Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC (original) (raw)
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2021
Approximate Bayesian Computation is used in this work for the selection and calibration of cell proliferation models. Four competing models based on ordinary differential equations are analyzed, by using the measurements of the proliferation of DU-145 prostate cancer viable cells during seven days. The selection criterion of the ABC algorithm is based on the Euclidean distance between the model prediction and the experimental observations. The Richards Model and the Generalized Logistic Model were selected by the ABC algorithm used in this work, providing accurate estimates of the evolution of the number of viable cells. Bayes factor revealed that there was no evidence in favor of any of these two selected models.
Tumor growth modeling: Parameter estimation with Maximum Likelihood methods
Computer methods and programs in biomedicine, 2018
In this work, we focus on estimating the parameters of the widely used Gompertz tumor growth model, based on measurements of the tumor's volume. Being able to accurately describe the dynamics of tumor growth on an individual basis is very important both for growth prediction and designing personalized, optimal therapy schemes (e.g. when using model predictive control). Our analysis aims to compute both the growth rate and the carrying capacity of the Gompertz function, along with the characteristics of the additive Gaussian process and measurement noise of the system. Three methods based on Maximum Likelihood estimation are proposed. The first utilizes an assumption regarding the measurement noise that simplifies the problem, the second combines the Extended Kalman Filter and Maximum Likelihood estimation, and the third is a nonstandard exact form of Maximum Likelihood estimation, where numerical integration is used to approximate the likelihood of the measurements, along with a...
Communications Medicine
Background In clinical practice, a plethora of medical examinations are conducted to assess the state of a patient’s pathology producing a variety of clinical data. However, investigation of these data faces two major challenges. Firstly, we lack the knowledge of the mechanisms involved in regulating these data variables, and secondly, data collection is sparse in time since it relies on patient’s clinical presentation. The former limits the predictive accuracy of clinical outcomes for any mechanistic model. The latter restrains any machine learning algorithm to accurately infer the corresponding disease dynamics. Methods Here, we propose a novel method, based on the Bayesian coupling of mathematical modeling and machine learning, aiming at improving individualized predictions by addressing the aforementioned challenges. Results We evaluate the proposed method on a synthetic dataset for brain tumor growth and analyze its performance in predicting two relevant clinical outputs. The m...
Mutation Research/Genetic Toxicology and Environmental Mutagenesis, 2012
Cancer is known to be a complex disease and its therapy is difficult. Much information is available on molecules and pathways involved in cancer onset and progression and this data provides a valuable resource for the development of predictive computer models that can help to identify new potential drug targets or to improve therapies. Modeling cancer treatment has to take into account many cellular pathways usually leading to the construction of large mathematical models. The development of such models is complicated by the fact that relevant parameters are either completely unknown, or can at best be measured under highly artificial conditions. Here we propose an approach for constructing predictive models of such complex biological networks in the absence of accurate knowledge on parameter values, and apply this strategy to predict the effects of perturbations induced by anti-cancer drug target inhibitions on an epidermal growth factor (EGF) signaling network. The strategy is based on a Monte Carlo approach, in which the kinetic parameters are repeatedly sampled from specific probability distributions and used for multiple parallel simulations. Simulation results from different forms of the model (e.g., a model that expresses a certain mutation or mutation pattern or the treatment by a certain drug or drug combination) can be compared with the unperturbed control model and used for the prediction of the perturbation effects. This framework opens the way to experiment with complex biological networks in the computer, likely to save costs in drug development and to improve patient therapy.
Bayesian computational methods in biomedical research
…, 2007
Example 2 Lopes, consider hematologic, i.e., blood count, data from a cancer chemotherapy trial. For each patient in the trial we record white blood cell count over time as the patient undergoes the first cycle of a chemotherapy treatment. Patients are treated at different doses of the chemotherapy agent(s). The main concern is inference about the number of days that the patient is exposed to a dangerously low white blood cell count. We proceed with a parametric model for the white blood cell profile over time. In words, we assume initially a constant baseline count, followed by a sudden drop when chemotherapy is initiated, and finally a slow S-shaped recovery back to baseline after the chemotherapy. The profile is indexed by a 7-dimensional vector of random effects (see Section 3.3 below) that parameterize a non-linear regression curve that reflects these features. Let θ i denote this 7-dimensional vector for patient i. Let f (t; θ i ) denote the value at time t
Bayesian method for modeling male breast cancer survival data
Asian Pacific Journal of Cancer Prevention Apjcp, 2014
Background: With recent progress in health science administration, a huge amount of data has been collected from thousands of subjects. Statistical and computational techniques are very necessary to understand such data and to make valid scientific conclusions. The purpose of this paper was to develop a statistical probability model and to predict future survival times for male breast cancer patients who were diagnosed in the USA during 1973-2009. Materials and methods: A random sample of 500 male patients was selected from the Surveillance Epidemiology and End Results (SEER) database. The survival times for the male patients were used to derive the statistical probability model. To measure the goodness of fit tests, the model building criterions: Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and Deviance Information Criteria (DIC) were employed. A novel Bayesian method was used to derive the posterior density function for the parameters and the predictive inference for future survival times from the exponentiated Weibull model, assuming that the observed breast cancer survival data follow such type of model. The Markov chain Monte Carlo method was used to determine the inference for the parameters. Results: The summary results of certain demographic and socio-economic variables are reported. It was found that the exponentiated Weibull model fits the male survival data. Statistical inferences of the posterior parameters are presented. Mean predictive survival times, 95% predictive intervals, predictive skewness and kurtosis were obtained. Conclusions: The findings will hopefully be useful in treatment planning, healthcare resource allocation, and may motivate future research on breast cancer related survival issues.
Objective Bayesian Snalysis for the Complementary Exponential Geometric Model Applied to Cancer Data
International Journal of Statistics and Probability, 2017
In this paper we provide a reference Bayesian framework to a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric (CEG). To this end, we presented some of the main properties of this model and its characteristics related to the reliability analysis. A simulation study is performed to analyse the frequentist properties of credible intervals from the reference posterior distribution among of the standard error and mean square error (MSE) of estimations. The presented methodology is illustrated by the use of a real data set which presents the study of time until the cure of cervix lesions, that are precursors cancer lesions in the cervix. According to to INCA (Cancer National Institute), cervical cancer stands as the fourth cause of death among women in Brazil. Together with breast cancer, it is one of the most common malignancy affecting women worldwide. For this reason, patients must be carefully evaluated for metastatic dise...
Personalized Tumor Growth Prediction Using Multiscale Modeling
The Journal of Basic and Clinical Health Sciences, 2020
Purpose: Cancer is one of the most complex phenomena in biology and medicine. Extensive attempts have been made to work around this complexity. In this study, we try to take a selective approach; not modeling each particular facet in detail but rather only the pertinent and essential parts of the tumor system are simulated and followed by optimization, revealing specific traits. This leads us to a pellucid personalized model which is noteworthy as it closely approximates existing experimental results. Methods: In the present study, a hybrid modeling approach which consists of cellular automata for discrete cell state representation and diffusion equations to calculate distribution of relevant substances in the tumor microenvironment is favored. Moreover, naive Bayesian decision making with weighted stochastic equations and a Bayesian network to model the temporal order of mutations is presented. The model is personalized according to the evidence using Markov Chain Monte Carlo. To validate the tumor model, a data set belonging to the A549 cell line is used. The data represents the growth of a tumor for 30 days. We optimize the coefficients of the stochastic decision-making equations using the first half of the timeline. Results: Simulation results of the developed model are promising with their low error margin (all correlation coefficients are over 0.8 under different microenvironment conditions) and simulated growth data is in line with laboratory results (r=0.97, p<0.01). Conclusions: Our approach of using simulated annealing for parameter estimation and the subsequent validation of the prediction with invitro tumor growth data are, to our knowledge, is novel.
A statistical model of the early phase of malignant tumor
Use of mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of cancerous tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. Herein we describe a statistical model of early period of tumor growth.