Quantifying Uncertainty and Robustness in a Biomathematical Model Based Patient-Specific Response Metric for Glioblastoma

Abstract

Glioblastomas, lethal primary brain tumors, are known for their heterogeneity and invasiveness. A growing literature has been developed demonstrating the clinical relevance of a biomathematical model, the Proliferation-Invasion (PI) model, of glioblastoma growth. Of interest here is the development of a treatment response metric, Days Gained (DG). This metric is based on individual tumor kinetics estimated through segmented volumes of hyperintense regions on T1-weighted gadolinium enhanced (T1Gd) and T2-weighted magnetic resonance images (MRIs). This metric was shown to be prognostic of time to progression. Further, it was shown to be more prognostic of outcome than standard response metrics. While promising, the original paper did not account for uncertainty in the calculation of the DG metric leaving the robustness of this cutoff in question. We harness the Bayesian framework to consider the impact of two sources of uncertainty: 1) image acquisition and 2) interobserver error in image segmentation. We first utilize synthetic data to characterize what non-error variants are influencing the final uncertainty in the DG metric. We then consider the original patient cohort to investigate clinical patterns of uncertainty and to determine how robust this metric is for predicting time to progression and overall survival. Our results indicate that the key clinical variants are the time between pre-treatment images and the underlying tumor growth kinetics, matching our observations in the clinical cohort. Finally, we demonstrated that for this cohort there was a continuous range of cutoffs between 94 and 105 for which the prediction of the time to progression and was over 80% reliable. While further validation must be done, this work represents a key step in ascertaining the clinical utility of this metric.