Predicting Treatment Efficacy via Quantitative MRI: A Bayesian Joint Model
The prognosis for patients with high-grade gliomas is poor, with a median survival of one year. Treatment efficacy assessment is typically unavailable until 5-6 months post diagnosis. Investigators hypothesize that quantitative MRI can assess treatment efficacy three weeks after therapy starts, thereby allowing salvage treatments to begin earlier. The purpose of this work is to build a predictive model of treatment efficacy using qMRI data and to assess its performance. The outcome is one0year survival status. We propose a joint, two-stage Bayesian model. In stage I, we smooth the image data with a multivariate spatio-temporal pairwise difference prior. We propose four summary statistics that are functionals of posterior parameters from the first stage model. In stage II, these statistics enter a generalized non-linear model (GNLM) as predictors of survival status. we use the probit link and a multivariate adaptive regression spline basis. Gibbs sampling and reversible jump Markov chain monte carlo are applied iteratively between the stages to estimate the posterior distribution. Through both simulation studies and model performance comparisons we find that we are able to attain higher overall correct classification rates by accounting for the spatio-temporal correlation in the images and by allowing for a more complex and flexible decision boundary provided by the GNLM.