應用感染鍊二項模式及隨機概念分析流行性感冒家戶資料 - 運用貝式統計

Application of Chain Binomial Model with Stochastic Concept to Influenza Household Data - A Bayesian Approach

許辰陽(Chen-Yang Hsu)

指導教授 ： 陳秀熙

國立臺灣大學/公共衛生學院/流行病學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.02224

摘要

摘 要
背景
感染鏈模式在1989年由Becker 提出，主要用於分析家戶內的疾病傳播資料。雖然感染鏈模式在基於條件二項分佈以及感染世代的架構下適合用於分析疾病傳播之演進，但此一模式有其固有之限制。首先，識別度(identifiability)以及過度參數化(overparameterization)使的將無法觀測的潛在的感染鏈模式運用於分析感染症常見的實際觀察資料時有所困難。其次，連續世代之逃脫感染聯合機率乃基於世代間之轉移以及條件獨立假設，此一假設在感染鏈模式中並未詳細闡明。再者，由 Becker 所提出的二項模式無法進一步分析資料中不同階層的變異性對於逃脫機率之影響。
藉著運用感染鏈模式的觀念，本文基於隨機過程建構了聯合機率；並運用貝氏共軛對方法在模式中納入參數的不確定性。貝氏階層模式(Bayesian Hierarchical model) 則運用於分析資料中不同層級的變異性，使得模式運用更符合生物特性，也使不同假說之比較得以進行。

方法與材料
本文首先以隨機過程方法探討感染鏈模式之建構。感染鏈模式可以一階馬可夫鏈的方式建立；基於隨機過程之概念，可以推演出兩個簡化模式：Greenwood 以及 Reed-Frost 模式的轉移機率矩陣。貝氏共軛對可運用於加入對於參數不確定性的描述，並建立包含此一特性的轉移機率矩陣。
貝氏階層模式則運用於分析家戶資料中在世代階層以及家戶階層中的變異，並且加入個體間的變異。
此一家戶資料是收集台北縣以群體為基礎的家戶資料。病例定義乃基於臨床診斷。個體資料收集了性別、年齡、施打流感疫苗情形以及診斷為病例之日期。家戶資料則收集了家戶內成員以及家戶人數。
本文首先運用General Becker’s model 以及 Becker’s GLM model 分析資料。貝氏階層模式則用於進一步分析不同階層間的變異以及衡量個體因素差異對於罹病的影響。

結果
General Becker’s model 分別考慮世代效應與不考慮世代效應之模式下得到的逃脫感染機率估計值約為 0.90-0.98。 過度參數化以及辨識度的問題表現於信賴區間過寬以及估計值超出合理範圍。 Becker 提出的數種模式中，以家戶隨機效應模式採用Greenwood 假說可得到與資料最佳之配適。 如同General Becker’s model， Berker’s GLM model 也有過度參數化以及辨識度的問題。
貝氏階層模式分析顯示模式中必須包含參數在世代階層以及家戶階層的隨機效應。

結論
本文藉著提出貝氏共軛對方法以及貝氏階層模式，使感染鏈模式的應用得以更為廣泛，也使的感染鏈模式中的統計問題得以解決。這些基於隨機過程的新模式，使應用模式分析流行性感冒資料更精確也更符合感染症的傳播特性。

關鍵字

家戶資料 ； 流行性感冒 ； 貝氏統計 ； 感染鏈模式

並列摘要

Abstract

Introduction
Proposed by Becker in 1989, chain model is used to analyze spread of disease within household. Although the chain model is suitable for modeling elaboration of disease in the frame of conditional binomial distribution and the setting of generation, there exist several inherent problems. First, identifiability and overparameterization hampered the application of the unobserved chain model to the observed size data, which is the often encountered type of data in infectious disease. Second, the joint probability in the successive generations of disease spreading is based on the assumption of conditional independence and the transition from generation to generation, which have not been addressed clearly. Third, incorporating the heterogeneity occurred from different levels of data structure is not possible in the standard approach of chain model proposed by Becker.
By using the concept of chain model, we delineated the construction of joint probability by stochastic process and using Bayesian conjugated approach to incorporate the uncertainty of parameters. Bayesian Hierarchical model was used to tackle the problem of multilevel heterogeneity in the data to apply the chain model with more biological plausibility and potent for hypothesis testing.
Material and Methods
Revisiting the chain model in the viewpoint of stochastic process was performed. The chain model was reformed into first-order Markov process and the transition matrix was derived for two simplified models, Greenwood and Reed-Frost methods, based on the concept of stochastic process. Bayesian conjugated approach was applied to incorporate the uncertainty of the parameters. The corresponding transition matrix for two aforementioned models based on stochastic concept and Bayesian conjugated approach was constructed.
Bayesian Hierarchical model was then applied to incorporate the heterogeneity of generation level and household level and accommodate individual characters to the chain model using household data.
The data is a population-based household data collected in Taipei county using clinical diagnosis of influenza as the definition of case. Information on individual level such as gender, age, status of vaccination and the date of diagnosis was collected. Information on household level such as the specific household one belongs to, number of household members was obtained.
General Becker’s model and Becker’s GLM model was first applied. The Bayesian Hierarchical model was then used to model the multilevel heterogeneity and evaluating the effect of individual factors.
Results
General Becker’s model with and without generation effect was fitted with the estimated escape probability around 0.90 – 0.98. Overparameterization and identifiability was reflected by wide confidence interval and the unreasonable value of estimates. Of models proposed by Becker, random household effect model with Greenwood assumption fits the data best. The effect of individual character was also observed by applying models to data treating those who were vaccinated as immune or still susceptible. As it is in general Becker’s mode, Becker’s GLM model was also subject to the problems of overparameterization and identifiability.
Bayesian Hierarchical model was then applied, which revealed the necessity to allow parameters to vary in household and generation levels.

Conclusion
The current thesis expanded chain binomial model by proposing a novel Bayesian conjugated and hierarchical model under Greenwood assumption to solve several statistical problems that cannot be solved in the previous chain model. These new statistical models under the concept of stochastic process can provide more precise and biological plausibility for studying the outbreak of influenza.

並列關鍵字

household data ； influenza ； Bayesian ； chain binimoal model

參考文獻

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