Sensitivity analysis on joint modelling of longitudinal and mixture cure outcomes with data missingness and outliers using INLA: application to aortic valve replacement surgery data

A. H Ekong; O. M Olayiwola; G. A Dawodu; O. A Wale-Orojo,; A. A Akintunde; I. A Osinuga

A. H Ekong Department of Statistics, Federal University of Agriculture Abeokuta
O. M Olayiwola Department of Statistics, Federal University of Agriculture Abeokuta
G. A Dawodu Department of Statistics, Federal University of Agriculture Abeokuta
O. A Wale-Orojo, Department of Statistics, Federal University of Agriculture Abeokuta
A. A Akintunde Department of Statistics, Federal University of Agriculture Abeokuta
I. A Osinuga

Abstract

Joint modelling under Bayesian paradigm has gained a lot of traction especially with sampling-based estimation, however approximate Bayesian estimation of integrated Laplace approximation (INLA) is slowly gaining grounds. Prior specification has also been a recurring discuss in Bayesian analysis with prior sentivity becoming part of the data analysis process. This work presents joint modelling of longitudinal and cure proportion using latent Gaussian model with INLA and prior sensitivity analysis for the model in the presence of data value missingness and outliers. The approach 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. Four different prior specification settings were studied for fixed and random effects and the association parameter. The study was applied to aortic valve replacement surgery data to assess the effects of covariates on a biomarker and risk of event, with spline trajectories. The best prior setting was arrived at via the lowest values of DIC, WAIC and log marginal-likelihood and was Gaussian prior for fixed effects and association parameter each with (mean, precision) values as (0, 0.001), (0, 0.001), (0, 0.001), and parameters from Wishart distribution on the precision matrix for random effects as (100, 1) and it gave robust results with missing values and outliers. The posterior estimates from the best prior settings showed significant covariates on the biomarker and on the conditional failure time latency model. The study contributes to the literature on approximate Bayesian alternative to jointly modelling of longitudinal and mixture cure outcomes in the area of prior specification and data value missingness and outiers.

Keywords: prior specification, association structure, Laplace approximation, shared random effect, nonlinear trajectory