Individualized growth prediction of mice skin tumors with maximum likelihood estimators. (March 2020) - Patmanidis, Spyridon; Charalampidis, Alexandros C.; Kordonis, Ioannis; Strati, Katerina; Mitsis, Georgios D.; Papavassilopoulos, George P.
Highlights: Maximum Likelihood estimators can provide reliable growth predictions on individual basis for certain types of cancer. The heterogeneity of tumor growth is an important factor and should be taken into consideration during modeling. The ML estimator provided estimates that predicted the future growth more accurately compared to the NLS estimator. Prior knowledge about the growth of a tumor has the potential to improve the predictions at early growth stages. Parallel computing can effectively reduce the execution time of the computationally demanding ML numerical solution. Abstract: 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. Methods: 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. Results: 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. Conclusion: 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.