School of Electrical and Computer Engineering, National Technical University of Athens, Iroon Polytechneiou 9, Zografou 15780, Athens, Greece.
Department of Electrical Engineering and Computer Science, Technische Universität Berlin, Einsteinufer 17, Berlin D-10587, Germany; CentraleSupélec, Avenue de la Boulaie, 35576 Cesson-Sévigné, France.
Comput Methods Programs Biomed. 2020 Mar;185:105165. doi: 10.1016/j.cmpb.2019.105165. Epub 2019 Nov 2.
BACKGROUND & OBJECTIVE: In this work, we focus on estimating the parameters of the Gompertz model in order to predict tumor growth. The estimation is based on measurements from mice skin tumors of de novo carcinogenesis. The main objective is to compare the Maximum Likelihood estimator with the best performance from our previous work with the Non-linear Least Squares estimator which is commonly used in the literature to estimate the growth parameters of the Gompertz model.
To describe tumor growth, we propose a stochastic model which is based on the Gompertz growth function. The principle of Maximum Likelihood is used to estimate both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise. Moreover, we examine whether a Maximum A Posteriori estimator is able to utilize any available prior knowledge in order to improve the predictions.
Experimental data from a total of 24 tumors in 8 mice (3 tumors each) were used to study the performance of the proposed methods with respect to prediction accuracy. Our results show that the Maximum Likelihood estimator is able to provide, in most cases, more accurate predictions. Moreover, the Maximum A Posteriori estimator has the potential to correct potentially non-realistic estimates for the carrying capacity at early growth stages.
In most cases, the Maximum Likelihood estimator is able to provide more reliable predictions for the tumor's growth on individual test subjects. The Maximum A Posteriori estimator, it has the potential to improve the prediction when the available experimental data do not provide adequate information by utilizing prior knowledge about the unknown parameters.
在这项工作中，我们专注于估计 Gompertz 模型的参数，以便预测肿瘤生长。该估计基于新发生癌形成的小鼠皮肤肿瘤的测量值。主要目标是比较最大似然估计与我们之前工作中性能最佳的非线性最小二乘估计，后者常用于文献中估计 Gompertz 模型的生长参数。
为了描述肿瘤生长，我们提出了一种基于 Gompertz 生长函数的随机模型。最大似然原理用于估计 Gompertz 函数的增长率和承载能力，以及加性高斯过程和测量噪声的特征。此外，我们还检查了最大后验估计是否能够利用任何可用的先验知识来提高预测。
总共 8 只小鼠的 24 个肿瘤（每个肿瘤 3 个）的实验数据用于研究所提出方法在预测准确性方面的性能。我们的结果表明，在大多数情况下，最大似然估计能够提供更准确的预测。此外，最大后验估计有可能在早期生长阶段纠正承载能力的潜在非现实估计。
在大多数情况下，最大似然估计能够为个体测试对象的肿瘤生长提供更可靠的预测。最大后验估计有可能通过利用未知参数的先验知识，在可用的实验数据不能提供足够信息时，改善预测。
