Age and Grouth Estimation using Mixed-Effects of Population and Individuals

Abstract

The subject of this project is to obtain a estimation of the growth form and age of tumors using models of aggregated tumor growths, such as the Logistic Models or the Gompertz Model. We will use a Bayesian Estimation structure known as nonlinear Mixed-Effect Estimation with Fat-tail distribution, from the few available data for each individual, but in a reasonable number when aggregated from similar populations subjected to the same type of carcinoma.A mixed Laplacian-Gaussian distribution is used to achieve greater robustness given the dispersion of data, in general poorly represented by conventional Gaussian models and associated methods such as least squares and their variations. More robust and flexible statistical models are critical in this type of estimation where little data for an individual is available.The scope of this project consists of using the non-linear Mixed Effects structure from the studied growth models - composing the individual data with the population approach obtained through the data of similar individuals - to obtain an a priori model estimating the growth curve and age of a tumor. The mixed effect is obtained by composing the population information as a priori with the few available measures of the individual. The adoption of the Fat-tail distribution allows estimating the values of the growth curve and the age of the tumor for each individual with good acuity. A comparison will be made between the cited growth models and others and also with the adjustments obtained through the traditional Gaussian distribution. It is intended to verify if the greater variability of events captured by these distributions and models will generate more accurate results of growth parameters and tumor age and that point to possible clinical use.