A Calibration Method for Random Models with Dependent Random Parameters: The Applied Case of Tumor Growth

In the real world, multiple dynamic biological phenomena present an intrinsic randomness due to their nature. One of the most common ways of modeling them is to use random differential or random difference equations, whose parameters are considered as random variables. However, since these are complex models, independence between these parameters is usually assumed just for simplicity, without even having tested this hypothesis in the phenomenon under study. On the other hand, the impossibility of solving the calibration of random models with classical deterministic optimization techniques has given rise to new stochastic calibration techniques, such as bio-inspired algorithms. In this paper, we present a calibration method based on the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm of a random model with a set of random parameters without assuming independence between them. The calibration goal is to find the multivariate probability distribution of the random parameters vector that best captures the uncertainty of the data by minimizing two fitness functions. To show the value of the method, we will apply it to a simple first-order difference model for the evolution of the growth of breast cancer.