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研究生:陳中興
研究生(外文):Chung-Hsing Chen
論文名稱:連續型變數之記數過程在傳染病資料上之應用
論文名稱(外文):Counting process approach to infectious disease data with continuous covariates
指導教授:張憶壽張憶壽引用關係熊昭熊昭引用關係
指導教授(外文):I-Shou ChangChao A. Hsiung
學位類別:博士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:46
中文關鍵詞:記數過程傳染病
外文關鍵詞:counting processinfectious disease
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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。
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.
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
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