Longitudinal semi-continuous data, which contain a fair amount of zeros along with positive values, is common in biomedical, econometric and health research. The existence of missing values in this kind of data creates additional difficulty in analysis. This thesis proposes a Compound Poisson mixed model to analyse the semi-continuous data with missing data using a selection-model approach. In the literature, the two-part model has been used most frequently to analyse semi-continuous data. In the two-part model, the zero values and positive responses from the same subject are modeled separately (Liu et al., 2012). This separation of zero and non-zero values is likely to destroy the serial dependence structure among the repeated responses within subjects. Therefore, we modelled the zero and positive responses together of the semi-continuous data while considering multilevel random effects. Our work is motivated by Ma et al. (2007) and Hasan et al. (2009). They have proposed a multilevel random effects zero in ated Poisson model for the clustered count data with excess zeros. Furthermore they use patten-mixture model to deal with the dropouts in the longitudinal unbalanced data. Recently, Yan et al. (2016) also analyse the semi-continuous longitudinal data with Tweedie's compound Poisson based on orthodox best linear unbiased predictor (BLUP) of the random effects given the data. This thesis applies a Tweedie's compound Poisson mixed model for longitudinal semi-continuous data using a Bayesian approach. Our approach can accommodate both the zero and non-zero parts of the semi-continuous responses simultaneously with multilevel random effects. The regression parameters and the random effects parameters are estimated by using the Markov chain Monte Carlo (MCMC) algorithm of the Bayesian approach. The method is demonstrated on Fluoride intake data and BSI data. Both data sets consist of a large number of zero responses as well as a substantial amount of dropout. To account for both excessive zeros and dropout patterns, we use a selection-model with compound Poisson mixed random effects for the unbalanced longitudinal data. We also conduct a simulation study to verify the proposed model.

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