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Abstract:
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In count data, the high counts that spread at right tail often augment overdispersion to an extent. A maximum likelihood ?t of a generalized regression model is sensitive to these extreme responses. Conventional methods such as removing patients with extreme high counts may cause bias and violate the intent-to-treat principle. Using transformation to reduce the impact from extreme values may not solve the problem, in addition, it changes the endpoint which may affect the clinical interpretation. In this presentation, we propose a mixture of Negative Binomial distribution and Bernoulli probability mass function to fit the count data with heavy high counts and overdispersion. Furthermore, we evaluate the sensitivity of the analysis using a tipping point to determine the threshold that separate the extreme values in Bernoulli probability mass function. The performance of several models under various scenarios, such as number of extreme counts and degree of over-dispersion are compared with simulations and show that the proposed models are more efficient than the conventional approaches.
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