Partial Logistic Artificial Neural Network with automatic relevance determination and Markov Chain Monte Carlo methods applied in medical survival studies

Abstract

This paper builds on previous work involving different Bayesian Neural Networks namely Partial Logistic Artificial Neural Network with Automatic Relevance Determination (PLANN-ARD) for Single Risk (SR) and Competing Risk (CR) [1, 6, 15, 16] and applied in the medical survival studies. The results obtained with these PLANN-ARD/PLANN-CR-ARD models are compared with the results obtained with a different set of Bayesian Neural Networks namely the Markov Chain Monte Carlo (MCMC) methods [19, 20]. This work is done in the recent context of evaluation of large number of classification models [25] on medical dataset(s) and more specifically in the context of evaluation of different types of Bayesian Neural Networks [23, 26–29] in the medical survival analysis domain. There is such an interest in studying various classification and regression models for outcome prediction in medical survival analysis. Two medical datasets are used herein: a node negative breast cancer dataset (SR analysis) and a Primary Biliary Cirrhosis (PBC) dataset (CR analysis). The PLANN-ARD/PLANN-CR-ARD models form a group of two neural network models which are based on gradient type of optimization algorithms for the calculus of the neural network parameters. The MCMC sampling methods represent another set of models which are used in this paper for SR study (MCMC-SR algorithm) and CR study (MCMC-CR algorithm) in medical survival domain. The MCMC sampling methods are implemented by a MCMC toolbox available in the literature [10, 11, 19–21]. The MCMC methods are sampling from the prior probability distributions of the model parameters and they include the Gibbs sampler, the Metropolis-Hastings sampler, the Hybrid Markov Chain Monte Carlo (HMCMC) sampler or the Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampler. The results obtained by the four BNNs are compared with the non-parametric estimates obtained through the survival study of the two medical datasets from above. The results show a superiority of the PLANN-ARD/PLANN-CR-ARD models with regard to the MCMC-SR/MCMC-CR algorithms from the point of view of the model selection task which was less computational expensive for the PLANN-ARD/PLANN-CR-ARD models.