Latent Gaussian Approach to Joint Modelling of Longitudinal and Mixture Cure Outcomes

Document Type : Original Article

Authors

1 Department of Statistics, College of Physical Sciences, Federal University of Agriculture Abeokuta, Ogun state, Nigeria.

2 Department of Statistics, Federal University of Agriculture Abeokuta, P.M.B 2240, Abeokuta, Ogun State, Nigeria

3 Department of Mathematics, Federal University of Agriculture Abeokuta, P.M.B 2240, Abeokuta, Ogun State, Nigeria

Abstract

Joint modelling has become pervasive in analysing data from survival and longitudinal studies. There are several technqiues on joint analyses of datasets from both studies simultaneously. Our interest here is on approximate Bayesian inference using latent Gaussian models (LGMs) to analyse longitudinal and mixture cure outcomes with shared random effect. Longitudinal outcome was modelled using spline function to account for nonlinearity in longitudinal trajectories often seen in real life datasets, while survival outcome was modelled using Cox proportional hazards and logistic link function for latency and incidence components respectively, to account for the possibility of cure proportion. The LGMs require three levels of hierachy involving joint likelihoods of paramters and hyperparameters, defining a multivariate normal distribution for a latent field and finally priors for the hyperparamters. Posterior estimates were evaluated using Integrated Laplace approximation. Simulation study compared linear, quadratic and spline specifications for longitudinal trajectories and showed similar results for quadratic and spline function in small sample sizes and linear specification good only in large sample size. The approach was applied to renal transplantation data which comprised glomerular filtration rate of kidneys and survival event of time to graft failure. The contribution of this paper is that it adds to the literature on approximate Bayesian alternative to jointly modelling nonlinear trajectories of longitudinal outcomes and survival outcome with possibility of cure proportions and showed its computational merit over sample-based Bayesian approach.

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