Background: The prevalence of HIV is increasing in Iran, so obtaining an estimate of the survival of HIV-infected persons can be helpful to prevent and control this infection. Objectives: This research aimed to use the Bayesian joint model by which identifies factors associated with the survival and determine the relationship between the trend of CD4 + T cell counts and survival time in HIV-infected persons. Methods: In this retrospective cohort study, we collected HIV/AIDS surveillance data from Mashhad's Counseling Center of Behavioral Diseases in the province of Khorasan Razavi, Northeast of Iran, during 1994-2014. Data collection included variables CD4 + T cells count, survival time, and other related factors. We used the Bayesian joint model to estimate the survival time and identify the factors associated with survival time in HIV-infected persons. Results: The study included 260 individuals, of whom 212 (81.54%) were male. The survival sub-model of the joint model identified gender (95% credible interval (CI): 0.486, 3.197) and antiretroviral treatment (95% CI:-1.935,-0.641) as the variables associated with the patients' survival. The longitudinal sub-model, which determined the variables associated with the number of CD4 + T-cells included time (95% CI:-0.934,-0.554), age (95% CI:-0.152,-0.011), and antiretroviral treatment (95% CI:-6.193,-3.505). Conclusions: Using CD4 + T cells as a covariate in the Bayesian joint model, the survival time for HIV-infected persons was estimated more precisely than separate model and it can be inferred that at the beginning of antiretroviral treatment, especially in men and controls, the CD4 + T cell counts can increase the survival time of HIV-infected persons.

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In order to give an excellent description of income distributions, although a large number of functional forms have been proposed, but the four-parameter generalized beta model of the second kind (GB2), introduced by J. B. McDonald [18], is now widely acknowledged which is including many other models as special or limiting cases.One of the fundamentals of statistical inference is the estimation problem of a function of unknown parameter in a probability distribution and computing the variance of the estimator or approximating it by lower bounds.In this paper, we consider two famous lower bounds for the variance of any unbiased estimator, which are Bhattacharyya and Kshirsagar bounds. We obtain the general forms of the Bhattacharyya and Kshirsagar matrices in the GB2 distribution. In addition, we compare different Bhattacharyya and Kshirsagar bounds for the variance of any unbiased estimator of some parametric functions such as mode, mean, skewness and kurtosis in GB2 distribution and conclude that in each case, which bound is better to use. The results of this paper can be useful for researchers trying to find the accuracy of the estimators.

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