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| 研究生： |
王泰期 Wang, Tai Chi |
|---|---|
| 論文名稱： |
空間自相關模型下空間群聚檢定 Spatial Clusters in a Global-dependence Model |
| 指導教授： | 余清祥 |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2013 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 107 |
| 中文關鍵詞： | 群聚偵測 、空間自相關 、空間掃描統計量 、空間自相關模型 、EM演算法 |
| 相關次數： | 點閱：155 下載：38 |
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因為疾病空間模式通常會與環境中的危險因子有很強烈的關聯性，因此流行病學家與社會大眾都對疾病的空間模式感到興趣。舉例來說，空間群聚就是一項非常受到重視的疾病空間模式，在眾多的空間群聚檢定方法種，Kulldorff和 Nagarwalla在1995年提出的空間掃描統計量是相當受到廣泛應用的方法，雖然這個統計方法可以檢定初空間資料的異質性，但是卻沒有辦法區隔這些異質性是來自於整體空間資料的相關性或是局部的空間群聚。在本篇論文中，我們將分別提出計次型的統計方法與貝氏統計方法兩種類型的空間群聚檢定方法來處理這樣的問題，其中計次型的統計方法為一兩階段的統計方法，首先採用EM演算法來估計空間自相關，並根據估計的結果與掃描窗格在偵測空間群聚；另一方面，貝氏方法則考慮加入群聚的中心位置及半徑作為事前的機率分布，進而透過MCMC的方法來計算出後驗分布的結果。除此之外，北卡羅來納的嬰兒猝死症和台灣老年人口癌症死亡資料將被用來示範與評價不同群聚檢定方法的差異與效果。
Contents
1 Introduction 11
2 Definitions of Cluster Patterns and The SaTScan 15
2.1 Definitions of clustering and local cluster . . . . . . . . . . . . 16
2.2 The SaTScan . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Simulation settings . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Simulation results of the SaTScan . . . . . . . . . . . . . . . . 20
2.5 Estimate of autocorrelation . . . . . . . . . . . . . . . . . . . 26
3 Frequentist Methods for Cluster Detection 29
3.1 Gaussian Method . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 The CAR model . . . . . . . . . . . . . . . . . . . . . 30
3.1.2 Approximation of CAR model . . . . . . . . . . . . . . 32
3.1.3 Pseudo-likelihood . . . . . . . . . . . . . . . . . . . . . 33
3.1.4 EM algorithm . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.5 Cluster model . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.6 Monte Carlo testing procedure . . . . . . . . . . . . . . 38
3.2 Auto-Poisson Method . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 Auto-Poisson model . . . . . . . . . . . . . . . . . . . 39
3.2.2 EM algorithm . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 Cluster detection . . . . . . . . . . . . . . . . . . . . . 44
3.2.4 Monte Carlo testing procedure . . . . . . . . . . . . . . 44
4 Bayesian Model for Cluster Detection 47
4.1 The spatial Bayesian model . . . . . . . . . . . . . . . . . . . 48
4.2 BYM model with clustered effects . . . . . . . . . . . . . . . . 49
4.3 Inference of clustered effects . . . . . . . . . . . . . . . . . . . 51
5 Simulations and Method Comparisons 55
5.1 EM estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Cluster detection results . . . . . . . . . . . . . . . . . . . . . 59
5.3 Brief summary . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Empirical Study 67
6.1 Sudden Infant Disease Syndrome . . . . . . . . . . . . . . . . 67
6.1.1 The SaTScan result . . . . . . . . . . . . . . . . . . . . 68
6.1.2 The result of the EM-Scan Gaussian method . . . . . . 69
6.1.3 The result of the EM-Scan auto-Poisson method . . . . 72
6.1.4 Results of the Bayesian model . . . . . . . . . . . . . . 73
6.2 Taiwan cancer data . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2.1 The cluster detection results . . . . . . . . . . . . . . . 75
6.3 Brief Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7 Conclusion and Discussion 83
7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Bibliography 94
A Partial Derivatives of CAR Model 95
B Estimates of Pseudo-Likelihood 97
C Consistence of Pseudo-Likelihood Estimates 99
D Metropolis-Hastings algorithm 103
E WinBUGS Code 105
Anselin, L. (1995). Local indicators of spatial associationlisa. Geographical analysis, 27 (2), 93–115.
Banerjee, S., Carlin, B., & Gelfand, A. (2004). Hierarchical Modeling and Analysis for Spatial Data. Chapman & Hall: London.
Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological), 36 (2), 192–236.
Besag, J. (1975). Statistical analysis of non-lattice data. The statistician, 179–195.
Besag, J. (1977). Efficiency of pseudo-likelihood estimation for simple gaussian fields. Biometrika, 64 , 616–618.
Besag, J. & Newell, J. (1991). The detection of clusters in rare diseases. Journal of the Royal Statistical Society. Series A (Statistics in Society), 143–155.
Besag, J., York, J., & Molli´e, A. (1991). Bayesian image restoration, withtwo applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43 (1), 1–59.
Best, N., Richardson, S., & Thomson, A. (2005). A comparison of bayesian spatial models for disease mapping. Statistical Methods in Medical Research, 14 (1), 35–59.
Clayton, D. & Bernardinelli, L. (1992). Bayesian methods for mapping disease risk. In P. Elliott, J. Cuzick, D. English, and R. Stern (Eds.), Geographical and Environmental Epidemiology: Methods for Small-Area Studies. Oxford: Oxford University Press.
Cressie, N. (1993). Statistics for Spatial Data, revised edition. Wiley: New York.
Cressie, N. & Chan, N. (1989). Spatial modeling of regional variables. Journal of the American Statistical Association, 84 (406), 393–401.
Gangnon, R. & Clayton, M. (2000). Bayesian detection and modeling of spatial disease clustering. Biometrics, 56 (3), 922–935.
Geary, R. (1954). The contiguity ratio and statistical mapping. The incorporated statistician, 5 (3), 115–146.
Getis, A. & Ord, J. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24 (3), 189–206.
Hammersley, J. M. & Clifford, P. (1971). Markov fields on finite graphs and lattices. 1971. Unpublished manuscript, cited in [Ish81].
Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57 (1), 97–109.
Huang, L., Kulldorff, M., & Gregorio, D. (2007). A spatial scan statistic for survival data. Biometrics, 63 (1), 109–118.
Huang, L., Pickle, L. W., & Das, B. (2008). Evaluating spatial methods for investigating global clustering and cluster detection of cancer cases. Statistics in Medicine, 27 (25), 5111–5142.
Jung, I. (2009). A generalized linear models approach to spatial scan statistics for covariate adjustment. Statistics in Medicine, 28 (7), 1131–1143.
Jung, I., Kulldorff, M., & Klassen, A. (2007). A spatial scan statistic for ordinal data. Statistics in Medicine, 26 (7), 1594–1607.
Knox, E. & Bartlett, M. (1964). The detection of space-time interactions. Journal of the Royal Statistical Society. Series C (Applied Statistics), 13 (1), 25–30.
Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics-Theory and Methods, 26 (6), 1481–1496.
Kulldorff, M. (2001). Prospective time periodic geographical disease surveillance using a scan statistic. Journal of the Royal Statistical Society: Series A (Statistics in Society), 164 (1), 61–72.
Kulldorff, M. (2006). Tests of spatial randomness adjusted for an inhomogeneity: a general framework. Journal of the American Statistical Association, 101 (475), 1289–1305.
Moran, P. (1950). Notes on continuous stochastic phenomena. Biometrika, 17–23.
Openshaw, S., Charlton, M., Craft, A., & Birch, J. (1988). Investigation of leukaemia clusters by use of a geographical analysis machine. The Lancet , 331 (8580), 272–273.
Ord, J. K. & Getis, A. (1995). Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27 (4), 286–306.
Ord, J. K. & Getis, A. (2001). Testing for local spatial autocorrelation in the presence of global autocorrelation. Journal of Regional Science, 41 (3), 411–432.
Patil, G. & Taillie, C. (2004). Upper level set scan statistic for detecting arbitrarily shaped hotspots. Environmental and Ecological Statistics, 11 (2), 183–197.
Rencher, A. (2000). Linear Models in Statistics. Wiley: New York.
Richardson, S., Thomson, A., Best, N., & Elliott, P. (2004). Interpreting posterior relative risk estimates in disease-mapping studies. Environmental Health Perspectives, 112 (9), 1016–1025.
Spiegelhalter, D., Thomas, A., Best, N., & Lunn, D. (2003). Winbugs user manual. Cambridge: MRC Biostatistics Unit .
Tango, T. & Takahashi, K. (2005). A flexibly shaped spatial scan statistic for detecting clusters. International Journal of Health Geographics, 4 (1), 11.
Thomas, A., Best, N., Lunn, D., Arnold, R., & Spiegelhalter, D. (2004). Geobugs user manual. Cambridge: MRC Biostatistics Unit .
Tiefelsdorf, M., Griffith, D., & Boots, B. (1999). A variance-stabilizing coding scheme for spatial link matrices. Environment and Planning A, 31 (1), 165–180.
Turnbull, B., Iwano, E., Burnett, W., Howe, H., & Clark, L. (1990). Monitoring for clusters of disease: application to leukemia incidence in upstate new york. American Journal of Epidemiology, 132 (supp1), 136–143.
Wang, T.-C. & Yue, C.-S. J. (2013a). A binary-based approach for detecting irregularly shaped clusters. International journal of health geographics, 12 (1), 25.
Wang, T.-C. & Yue, C.-S. J. (2013b). Spatial clusters in a global-dependence model. Spatial and Spatio-temporal Epidemiology, 5 , 39–50.
Zeger, S. L., Liang, K.-Y., & Albert, P. S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics, 1049–1060.
