連續型變數之記數過程在傳染病資料上之應用

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：35

、訪客IP：18.222.147.4

姓名

陳中興(Chung-Hsing Chen) 查詢紙本館藏

畢業系所

數學系

論文名稱

連續型變數之記數過程在傳染病資料上之應用
(Counting process approach to infectious disease data with continuous covariates)

相關論文

★ 用Pfam-A建議BLAST之計分表(Scoring Matrix)與空格罰分(Gap Penality)	★ Motif長度未知之貝氏多重序列比對方法
★ 現狀家庭數據在相關伽瑪致病傾向模型之無母數估計	★ 伯氏先驗分布在貝氏存活分析與貝氏遞升迴歸的應用
★ 利用兄弟數據之多點遺傳連鎖分析方法	★ 半母數混合模型估計的一致性及其應用
★ 隨機右設限數據之風險率的貝氏估計方法	★ 利用Bernstein多項式來研究二元迴歸
★ 從傳染病家庭資料估計與時間相關的傳佈參數	★ 數據依賴誤差之階梯函數迴歸的貝氏方法
★ 由伯氏多項式對形狀限制的回歸函數定義最大概似估計量

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

這篇論文提出一個分析傳染病資料的新模型與演算法。利用點過程（point process）並且考慮連續型的解釋變數（continuous explanatory variable）以及更廣泛的感染函數（infectivity function）去建構出家庭中每一個人被感染與被移除（removal）的條件機率。
我們定義兩個記數過程（counting process），各自代表著在一個家庭中每一個人何時被感染與何時被移除。這些發生的條件機率可以用來描述傳染病的擴散速度；同時，這些條件機率也受到一些個人的特徵與我們設計的函數所影響。我們利用貝氏分析（Bayesian inference）裡常用的馬可夫鏈蒙地卡羅（Markov Chain Monte Carlo）演算法發展出一種特別的演算法¬，並且用它分析傳染病的特性與人的特徵對傳染病的影響；包括分析模擬的結果以及分析真實資料的結果。

摘要(英)

This paper proposes a point process model for infectious disease data that take into consideration continuous explanatory variables regarding infectivity, susceptibility to infection and removal rate and allow parametric family of baseline infectivity functions.
For each individual in a closed community, we define two counting processes; one jumps when this individual gets infected and the other jumps when this individual gets removed. The intensities of these counting processes are used to describe the spread of the infectious disease. These intensities have one component describing the way that individual covariates may affect infectivity, susceptibility to infection or removal; these intensities also have a baseline infectivity function, belonging to a parametric family of functions. Customized MCMC algorithms are developed for Bayesian inference based on removal times and covariates of each individual. Simulation studies and analysis of real infectious data are provided to illustrate the numerical performance of the methods.

關鍵字(中)

★ 記數過程
★ 傳染病

關鍵字(英)

★ counting process
★ infectious disease

論文目次

Contents
1 Introduction 1
2 A point process model for infectious disease data 5
2.1 The model ......................................... 5
2.2 Identifiability of the parameters ................. 8
2.3 The likelihood .................................... 11
3 Bayesian inference based on removal times 13
3.1 Inference when the epidemic is over ............... 13
3.2 Inference during the epidemic ..................... 17
4 Simulation studies 23
4.1 Generating data for point processes ............... 23
4.2 Final size of the epidemics ....................... 24
4.3 Performance of the algorithms ..................... 26
5 Application to smallpox data 31
6 Measuring the missing information 33
7 Discussion 36
References 38

參考文獻

Aalen, O. O. (1980) A model for non-parametric regression analysis
of counting processes. Lecture Notes in Statist, 2, 1-25, Springer,
New York.
Addy, C. L., Longini, I. M. and Haber, M. (1991) A generalized
stochastic model for the analysis of infectious disease final size
data. Biometrics, 47, 961-974.
Andersson, H. and Britton, T. (2000) Stochastic Epidemic Models and
Their Statistical Analysis. Springer Lecture Notes in Statistics,
New York.
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious
Diseases and its Applications. Griffin, London.
Bailey, N. T. J. and Thomas, A. S. (1971) The estimation of
parameters from population data on the general stochastic epidemic.
Theor. Pop. Biol., 2, 53-70.
Baker, R. D. and Stevens, R. H. (1995) A random-effects model for
analysis of infectious disease final-state data. Biometrics, 51,
956-968.
Ball, F. (1986) A unified approch to the distribution of total size
and total area under the trajectory of infectives in epidemic
models. Adv. Appl. Prob., 18, 289-310.
Ball, F., Mollison, D. and Scalia-Tomba, G. (1997) Epidemics with
two levels of mixing. Ann. Appl. Prob., 7, 46-89.
Becker, N. G. (1989) Analysis of Infectious Disease Data.} Chapman &
Hall, London.
Becker, N. G. and Britton, T. (1999) Statistical studies of
infectious disease incidence. J. R. Statist. Soc. B, 61, 287-307.
Becker, N. G. and Hopper, J. L. (1983) The infectiousness of a
disease in a community of households. Biometrika}, 70, 29-39.
Becker, N. G. and Yip, P. (1989) Analysis of variation in an
infection rate. Australian Journal of Statistics, 31, 42-52.
Bremaud, P. (1981) Point Processes and Queues, Martingale Dynamics.
Springer-Verlag, New York.
Britton, T. (1998) Estimation in multitype epidemics. J. R. Statist.
Soc. B, 60, 663-679.
Brooks, S. P. and Gelman, A. (1997) General methods for monitoring
convergence of iterative simulation. Journal of Computational and
Graphical Statistics, 7, 434-455.
Demiris, N. and O'Neill, P. D. (2005) Bayesian inference for
epidemics with two levels of mixing. Scand. J. Statist., 32,
265-280.
Green, P. J. (1995) Reversible jump Markov chain Monte Carlo
computation and Bayesian model determination. Biometrika, 82, Part
4, 711-732.
Hethcote, H. W. and Van Ark, J. W. (1987) Epidemiological models for
heterogeneous populations: proportionate mixing, parameter
estimation and immunization programs. Math. Biosci., 84, 85-118.
Longini, I. M. and Koopman, J. S. (1982) Household and community
transmission parameters from final distributions of infections in
households. Biometrics, 38, 115-126.
Nicolae, D. L., Meng, X.-L. and Kong, A. (2008) Quantifying the
fraction of missing information for hypothesis testing in
statistical and genetic studies. Statistical Science, To appear.
O'Neill, P. D. and Becker, N. G. (2001) Inference for an epidemic
when susceptibility varies. Biostatistics, 2, 99-108.
O'Neill, P. D. and Roberts, G. O. (1999) Bayesian inference for
partially observed stochastic epidemics. J. R. Statist. Soc. A, 162,
121-129.
Rhodes, P. H., Halloran, M. E. and Longini, I. M. (1996) Counting
process models for infectious disease data: distinguishing exposure
to infection from susceptibility. J. R. Statist. Soc. B, 58,
751-762.
Robert, C. P. and Casella, G. (2004) Monte Carlo Statistical Methods
(2nd Edition). Springer-Verlag, New York.
Thompson, D. and Foege, W.(1968) Faith Tabernacle smallpox epidemic.
AbakaJiki, Nigeria. Geneva, Switzerland: World Health
Organization. (WHO/SE/68.3) (http://
whqlibdoc.who.int/smallpox/SE\_68.3.pdf).

指導教授

張憶壽、熊昭
(I-Shou Chang、Chao A. Hsiung)

審核日期

2008-7-1

推文