Application of Chain Binomial Model with Stochastic Concept to Influenza Household Data A Bayesian Approach
Date Issued
2009
Date
2009
Author(s)
Hsu, Chen-Yang
Abstract
Abstractntroductionroposed 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. y 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. aterial and Methodsevisiting 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. ayesian 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.he 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.eneral 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.esultseneral 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.ayesian Hierarchical model was then applied, which revealed the necessity to allow parameters to vary in household and generation levels. onclusionhe 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.
Subjects
household data
influenza
Bayesian
chain binimoal model
SDGs
Type
thesis
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