Abstract
Survival analysis has seen in recent times more of joint modelling of longitudinal and survival data using approximate hierarchical Bayesian method. This study modelled jointly multivariate and cure proportion with spatial variation using latent Gaussian models (LGMs). Spline specification was used to capture nonlinear trajectories of the multivariate longitudinal biomarkers in the LGM paradigm. Spatial dependence was assumed for neighbouring locations with an improper multivariate conditionally autoregressive prior on the spatial random effects, while inverse-Wishart prior was assumed for the covariance matrix of the random effects and Gaussian priors for the fixed effects. The penalised complexity prior was assumed for the Weibull shape parameters of the baseline hazard function for the event-time and binomial distribution for latent cure classification variable. Posterior distributions were evaluated using INLA. The study was applied to longitudinal and survival HIV/AIDS patients datasets. The random spatial variability was seen to be significant for both biomarkers, random intercept for BMI and cure probabilities. The full conditional distribution of latent variable gave a predicted cure proportion of 61%. The susceptible group on the hand, had a full conditional distribution of latent incidence variable predicting susceptible proportion of 39%. Flexibility of LGM for Bayesian hierarchical was demonstrated easily for multivariate joint model with spatial cure proportion.