Ioannis Ntzoufras

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Bayesian analysis of the differences of count data

(old title: Bayesian Analysis of Paired Count Data)

Dimitris Karlis and Ioannis Ntzoufras (2006)

Statistics in Medicine Statistics in Medicine 25, 1885-1905.

Abstract

Paired count data usually arise in medicine when we consider measurements  before and after treatment. Although continuous measurements have been treated thoroughly in the past, research on paired count data is limited. In the present paper we initiate our work using the assumption that the correlated paired count data follow a bivariate Poisson distribution in order to derive the distribution of their difference. This distribution is used for hypothesis testing under both classical and Bayesian framework. The derived distribution is shown to be the same to the one derived for the difference of the independent Poisson counts, thus recasting interest on the distribution introduced by Skellam (1946). Using this distribution we remove correlation, which naturally exists on paired data, and we improve the quality of our inference since we use exact distributions instead of normal approximationsEstimation procedures based on the Bayesian theory are presented and discussed in detail. Finally, we construct frequentist and Bayesian hypotheses tests. Examples are used to illustrate the proposed methodology.

Keywords: Bivariate Poisson distribution; Difference of random variables; EM algorithm; Hypothesis Tests, MCMC, Reversible Jump, Zero-inflated distributions.

[ Download paper from Statistics in Medicine]

[Additional Details: Chib's Method - 3/3/2005]

[Oral Presentation in 3rd World Conference on CSDA]

Statistics in Medicine (to appear)

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