A Bayesian Nonparametric Regression Model With Normalized Weights: A Study of Hippocampal Atrophy in Alzheimer’s Disease

Hippocampal volume is one of the best established biomarkers for Alzheimer's disease. However, for appropriate use in clinical trials research, the evolution of hippocampal volume needs to be well understood. Recent theoretical models propose a sigmoidal pattern for its evolution. To support this theory, the use of Bayesian nonparametric regression mixture models seems particularly suitable due to the flexibility that models of this type can achieve and the unsatisfactory predictive properties of semiparametric methods. In this article, our aim is to develop an interpretable Bayesian nonparametric regression model which allows inference with combinations of both continuous and discrete covariates, as required for a full analysis of the dataset. Simple arguments regarding the interpretation of Bayesian nonparametric regression mixtures lead naturally to regression weights based on normalized sums. Difficulty in working with the intractable normalizing constant is overcome thanks to recent advances in MCMC methods and the development of a novel auxiliary variable scheme. We apply the new model and MCMC method to study the dynamics of hippocampal volume, and our results provide statistical evidence in support of the theoretical hypothesis.