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Medical Applications of Finite Mixture ModelsModeling Count Data

Medical Applications of Finite Mixture Models: Modeling Count Data Chapter 3 As already emphasized in Chap. 2, patients are not alike. Sometimes there is sub- stantial variability between patients which cannot be immediately explained by known covariates. For example, the frequency of symptoms may show consider- able heterogeneity. Often covariates which are responsible for this behavior are not known or not observable. As a result, this phenomenon is frequently called unob- served heterogeneity. From a biostatistical perspective the statistician needs to find a suitable model which identifies unobserved heterogeneity and which if covariates are available accounts for these known covariates. In this chapter this type of model is applied to count data. 3.1 Example: Morbidity in Northeast Thailand In a cohort study in northeast Thailand the health status of 602 preschool children was checked every 2 weeks from June 1982 until September 1985 (Schelp et al. 1990). In this time period it was recorded how often the children showed symptoms of fever, cough, running nose, or these symptoms together. The frequencies of these illness spells are given in Table 3.1. The data set has been discussed by several authors (Bohning ¨ et al. 1992; Eilers 1995). Frequently for this kind of count data a Poisson distribution with X http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Medical Applications of Finite Mixture ModelsModeling Count Data

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Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2009
ISBN
978-3-540-68650-7
Pages
1 –26
DOI
10.1007/978-3-540-68651-4_3
Publisher site
See Chapter on Publisher Site

Abstract

Chapter 3 As already emphasized in Chap. 2, patients are not alike. Sometimes there is sub- stantial variability between patients which cannot be immediately explained by known covariates. For example, the frequency of symptoms may show consider- able heterogeneity. Often covariates which are responsible for this behavior are not known or not observable. As a result, this phenomenon is frequently called unob- served heterogeneity. From a biostatistical perspective the statistician needs to find a suitable model which identifies unobserved heterogeneity and which if covariates are available accounts for these known covariates. In this chapter this type of model is applied to count data. 3.1 Example: Morbidity in Northeast Thailand In a cohort study in northeast Thailand the health status of 602 preschool children was checked every 2 weeks from June 1982 until September 1985 (Schelp et al. 1990). In this time period it was recorded how often the children showed symptoms of fever, cough, running nose, or these symptoms together. The frequencies of these illness spells are given in Table 3.1. The data set has been discussed by several authors (Bohning ¨ et al. 1992; Eilers 1995). Frequently for this kind of count data a Poisson distribution with X

Published: Dec 8, 2008

Keywords: Mixture Model; Bayesian Information Criterion; Negative Binomial Distribution; Poisson Regression Model; Likelihood Ratio Statistic

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