Bayesian Joint Modelling of Survival of HIV/AIDS Patients Using Accelerated Failure Time Data and Longitudinal CD4 Cell Counts
Markos Abiso Erango *
School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia
Ayele Taye Goshu
School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia
Gemeda Bedaso Buta
Department of Statistics, Madda Walabu University, Ethiopia
Ahmed Hassen Dessiso
Department of Statistics, Madda Walabu University, Ethiopia
*Author to whom correspondence should be addressed.
Abstract
Objective: This paper aims to compare various Bayesian joint models based on the accelerated failure time distributions in analyzing longitudinal observations on CD4 cell counts as growth measurements and time-to-death events of HIV/AIDS patients. Three accelerated failure time distributions, namely, Weibull, lognormal and loglogistic distributions are considered.
Methods: We consider a total of 354 random sample of HIV/AIDS patients who had been under ART follow-up at Shashemene Referral Hospital in Ethiopia from January 2006 to December 2012. Linear mixed effects model is used for the longitudinal outcomes (square root of CD4 cell counts) with normality assumption, while three parametric accelerated failure time distributions are studied for the time-to-event data. The Bayesian joint models are defined with association parameters and analyzed using Gibbs sampler algorithm. Non-informative prior distributions are assumed. The model selection criteria DIC is employed to identify the model with best fit to the data. Another data set obtained by similar setting is also further analyzed using same models.
Results: Both data sets reveal hump-shaped hazard rate functions. The findings from all the Bayesian joint models are consistent. The association parameter in each Bayesian joint model is significant for Weibull and lognormal cases in the second data set. This implies that there is dependence between the two processes: longitudinal CD4 cell counts and the time-to-death event under Weibull and lognormal models. With investigation of the empirical hazard function and the DIC criteria, the Bayesian loglogistic and Bayesian lognormal are selected for the first and second data sets, respectively.
Conclusions: The joint models provide consistent results with higher precision as compared to their respective separate models. We recommend Bayesian joint AFT models for such data with careful consideration of shape of hazard rate functions that the data reveal.
Keywords: Accelerated failure time, Bayesian joint model, CD4 cell count, HIV/AIDS, linear mixed effects, Longitudinal, survival analysis