Assessing the identifiability of model selection frameworks for the prediction of patient outcomes in the clinical breast cancer setting

We develop a family of mathematical models to predict patient-specific response to neoadjuvant therapy in breast cancer. The models capture key features of tumor growth, therapeutic response, and tissue mechanics that are informed by diffusion weighted and dynamic contrast-enhanced magnetic resonance imaging. We then calibrate the models to synthetic and clinical data using Bayesian inference to give a description of the parameter uncertainties. Given the family of models and the calibration scheme, we perform three analyses. First, we test the identifiability of each model; that is, given synthetic data with the same level of noise as that seen in the clinical setting, are we able to accurately recover parameter values employed to generate the data? Second, we test the identifiability of the framework itself; that is, when data is generated by one model from the family, is that model selected as the best one during the calibration? Third, we apply our model family to predict patient-specific response on a cohort of 32 patients with triple negative breast cancer. For analysis 1, we show that we can recover the parameters used to generate synthetic data (with 5%, 10%, and 15% Gaussian noise — greater than that typically seen in magnetic resonance imaging in the clinical setting) with a mean error of 5.9% (+/−1.4%). For analysis 2, the model used to generate the data is selected as the best model for over 50% of the synthetic data sets, provided that the noise level in the synthetic data is less than 10%. For analysis 3, we show that the calibrated drug efficacy rate in the diffusion and proliferation mechanically coupled, drug informed, reaction–diffusion model strongly correlates with patient response to therapy with an area under the curve score of 0.85 in a receiver operator characteristic analysis. Thus, our framework shows that, within the noise levels encountered in the clinical setting, a high level of rigor can be achieved for mathematical model parameterizations and selections, and this translates into high accuracy for predicting responders and non-responders to neoadjuvant therapy.