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CD4 count is used to measures the number CD4 cells in the blood mostly during ART treatment to know the risk progression of HIV in the HIV infected patients. This continuously measured CD4 count during the treatment period results longitudinal data having correlation and over dispersion effects. While modeling such data to identify associated factors of change in CD4 count to monitor the progression of HIV most of the study did not considered these two main effects. The main aim of this study was also to consider these two main effect to identify the risk factors CD4 count progression based on 239 HIV infected TB patients who were 18 years old and above taking ART treatment from $1^{st}$ September 2009 to $1^{st}$ July 2014 at Jimma University Specialize Hospital. The result of study showed Poisson normal Gamma combine model which handles correlation and over dispersion effects of CD4 count simultaneously was an appropriate fit of the data among different Poisson mixed combined models considered for the study based on Akaki information criteria (AIC)comparisons. The estimated model depicts linear time and it's interaction effect with functional status category group of the patients have positive effect whereas quadratic time has the negative effect on the progression of CD4 count. The model also showed baseline bedridden and ambulatory functional status group patients has lower average CD4 count measurements in comparison with working functional status group patients counterparts. Therefore, while modeling CD4 count correlation and over dispersion should be taken in to consideration since the CD4 count value was correlated due to repeated measurement and it's variance larger than mean leading to over dispersion. Being at bedridden, ambulatory functional status at baseline in comparison with working functional status group and having quadratic time effects were also the associated risk factors that lowers the CD4 count measurements of the patients during the ART treatment period at the study area.

international journal of statistics and probability

Application of Poisson Mixed Combined Models for Identifying Correlations of CD4 Count Progression in HIV Infected TB Patients During ART Treatment Period