Joint Bayesian Image and Prediction Modeling.

Abstract

In this dissertation, I focus on Bayesian joint modeling of neuroimaging data and outcomes. In the first project, I propose a joint classification model to predict treatment efficacy, as measured by one-year survival status, based on quantitative MRI (qMRI) for patients with malignant gliomas. In stage I, I smooth the images using a multivariate spatio-temporal pairwise-difference prior and propose four summary statistics. In stage II, I build a generalized non-linear model with stage I summary statistics as covariates and use Multivariate Adaptive Regression Splines as the basis functions.

To assess therapeutic efficacy more efficiently, I modify stage II to incorporate censoring. I propose a Bayesian joint survival model and model patients’ health status as a latent Wiener process. Patients' survival time is modeled as the first hitting time (FHT) to an absorbing state (i.e. death). I link the summary statistics derived from the qMRI data to the distribution parameters of the FHT via a Bayesian hierarchical model.

My third project is motivated by the challenges of using MRI to diagnose an irreversible and progressive brain disease: Alzheimer's disease. In an MRI study, white matter changes are highly heterogeneous and differ in size and location making it difficult to use MRI as an accurate diagnostic tool. To mitigate these problems, I propose to jointly model MRI data and the disease status (normal, mild cognitive impairment or Alzheimer’s disease) using wavelets. In stage I, a 3-D discrete wavelet transformation is applied on the MRI data. The Bayesian Lasso is used to denoise the wavelet images and then I derive summary statistics based on these denoised images. In stage II, I include the summary statistics from stage I as covariates and build a cumulative probit regression model to predict the polychotomous disease status.

Through both simulation studies and model performance comparisons, I show that our modeling approach can improve prediction by accounting for correlation in the images and by jointly modeling the images and outcomes.