This work is motivated by a quantitative Magnetic Resonance Imaging study of the differential tumor/healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake, a surrogate for permeability, in the tumor relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang, Johnson, Little, and Cao (2008a and 2008b) discuss two parallel approaches to “denoise” a single image of change in contrast uptake from baseline to a single follow-up visit of interest. In this work we explore the longitudinal profile of the tumor/healthy tissue change in contrast uptake. In addition to the spatial correlation, we account for temporal correlation by jointly modeling multiple images on the individual subjects over time. We fit a two-stage model. First, we propose a longitudinal image model for each subject. This model simultaneously accounts for the spatial and temporal correlation and denoises the observed images by borrowing strength both across neighboring pixels and over time. We propose to use the area under the receiver operating characteristics (ROC) curve (AUC) to summarize the differential contrast uptake between tumor and healthy tissue. In the second stage, we fit a population model on the AUC values and estimate when it achieves the maximum.



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