Robust Mixed-Effect Estimation of Tumor Growth and Age Based on Gompertz Model

Abstract

This letter considers the problem of estimating tumor growth and tumor age using the Gompertz model within the nonlinear mixed-effect framework. In particular, the choice for the prior for the population model parameters is the Normal-Laplace distribution. The Maximum A Posteriori (MAP) method provides a robust estimation scheme that leverages the fat-tail properties of such a distribution. Due to the non-differentiability of the distribution, the resulting estimator shows an inaction region in which, for small residues, the best estimate remains the population prior. In addition, a change of variable in the usual Gompertz model sets the tumor age as an extra parameter, which is straightforwardly estimated. This information might provide helpful insights into clinical cancer treatment. Numerical experiments suggest that the proposed estimation scheme renders significantly more accurate estimates in such a vital problem.