A latent gaussian joint modelling of multivariate longitudinal and mixture cure outcomes with application to aortic valve replacement surgery data

This study examined the effects of different association structures and multivariate longitudinal trajectories, including linear, quadratic and spline functions, on the estimation of time to event and cure proportion under the latent Gaussian model approach with application aortic valve replacement surgery data. The Bayesian framework assumed inverse-Wishart prior distribution for the covariance matrix of the random effects and Gaussian priors for the joint model fixed effects, while the penalised complexity prior was assumed for the Weibull shape parameters of the baseline hazard function. Posterior distributions were evaluated using Integrated Laplace approximation. The modelling approach was applied to aortic valve replacement surgery data to assess the effects of covariates on three longitudinal biomakers on risk of death as well as prediction of cure proportion. Spline trajectories for the multivariate longitudinal biomakers with current slope association was the best fit for the data. The full conditional distribution of latent incidence variable predicted a cure proportion of 36.33% and type of treatment valve with gender of patients were significant in the proportion of cure, risk of death and longitudinal outcomes. The probability of cure depended on the type of implanted aortic prosthesis and gender of patients.