A mechanistic model for prediction of metastatic relapse in early-stage breast cancer using routine clinical features

International audience ; 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. ...