2.5 is 1.0399 [1.0041, 1.0731], and SO2 is also a significant factor while HR is 1.8859 [1.6428, 2.1137].

中文參考文獻
台灣空氣汙染防制法施行細則第二條(民國92年07月23日)。取自https://law.moj.gov.tw/
衛生福利部統計處(2017)。106年國人死因統計結果。取自https://www.mohw.gov.tw/cp-3795-41794-1.html

英文參考文獻
American Diabetes Association. (2018). 2. Classification and diagnosis of diabetes: standards of medical care in diabetes—2018. Diabetes care, 41(Supplement 1), S13-S27.
Banerjee, S., & Carlin, B. P. (2002). Spatial semiparametric proportional hazards models for analyzing infant mortality rates in Minnesota counties. In Case Studies in Bayesian Statistics (pp. 137-151). Springer, New York, NY.
Banerjee, S., Wall, M. M., & Carlin, B. P. (2003). Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota. Biostatistics, 4(1), 123-142.
Brook, R. D., Rajagopalan, S., Pope III, C. A., Brook, J. R., Bhatnagar, A., Diez-Roux, A. V., et al. (2010). Particulate matter air pollution and cardiovascular disease: an update to the scientific statement from the American Heart Association. Circulation, 121(21), 2331-2378.
Cressie N.A.C. (1993). Statistics for Spatial Data. John Wiley & Sons, New York.
Chang, C. C., Tsai, S. S., Ho, S. C., & Yang, C. Y. (2005). Air pollution and hospital admissions for cardiovascular disease in Taipei, Taiwan. Environmental Research, 98(1), 114-119.
Chow, J. C., Watson, J. G., Mauderly, J. L., Costa, D. L., Wyzga, R. E., Vedal, S., ... & Wolff, G. T. (2006). Health effects of fine particulate air pollution: lines that connect. Journal of the air & waste management association, 56(10), 1368-1380.
Chiles, J. P., & Delfiner, P. (2009). Geostatistics: modeling spatial uncertainty (Vol. 497). John Wiley & Sons.
Chang, C. C., Kuo, C. C., Liou, S. H., & Yang, C. Y. (2013). Fine particulate air pollution and hospital admissions for myocardial infarction in a subtropical city: Taipei, Taiwan. Journal of Toxicology and Environmental Health, Part A, 76(7), 440-448.
Cesaroni, G., Forastiere, F., Stafoggia, M., Andersen, Z. J., Badaloni, C., Beelen, R., ... & Fratiglioni, L. (2014). Long term exposure to ambient air pollution and incidence of acute coronary events: prospective cohort study and meta-analysis in 11 European cohorts from the ESCAPE Project. British Medical Journal, 348, f7412.
Chen, G., Wang, A., Li, S., Zhao, X., Wang, Y., Li, H., ... & Wang, Y. (2019). Long-Term Exposure to Air Pollution and Survival After Ischemic Stroke: The China National Stroke Registry Cohort. Stroke, 50(3), 563-570.
DAROC (2018). DAROC Clinical Practice Guidelines for Diabetes Care. Taiwan, Diabetes Association of the Republic of China.
Filleul, L., Rondeau, V., Vandentorren, S., Le Moual, N., Cantagrel, A., Annesi-Maesano, I., ... & Vervloet, D. (2005). Twenty five year mortality and air pollution: results from the French PAARC survey. Occupational and Environmental Medicine, 62(7), 453-460.
Henderson, R., Shimakura, S., & Gorst, D. (2002). Modeling spatial variation in leukemia survival data. Journal of the American Statistical Association, 97(460), 965-972.
Holman, R. R., Paul, S. K., Bethel, M. A., Matthews, D. R., & Neil, H. A. W. (2008). 10-year follow-up of intensive glucose control in type 2 diabetes. New England Journal of Medicine, 359(15), 1577-1589.
Jerrett, M., Burnett, R. T., Ma, R., Pope III, C. A., Krewski, D., Newbold, K. B., ... & Thun, M. J. (2005). Spatial analysis of air pollution and mortality in Los Angeles. Epidemiology, 727-736.
Jerrett, M., Burnett, R. T., Beckerman, B. S., Turner, M. C., Krewski, D., Thurston, G., ... & Gapstur, S. M. (2013). Spatial analysis of air pollution and mortality in California. American journal of respiratory and critical care medicine, 188(5), 593-599.
Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457-481.
Lakka, H. M., Laaksonen, D. E., Lakka, T. A., Niskanen, L. K., Kumpusalo, E., Tuomilehto, J., & Salonen, J. T. (2002). The metabolic syndrome and total and cardiovascular disease mortality in middle-aged men. Jama, 288(21), 2709-2716.
Li, Y., & Ryan, L. (2002). Modeling spatial survival data using semiparametric frailty models. Biometrics, 58(2), 287-297.
Lipsett, M. J., Ostro, B. D., Reynolds, P., Goldberg, D., Hertz, A., Jerrett, M., ... & Bernstein, L. (2011). Long-term exposure to air pollution and cardiorespiratory disease in the California teachers study cohort. American journal of respiratory and critical care medicine, 184(7), 828-835.
Peters, A., Dockery, D. W., Muller, J. E., & Mittleman, M. A. (2001). Increased particulate air pollution and the triggering of myocardial infarction. Circulation, 103(23), 2810-2815.
Sinnott, R. W. (1984). Virtues of the Haversine. Sky Telesc, 68(2), 159.
Su, T. C., Chen, S. Y., & Chan, C. C. (2011). Progress of ambient air pollution and cardiovascular disease research in Asia. Progress in cardiovascular diseases, 53(5), 369-378.
Tobler, W. R. (1970). A computer movie simulating urban growth in the Detroit region. Economic geography, 46(sup1), 234-240.
Tsai, S. S., Huang, C. H., Goggins, W. B., Wu, T. N., & Yang, C. Y. (2003). Relationship between air pollution and daily mortality in a tropical city: Kaohsiung, Taiwan. Journal of toxicology and environmental health. Part A, 66(14), 1341-1349.
Tsai, D. H., Wang, J. L., Chuang, K. J., & Chan, C. C. (2010). Traffic-related air pollution and cardiovascular mortality in central Taiwan. Science of the Total Environment, 408(8), 1818-1823.
Taylor, B.M. (2015). Auxiliary Variable Markov Chain Monte Carlo for Spatial Survival and Geostatistical Models. arXiv preprint arXiv:1501.01665.
Thurston, G. D., Ahn, J., Cromar, K. R., Shao, Y., Reynolds, H. R., Jerrett, M., ... & Hayes, R. B. (2015). Ambient particulate matter air pollution exposure and mortality in the NIH-AARP diet and health cohort. Environmental health perspectives, 124(4), 484-490.
Taylor, B., & Rowlingson, B. (2017). spatsurv: an R package for Bayesian inference with spatial survival models. Journal of Statistical Software, 77(4), 1-32.
Taylor, B. M., Rowlingson, B. S., Zheng, Z., & Taylor, M. B. M. (2018). Package ‘spatsurv’.
Vaupel, J. W., Manton, K. G., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16(3), 439-454.
World Health Organization. (1999). Definition, diagnosis and classification of diabetes mellitus and its complications: report of a WHO consultation. Part 1, Diagnosis and classification of diabetes mellitus (No. WHO/NCD/NCS/99.2). Geneva: World health organization.
Wannamethee, S. G., Shaper, A. G., Whincup, P. H., Lennon, L., & Sattar, N. (2011). Impact of diabetes on cardiovascular disease risk and all-cause mortality in older men: influence of age at onset, diabetes duration, and established and novel risk factors. Archives of internal medicine, 171(5), 404-410.