Abstract 2737: A mechanistic model for prediction of metastatic relapse in early-stage breast cancer using routine clinical features
Authors: Bigarré Célestin , Finetti Pascal , Bertucci François , Muracciole Xavier , Benzekry Sébastien 
Published: June 2022

Abstract
Estimation of the risk of metastatic relapse is a major challenge to decide treatment options for early-stage breast cancer patients. To date, metastasis free survival (MFS) analysis mainly relies on classical - agnostic - statistical models (e.g., Cox regression). Instead, we propose to derive mechanistic models to predict MFS.
The data consisted of patients who did not receive adjuvant systemic therapy from two databases: one (data 1, N = 163) with routine clinical features and the PAI-1 and uPA biomarkers and two (data 2, N = 692) with 11 routine clinical features. The mathematical models are based on a partial differential equation describing a size-structured population of metastases. They predict MFS from the size of the tumor at diagnosis and two mathematical parameters, α and μ describing respectively the tumor growth speed and metastatic dissemination potential. Using mixed-effects modeling, the population distributions of α and μ were assumed to be lognormal and to depend on routine clinical variables, whereas the observation error was assumed lognormal on the time-to-relapse. Variable selection consisted first in a univariate Wald test for all covariates with effect either on α or μ. We then used a backward elimination procedure. Significance of the covariates in the final model was assessed by a multivariable Wald test. Concordance indexes (c-index) were computed to assess the predictive power in cross-validation procedures as well as test sets.
The model was implemented as an R package using optimized C++ code for the mechanistic part and enabling parallelization, resulting in a 4-fold reduction of the computing compared to a former python implementation. Nevertheless, over 4 hours are still needed to run a 100 samples bootstrap on a distributed computing cluster. The model selection procedure on data 1 revealed an association of PAI1 and age with μ, and of Estrogen receptor level with alpha, consistent with the established biological link between PAI-1 and tumor invasiveness. The resulting model achieved good prediction performances with a c-index of 0.72 in 5 folds cross-validation. Using only routine clinical markers, the algorithm on data 2 selected a model with the grade and Progesterone Receptors in α, Ki67 and node status in μ. These were able to adequately describe the data on calibration plots but performed poorly in prediction with a cross validated c-index of 0.60.
Mechanistic modeling was able to unravel the biological and predictive role of PAI-1 but showed limited predictive power when using only on routine clinical features.
Citation Format: Célestin Bigarré, Pascal Finetti, François Bertucci, Xavier Muracciole, Sébastien Benzekry. A mechanistic model for prediction of metastatic relapse in early-stage breast cancer using routine clinical features [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2737.