Machine learning combined to mechanistic modeling of differential effects of neoadjuvant sunitinib on primary tumor and metastatic growth
C. Nicolò (1,2), M. Mastri (3), J. ML Ebos (3,4), S. Benzekry (1,2)
(1) MONC team, Inria Bordeaux Sud-Ouest, Talence, France, (2) Institut de Mathématiques de Bordeaux, Bordeaux University, Talence, France, (3) Department of Cancer Genetics and Genomics, Roswell Park Comprehensive Cancer Center, Buffalo, NY, USA, (4) Department of Medicine, Roswell Park Comprehensive Cancer Center, Buffalo, NY, USA.
Despite proven clinical action of angiogenic inhibitors , recent experimental evidence also suggests differential effects of these drugs on primary and secondary tumors –. In this work we extended our previous mechanistic model  to describe the effect of neoadjuvant sunitinib therapy in an ortho-surgical mouse model of spontaneous metastatic breast cancer. Model development was guided by a large experimental data set of 104 mice treated with multiple scheduling strategies. The experimental data comprised longitudinal measurements of primary tumor (PT) size and metastatic burden (MB), as well as survival data and pre-surgical biomarkers (circulating tumor cells (CTCs) and myeloid-derived suppressor cells (MDSCs) counts and proliferation and endothelial immunohistochemical markers).
- Understand the differential effects of Suntinib on primary tumor and metastatic growth
- Establish a minimal kinetics-pharmacodynamics (K-PD) model of neoadjuvat suntinib therapy
- Assess the predictive power of biomarkers on the model parameters
We adapted a previously established mathematical model  to include the effect of neoadjuvant sunitinib therapy by assuming that the drug reduces the primary tumor growth rate by a term proportional to its concentration. As no pharmacokinetic data were collected in our study, we used a K-PD approach (one compartment model with elimination rate from the literature ).
PT and MB data were fitted simultaneously for vehicle and sunitinib-treated animals using a nonlinear-mixed effects modeling approach . Maximum likelihood estimates of the population parameters were obtained using the Stochastic Approximation of Expectation-Maximization (SAEM) algorithm implemented in the nlmefitsa Matlab function .
Effects of covariates on the model parameters were assessed using linear regression and a number of machine learning regression techniques (artificial neural networks, support vector machines, random forest models)  using the train function of the R caret package , .
Survival times were analyzed using the Monolix software . A log-logistic distribution was used. We utilized the COSSAC (Conditional Sampling for Stepwise Approach based on Correlation tests) covariate selection algorithm for automatic building of the covariate model .
We used parameter values estimated from a previous study on control groups  to generate model predictions under the assumptions of effect (A) or no effect of therapy on metastatic growth (B). Population distributions obtained under the hypothesis A failed to describe the data, whereas simulations under hypothesis B reproduced the behavior of the experimental data notably well. This was observed in all the treated groups and suggested rejection of the assumption A, with B being a valid possible alternative.
Based on these results, the K-PD model we developed considered that the antiangiogenic agent affects only primary tumor growth. The calibrated K-PD model was able to describe both the structural dynamics and inter-subject variability of the experimental data in both vehicle and treated animals. The model parameters were identified with good precision (relative standard error ≤ 17%) thanks to the large number of animals (n=104). Confirming previous results , interanimal variability was mainly characterized by a model parameter μ expressing the metastatic potential of the tumor, which was also found to be significant for predicting survival. However, the biomarkers included in all tested machine learning algorithms demonstrated only limited predictive power on the mathematical parameters (R2 = 0.13 – 0.2, best relative error on 9.83 10.70 %).
We developed a K-PD model for describing the effects of neoadjuvant antiangiogenic treatment on primary and metastatic growth dynamics. Analysis of a large data set revealed a highly heterogeneous population in terms of the metastatic potential parameter μ. Identifying biological predictors of μ would be of critical clinical interest by providing more individualized. According to our analysis of the biomarkers as covariates in the model, expression of Ki67 and CD31 in the primary tumor, and pre-surgical CTC and MDSC levels are not significant predictors of metastatic potential and survival. Although likely to depend on the animal model of cancer, these results highlight the need to investigate other molecular and cellular markers.
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