A sample size analysis of a mathematical model of longitudinal tumor volume and progression‐free survival for Bayesian individual dynamic predictions in recurrent high‐grade glioma

Patients with recurrent high-grade glioma (rHGG) have a poor prognosis with median progression-free survival (PFS) of <7 months. Responses to treatment are heterogenous, suggesting a clinical need for prognostic models. Bayesian data analysis can exploit individual patient follow-up imaging studies to adaptively predict the risk of progression. We propose a novel sample size analysis for Bayesian individual dynamic predictions and demonstrate proof of principle. We coupled a nonlinear mixed effects tumor growth inhibition model with a survival model. Longitudinal tumor volumes and time-to-progression were simulated for 2000 in silico rHGG patients. Bayesian individual dynamic predictions of PFS curves were evaluated using area under the receiver operating characteristic curve (AUC) and Brier skill score (BSS). We investigated the effects of sample size on AUC and BSS margins of error. A power law relationship was observed between sample size and margins of error of AUC and BSS. Sample size was also found to be negatively correlated with margins of error and landmark time. We explored the use of this sample size analysis as a clinical look-up table for prospective clinical trial design and retrospective clinical data analysis. Here, we motivate the application of Bayesian individual dynamic predictions as a clinical end point for clinical trial design. Doing so could aid in the development of study protocols with patient-specific adaptations (escalate or de-escalate dose or frequency of drug administration, increase or decrease the frequency of follow-up, or change therapeutic modality) according to patient-specific prognosis. Future developments of this approach will focus on further model development and validation.