THE EFFECT OF STATISTICAL ERROR MODEL FORMULATION ON THE FIT AND SELECTION OF MATHEMATICAL MODELS OF TUMOR GROWTH FOR SMALL SAMPLE SIZES

H.T Banks Et Al

doi:10.12732/ijpam.v117i1.16

Abstract

THE EFFECT OF STATISTICAL ERROR MODEL FORMULATION ON THE FIT AND SELECTION OF MATHEMATICAL MODELS OF TUMOR GROWTH FOR SMALL SAMPLE SIZES

Highlights

Some standard and simple mathematical models are commonly used in tumor growth modeling and prediction studies ([9, 13, 14, 19, 23, 21, 25, 26])
We examine how the choice of statistical error model affects the accuracy and uncertainty of the mathematical model fits to data
In order to assess the effect of the statistical error model choice on model fit and certainty in parameter estimation, we examine the change in parameter estimates, standard errors (SEs) and mean squared errors (MSEs) for each of the seven mathematical models and three tumor data sets with respect to the change in statistical error model

Summary

Introduction

Some standard and simple mathematical models are commonly used in tumor growth modeling and prediction studies ([9, 13, 14, 19, 23, 21, 25, 26]). Our primary goal is to better understand statistical error models that arise in the observation process for tumor data collection. We examine how the choice of statistical error model (and the form of least squares employed in the inverse problem) affects the accuracy and uncertainty of the mathematical model fits to data. We investigate this in a selection for tumor growth data from studies on mice with a small number of sampling observations [9, 14]. Our effort can be considered a further step in the goals of the authors of [9] in their efforts to more fully understand the form of the observation errors in tumor data collection processes

Methods

Results

Conclusion