本研究提出一個兩階段的時空模型來分析空氣污染與健康的關係。我們選取在台灣的49個有設置空氣品質監測站的鄉鎮市區做為研究地區。資料包含這些小地區中1997-2001年的各地區每日因呼吸道疾病而就醫的門診人數與空氣污染物濃度與氣象監測資料。在第一階段中，對每一個月所有地區的每日因呼吸道疾病而就醫的門診人數與空氣污染配適時空模型，並利用氣象條件等因素做調整。在第二階段裡，利用線性混合效果模型將第一階段所獲得的60 個月空氣污染物係數估計值來獲得代表這五年全國整體污染物係數的估計。本文利用模擬研究來探討當季節因素與不可解釋的因素，例如像流行性感冒等存在時會對文獻上其他時空模型中參數的估計所造成的影響，同時與我們所提出的方法作一比較。

We proposed a spatiotemporal model to investigate the association between the acute health effects and daily numbers of clinic visits for respiratory illness. The data include clinic records due to respiratory illness and environmental variables from air quality monitoring stations in Taiwan during 1997-2001. A small-area design and two-phase modeling were used for the analysis. In the first phase, we constructed a Poisson regression with autogressive residual process and spatial correlation to obtain the pollution coefficient of each single month. In the second phase, we combined the information from phase one model to improve estimates of the pollution coefficients of each month and to obtain an overall pollution coefficient across the temporal course. Simulation study was used to illustrate the bias of estimation when there are seasonal, spatial and the unexplained effects in the data.

1. Atkinson, R. W., Anderson, H. R., Sunyer, J., Ayres, J., Baccini, M., Vonk, J. M., Boumghar, A., Forastiere, F., Forsberg, B., Touloumi, G., Schwartz, J. and Katsouyanni, k. (2003), “Acute Effects of Particulate Air Pollution on Respiratory Admissions,” Special Report, Preprint Version. Health Effects Institutes, Cambridge MA.
2. Burnett, R. T., Dales, R. E., Raizenne, M.E., Krewski, D., Summers, P. W., Roberts, G. R., Raadyoung, M., Dann, T. and Brook, J. (1994), “Effects of Low ambient Levels of Ozone and Sulfates on the Frequency of Respiratory Admissions to Ontario Hospital,” Environmental Research, Vol. 65, Issue 2,172-194.
3. Burnett, R. T. and Goldberg, M. S. (2003), “Size-Fractionated Particulate Mass and Daily Mortality in Eight Canadian Cities,” Special Report, Preprint Version. Health Effects Institutes, Cambridge MA.
4. Chib, S. and Greenberg, E. (1995), “Understanding the Metropolis-Hasting Algorithm,” American Statistical Association, Vol. 49, No. 4, 327-335.
5. Congdon. P. (1994), “Spatiotemporal Analysis of Area Mortality,” The Statistician, Vol. 43, No. 4, 513-528.
6. Coull, B. A., Schwartz, J. and Wand, M. P. (2001), “Respiratory Health and Air Pollution: Additive Mixed Model Analyses,” Biostatistics, Vol. 2, No. 3, 337-349.
7. Cressie, N. A. (1993), Statistics for Spatial Data, New York: John Wiley & Sons.
8. Carlin, B. P. and Louis, T. A. (2000), Bayes and Empirical Bayes Methods for Data Analysis, 2nd ed., London: Chapman and Hall.
9. Dey, D. K., Ghosh, S. K. and Mallick, B. K., (2000), Generalized Linear Models: A Bayesian Perspective, New York: Marcel Dekker.
10. Dominici, F., Samet, S. M. and Zeger, S. L. (2000), “Combining Evidence on Air Pollution and Daily Mortality from the 20 Largest US Cities: a Hierarchical Modeling Strategy,” Journal of the Royal Statistical Society, Series A, Vol. 163, No.3, 263-302.
11. Dominici, F., McDermott, A., Zeger, S. L. and Samet, J. M. (2002a), “On the Use of Generalized Additive Models in Time-Series Studies of Air Pollution and Health,” American Journal of Epidemiology, Vol. 156, No. 3, 193-203.
12. Dominici, F., Daniels, M., Zeger, S. L and Samet, J. M. (2002b), “Air Pollution and Mortality: Estimating Regional and National Dose-Response Relationships,” Journal of the American Statistical Association, Vol. 97, No. 457, 100-111.
13. Dominici, F., McDermott, A., Zeger, S. L. and Samet, J. M. (2003), “Airborne Particulate Matter and Mortality: Timescale Effects in for US Cities,” American Journal of Epidemiology, Vol. 57, No. 12, 1055-1065.
14. Dominici, F., McDermott, A., Hastie, T. (2003), “Improved Semipararmeteric Time Series Models for Air Pollution and Mortality,” Technical Report.
15. Elliott, P., Wakefield, J. C., Best, N. G. and Briggs, D. J. (2000), Spatial Epidemiology: Methods and Applications, Oxford: Oxford University Press.
16. Fairley, D. (20003), “Mortality and Air Pollution for Santa Clara County California, 1989-1996,” Special Report, Preprint Version. Health Effects Institutes, Cambridge MA.
17. Gamermam, D. (1997), Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, London: Chapman and Hall.
18. Gelfand, A. E. and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, Vol. 85, No. 410, 398-409.
19. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995), Bayesian Data Analysis, London: Chapman and Hall.
20. Gelman, A. and Rubin, D. B. (1992), “Inference from Iterative Simulation Using Multiple Sequences,” Statistical Science, Vol. 7, No. 4, 457-511.
21. Gilks, W. E., Richardson, S. and Spiegelhalter D. J. (1996), Markov Chain Monte Carlo in Practice, London: Chapman and Hall.
22. Gold, D. R., Schwartz, J., Litonjua, A., Verrier, R., and Zanobetti, A. (2003), “Ambient Pollution and Reduced Heart Rate Variability,” Special Report, Preprint Version. Health Effects Institutes, Cambridge MA.
23. GoldBerg, M. A. and Burnett, R. T. (2003), “Revised Analysis of the Montreal Time-Series Study,” Special Report, Preprint Version. Health Effects Institutes, Cambridge MA.
24. Hajat, S., Haines, A., Atkinson, R. W., Bremner, S. A., Anderson, H. R. and Emberlin, J. (2001), “Association between Air Pollution and Daily Consultations with General Practitioners for Allergic Rhinitis in London, United Kingdom,” American Journal of Epidemiology, Vol. 153, No. 7, 704-714.
25. Hastie, T. J. and Tibshirani, R. J. (1986), “Generalized Additive Models,” Statistical Science, Vol. 1, No. 3, 297-318.
26. Hastie, T. J. and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman and Hall.
27. Hwang, J.-S., Chen, Y.-J., Wang, J.-D., Lai, Y.-M., Yang, C.-Y. and Chan, C.-C. (2000), “Subject-Domain Approach to the Study of Air Pollution Effects in Schoolchildren’s Illness Absence,” American Journal of Epidemiology, Vol. 152, No. 1, 67-74.
28. Hwang, J.-S. and Chan, C.-C. (2002), “Effects of Air Pollution on Daily Clinic Visits for Lower Respiratory Tract Illness,” American Journal of Epidemiology, Vol. 155, No. 1, 1-10.
29. Hwang, J.-S., Hu, T. H. and Chan, C. C. (2004), “Air Pollution Mix and Emergency Room Visits for Respiratory and Cardiac Diseases in Taipei,” Journal of Data Science, Vol. 24, No. 4. (in press).
30. Jorgensen, B., Christensen, S. L., Song, X.-K. and Sun, Li. (1996), “A Longitudinal of Emergency Room Visits and Air Pollution for Prince George, British Columbia,” Statistics in Medicine, Vol. 15, 823-836.
31. Knorr-Held, L. (1999), “Bayesian Modeling of Inseparable Space-Time Variation in Disease Risk,” Technical Report.
32. Korn, E. L. and Whittemore, A. S. (1979), “Methods for Analyzing Panel Studies of Acute Health Effects of Air Pollution,” Biometrics, Vol. 35, 795-802.
33. Lawson, A. B. (1994), “Using Spatial Gaussian Priors to Model Heterogeneity in Environment Epidemiology,” The Statistician, Vol. 43, No. 1, 69-76.
34. Lin, M., Chen, Y., Villeneuve, P. J., Burnett, R. T., Lemyre, L., Hertzman, C., McGrail, K. M. and Krewski, D. (2004), “Gaseous Air Pollutants and Asthma Hospitalization of Children with Low Household Income in Vancouver, British Columbia, Canada,” American Journal of Epidemiology, Vol. 159, No. 3, 294-303.
35. McCulloch, C. E. and Searle, S. R. (2001), Generalized, Linear, and Mixed Models, New York: John Wiley and Sons, Inc.
36. McCullagh, P. and Nelder, J. A. (1989), Generalized Linear Models, 2nd ed., London: Chapman and Hall.
37. McNeny, B. and Petkau, J. (1994), “Overdispersed Poisson Regression Models for Studies of Air Pollution and Human Health,” The Canadian Journal of Statistics, Vol. 22, No. 4, 421-440.
38. Pinheiro, J. C. and Bates, D. M. (2000), Mixed-Effects Models in S and S-PLUS, New York: Spring-Verlag.
39. Press, S. J. (2003), Subjective and Objective Bayesian Statistics, 2nd ed., New York: John Wiley and Sons, Inc.
40. Tanner, M. A. (1996), Tools for Statistical Inference, 3rd ed., New York: Spring-Verlag.
41. Zidek, J. V., White, R., Le, N. D., Sun, W. and Burnett, R. T. (1998), “Imputing Unmeasured Explanatory Variables in Environmental Epidemiology with Application to Health Impact Analysis of Air Pollution,” Environmental and Ecological Statistics, Vol. 5, 99-115.