Bayesian spatial mixture of experts for a flexible dose-response assessment after brain radiotherapy

Overview & Synopsis

Radiotherapy (RT) is one of the most important treatments for brain tumors. However, its potential toxicity on the central nervous system is a highly relevant clinical issue as cognitive dysfunction, mainly related to radiation-induced leukoencephalopathy, may alter the quality of life of patients. As part of the RADIO-AIDE research project, the aim of this work is to model and learn about the potential relationship between the dose of ionizing radiation absorbed in a voxel of the brain after RT (from CT-scan images) and the presence/absence of brain lesions in these voxels (from segmented brain MRI data). We propose to extend the class of mixture of experts’ models, including the well-known Gaussian Locally Linear Mapping model (GLliM), to a binary outcome and a spatially structured predictor. We thus propose and compare several mixtures of experts’ models based on a piecewise logistic regression and different spatial components (hidden Potts model, conditionally auto-regressive model) to account for dependency between neighboring voxels. Various Bayesian statistical learning methods (variational Bayes, MCMC, SMC) are implemented and compared from simulated data as well as real data from the EpiBrainRad prospective cohort, which includes patients treated with radiochemotherapy for glioblastoma. Many modelling perspectives and Bayesian computational challenges will also be discussed.