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This article aims to joint modeling of longitudinal CD4 cells count and time to death in HIV patients based on the AFT model. The modeling of the longitudinal count response, a GLME model under the family of PSD, was used. In contrast, for the TTE data, the parametric AFT model under the Weibull distribution was investigated. These two responses are linked through random effects correlated with the normal distribution. The longitudinal and survival data are then assumed independent, given the latent linking process and any available covariates. Considering excess zeros for two responses and right censoring, presented a joint model that has not yet been investigated by other researchers. The parameters were also estimated using MCMC methods.

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 In this paper, a new Dirichlet process mixture model with the generalized inverse Weibull distribution as the kernel is proposed. After determining the prior distribution of the parameters in the proposed model, Markov Chain Monte Carlo methods were applied to generate a sample from the posterior distribution of the parameters. The performance of the presented model is illustrated by analyzing real and simulated data sets, in which some data are right-censored. Another potential of the proposed model demonstrated for data clustering. Obtained results indicate the acceptable performance of the introduced model.