The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Sébastien Benzekry - One of the best experts on this subject based on the ideXlab platform.
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Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors
PLoS Computational Biology, 2020Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a reduced Gompertz function consisting of a single individual Parameter (and one Population Parameter). Leveraging the Population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.
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Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gom-pertz within the statistical framework of nonlinear mixed-effects modelling , which allowed us to account for inter-animal variability within a Population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz Parameters. Combining this observation with rigorous Population Parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual Parameter. Using Bayesian inference, we further applied the Population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.
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A reduced Gompertz model for predicting tumor age using a Population approach
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed for the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and-more notably-Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual Parameter. Leveraging the Population approach using bayesian inference, we estimated the time of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line. These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summary Mathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a Population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two Parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual Parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis.
Cristina Vaghi - One of the best experts on this subject based on the ideXlab platform.
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Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors
PLoS Computational Biology, 2020Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a reduced Gompertz function consisting of a single individual Parameter (and one Population Parameter). Leveraging the Population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.
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Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gom-pertz within the statistical framework of nonlinear mixed-effects modelling , which allowed us to account for inter-animal variability within a Population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz Parameters. Combining this observation with rigorous Population Parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual Parameter. Using Bayesian inference, we further applied the Population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.
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A reduced Gompertz model for predicting tumor age using a Population approach
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed for the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and-more notably-Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual Parameter. Leveraging the Population approach using bayesian inference, we estimated the time of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line. These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summary Mathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a Population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two Parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual Parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis.
Marianne Frisén - One of the best experts on this subject based on the ideXlab platform.
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Effect of uncertainty about Population Parameters on pharmacodynamics-based prediction of clinical trial power
Contemporary clinical trials, 2005Co-Authors: Holger Kraiczi, Marianne FrisénAbstract:Clinical trial simulation (CTS) may be applied to predict power of intended drug trials on the basis of pharmacokinetic/pharmacodynamic (PKPD) drug models. The validity of such predictions will, among other factors, depend on the degree of uncertainty about Population Parameters entering the simulation. In the current article, we illustrate how Population Parameter uncertainty may be incorporated in the overall simulation model, using a worked example to demonstrate our approach. Moreover, we suggest an ANOVA-based method for sensitivity analysis, aimed at distinguishing important Population Parameters, required to be input in the model with a low degree of uncertainty for precise power predictions, from unimportant Parameters, which may be entered with a high degree of uncertainty without affecting the reliability of predictions. Our results from simulations with different settings of hyperParameters and doses suggest that indices derived from this type of sensitivity analysis may be used for grading the influence on prediction quality of uncertainty about different Population Parameters and, thus, facilitate the allocation of resources expended for the preparation of a successful CTS project.
Raphaëlle Fanciullino - One of the best experts on this subject based on the ideXlab platform.
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Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors
PLoS Computational Biology, 2020Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a reduced Gompertz function consisting of a single individual Parameter (and one Population Parameter). Leveraging the Population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.
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Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gom-pertz within the statistical framework of nonlinear mixed-effects modelling , which allowed us to account for inter-animal variability within a Population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz Parameters. Combining this observation with rigorous Population Parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual Parameter. Using Bayesian inference, we further applied the Population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.
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A reduced Gompertz model for predicting tumor age using a Population approach
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed for the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and-more notably-Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual Parameter. Leveraging the Population approach using bayesian inference, we estimated the time of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line. These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summary Mathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a Population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two Parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual Parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis.
Joseph Ciccolini - One of the best experts on this subject based on the ideXlab platform.
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Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors
PLoS Computational Biology, 2020Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by means of ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model, which could be used to reduce the dimensionality and improve predictive power. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 833 measurements in 94 animals. Candidate models of tumor growth included the exponential, logistic and Gompertz models. The exponential and-more notably-logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The previously reported Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R2 > 0.92 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a reduced Gompertz function consisting of a single individual Parameter (and one Population Parameter). Leveraging the Population approach using Bayesian inference, we estimated times of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using Bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy (prediction error) was 12.2% versus 78% and mean precision (width of the 95% prediction interval) was 15.6 days versus 210 days, for the breast cancer cell line. These results demonstrate the superior predictive power of the reduced Gompertz model, especially when combined with Bayesian estimation. They offer possible clinical perspectives for personalized prediction of the age of a tumor from limited data at diagnosis. The code and data used in our analysis are publicly available at https://github.com/cristinavaghi/plumky.
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Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gom-pertz within the statistical framework of nonlinear mixed-effects modelling , which allowed us to account for inter-animal variability within a Population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz Parameters. Combining this observation with rigorous Population Parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual Parameter. Using Bayesian inference, we further applied the Population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.
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A reduced Gompertz model for predicting tumor age using a Population approach
2019Co-Authors: Cristina Vaghi, Anne Rodallec, Raphaëlle Fanciullino, Joseph Ciccolini, Jonathan Mochel, Michalis Mastri, Clair Poignard, John Ebos, Sébastien BenzekryAbstract:Tumor growth curves are classically modeled by ordinary differential equations. In analyzing the Gompertz model several studies have reported a striking correlation between the two Parameters of the model. We analyzed tumor growth kinetics within the statistical framework of nonlinear mixed-effects (Population approach). This allowed for the simultaneous modeling of tumor dynamics and inter-animal variability. Experimental data comprised three animal models of breast and lung cancers, with 843 measurements in 94 animals. Candidate models of tumor growth included the Exponential, Logistic and Gompertz. The Exponential and-more notably-Logistic models failed to describe the experimental data whereas the Gompertz model generated very good fits. The Population-level correlation between the Gompertz Parameters was further confirmed in our analysis (R 2 > 0.96 in all groups). Combining this structural correlation with rigorous Population Parameter estimation, we propose a novel reduced Gompertz function consisting of a single individual Parameter. Leveraging the Population approach using bayesian inference, we estimated the time of tumor initiation using three late measurement timepoints. The reduced Gompertz model was found to exhibit the best results, with drastic improvements when using bayesian inference as compared to likelihood maximization alone, for both accuracy and precision. Specifically, mean accuracy was 12.1% versus 74.1% and mean precision was 15.2 days versus 186 days, for the breast cancer cell line. These results offer promising clinical perspectives for the personalized prediction of tumor age from limited data at diagnosis. In turn, such predictions could be helpful for assessing the extent of invisible metastasis at the time of diagnosis. Author summary Mathematical models for tumor growth kinetics have been widely used since several decades but mostly fitted to individual or average growth curves. Here we compared three classical models (Exponential, Logistic and Gompertz) using a Population approach, which accounts for inter-animal variability. The Exponential and the Logistic models failed to fit the experimental data while the Gompertz model showed excellent descriptive power. Moreover, the strong correlation between the two Parameters of the Gompertz equation motivated a simplification of the model, the reduced Gompertz model, with a single individual Parameter and equal descriptive power. Combining the mixed-effects approach with Bayesian inference, we predicted the age of individual tumors with only few late measurements. Thanks to its simplicity, the reduced Gompertz model showed superior predictive power. Although our method remains to be extended to clinical data, these results are promising for the personalized estimation of the age of a tumor from limited measurements at diagnosis. Such predictions could contribute to the development of computational models for metastasis.