A Bayesian Joint Model Of Longitudinal And Time-to-event Data For The Aids Treatment Effectiveness Evaluation

Chinese government started providing highly active antiretroviral therapy(HAART)free of charge in 2004.However,up to date,few model-based studies for the treatment effectiveness evaluation of Chinese HAART have been published and almost all of these studies just only focus on modeling CD4 data(CD8 etc.)without taking into account the correlation between CD4 and survival data.Such use of independent models can cause biased estimates in the treatment effectiveness evaluation of Chinese HAART.To handle this correlation,a joint modelling approach is needed.In the traditional joint models of a longitudinal and time-to-event data,a linear mixed effects model assuming normal random errors is used to model the longitudinal process.However,in many HIV clinical data especially in Chinese HIV clinical data,the normality assumption is violated and the linear mixed model is not an appropriate sub-model in the joint models.In addition the quantiles of the longitudinal process is the main concern of the clinician.So we adopt a fully Bayesian version that the linear quantile mixed model for the longitudinal process in the joint model,implemented via Bayesian Method and Markov chain Monte Carlo(MCMC)methods to estimate the parameters in our joint model.We use the approach to jointly model the longitudinal and survival data from an AIDS clinical trial comparing two treatments to illustrate the good performance of our method.As a comparison we construct the traditional joint models of a longitudinal and time-to-event data.Although the AIC and BIC values of the linear quantile mixed model are larger than the linear mixed model,the fitting residuals of the longitudinal process based on the linear quantile mixed model are more densely clustered around the standard residual line,and the residuals' QQ plot is closer to the normal distribution,indicating that when the linear quantile mixed model is used to replace the linear mixed model in the traditional joint model,the data fitting effect will be better.Moreover,our method provides quantile-specific parameter estimates at a set of different quantiles and the clinicians can choose the quantiles of interest and the corresponding inference.