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Title: A new Bayesian joint model for longitudinal count data with many zeros, intermittent missingness, and dropout Authors:  Jing Wu - University of Rhode Island (United States) [presenting]
Ming-Hui Chen - University of Connecticut (United States)
Elizabeth Schifano - University of Connecticut (United States)
joseph ibrahim - University of North Carolina (United States)
jeffrey fisher - University of Connecticut (United States)
Abstract: In longitudinal clinical trials, it is common that subjects may permanently withdraw from the study (dropout), or return to the study after missing one or more visits (intermittent missingness). It is also routinely encountered in HIV prevention clinical trials that there is a large proportion of zeros in count response data. A sequential multinomial model is adopted for dropout and subsequently a conditional model is constructed for intermittent missingness. The new model captures the complex structure of missingness and incorporates dropout and intermittent missingness simultaneously. The model also allows us to easily compute the predictive probabilities of different missing data patterns. A zero inflated Poisson mixed-effects regression model is assumed for the longitudinal count response data. We also propose an approach to assess the ove all treatment effects under the zero-inflated Poisson model. We further show that the joint posterior distribution is improper if uniform priors are specified for the regression coefficients under the proposed model. Variations of the g-prior, Jeffreys prior, and maximally dispersed normal prior are thus established as remedies for the improper posterior distribution. An efficient Gibbs sampling algorithm is developed using a hierarchical centering technique. A modified logarithm of the pseudomarginal likelihood (LPML) is used to compare the models under different missing data mechanisms.