Tumor growth modeling: Parameter estimation with Maximum Likelihood methods

Patmanidis, Spyridon; Charalampidis, Alexandros C.; Kordonis, Ioannis; Mitsis, Georgios D.; Papavassilopoulos, George P.

doi:10.1016/j.cmpb.2018.03.014

Cited by 18 publications

(14 citation statements)

References 37 publications

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“…The stochastic discrete time state-space representation of the Gompertz model, which was introduced in [16] and also used in [17], was used here to describe the growth dynamics. This model can be formulated as follows:…”

Section: Tumor Growth Modelingmentioning

confidence: 99%

“…, which is significantly smaller than [0, X max ], can be used as the interval of integration [17]. For a more detailed description of the Maximum Likelihood Estimator, the reader may refer to Section 3.1.3 Numerical Maximum Likelihood in [17].…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

“…In our previous works, we proposed and tested with synthetic data a methodology that estimates the unknown parameters of the Gompertz model [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…The properties of Maximum Likelihood Estimators (MLEs) have been extensively in the past and can be also found in [25]. The MLE implementation was presented in detail in [17] and was able to estimate the growth parameters of the Gompertz model with accuracy on synthetic tumor data. The difficulty of working with HMMs lies in the inability to measure the hidden states.…”

Section: Introductionmentioning

confidence: 99%

“…Some other challenges are the uncertainty which arises due to the small size of the datasets and the calibration that the algorithm needs in order to provide accurate estimates [16,17].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A comparison between Nonlinear Least Squares and Maximum Likelihood estimation for the prediction of tumor growth on experimental data of human and rat origin

Patmanidis

Chignola

Charalampidis

et al. 2019

Biomedical Signal Processing and Control

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Several mathematical models have been developed to explain the growth of tumors and used to fit experimental or clinical data. Their predictive poweri.e. their ability to forecast the future growth on the basis of present knowledge-however, has been rarely explored. Here, we investigate whether a Hidden Markov Model (HMM) based on the well-established Gompertz tumor growth function with additive Gaussian noise could effectively be used to predict the future growth of experimental tumors. The idea behind this work is that one might achieve more accurate predictions if estimates of the unknown parameters of the HMM are used instead of those obtained by fits of the deterministic Gompertz model to the data. We use the principle of Maximum Likelihood

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Section: Tumor Growth Modelingmentioning

confidence: 99%

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

“…In our previous works, we proposed and tested with synthetic data a methodology that estimates the unknown parameters of the Gompertz model [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Some other challenges are the uncertainty which arises due to the small size of the datasets and the calibration that the algorithm needs in order to provide accurate estimates [16,17].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A comparison between Nonlinear Least Squares and Maximum Likelihood estimation for the prediction of tumor growth on experimental data of human and rat origin

Patmanidis

Chignola

Charalampidis

et al. 2019

Biomedical Signal Processing and Control

Self Cite

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Development of a Model to Estimate the Association Between Delay in Cancer Treatment and Local Tumor Control and Risk of Metastases

Stovezky

Brenner

et al. 2021

JAMA Netw Open

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IMPORTANCE The coronavirus disease 2019 (COVID-19) pandemic has led to treatment delays for many patients with cancer. While published guidelines provide suggestions on which cases are appropriate for treatment delay, there are no good quantitative estimates on the association of delays with tumor control or risk of new metastases. OBJECTIVES To develop a simplified mathematical model of tumor growth, control, and new metastases for cancers with varying doubling times and metastatic potential and to estimate tumor control probability (TCP) and metastases risk as a function of treatment delay interval. DESIGN, SETTING, AND PARTICIPANTS This decision analytical model describes a quantitative model for 3 tumors (ie, head and neck, colorectal, and non-small cell lung cancers). Using accepted ranges of tumor doubling times and metastatic development from the clinical literature from 2001 to 2020, estimates of tumor growth, TCP, and new metastases were analyzed for various treatment delay intervals. MAIN OUTCOMES AND MEASURES Risk estimates for potential decreases in local TCP and increases in new metastases with each interval of treatment delay. RESULTS For fast-growing head and neck tumors with a 2-month treatment delay, there was an estimated 4.8% (95% CI, 3.4%-6.4%) increase in local tumor control risk and a 0.49% (0.47%-0.51%) increase in new distal metastases risk. A 6-month delay was associated with an estimated 21.3% (13.4-30.4) increase in local tumor control risk and a 6.0% (5.2-6.8) increase in distal metastases risk. For intermediate-growing colorectal tumors, there was a 2.1% (0.7%-3.5%) increase in local tumor control risk and a 2.7% (2.6%-2.8%) increase in distal metastases risk at 2 months and a 7.6% (2.2%-14.2%) increase in local tumor control risk and a 24.7% (21.9%-27.8%) increase in distal metastases risk at 6 months. For slower-growing lung tumors, there was a 1.2% (0.0%-2.8%) increase in local tumor control risk and a 0.19% (0.18%-0.20%) increase in distal metastases risk at 2 months, and a 4.3% (0.0%-10.6%) increase in local tumor control risk and a 1.9% (1.6%-2.2%) increase in distal metastases risk at 6 months. CONCLUSIONS AND RELEVANCE This study proposed a model to quantify the association of treatment delays with local tumor control and risk of new metastases. The detrimental associations were greatest for tumors with faster rates of proliferation and metastasis. The associations were smaller, but still substantial, for slower-growing tumors.

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Time Series Data to Mathematical Model

Padmanabhan

Meskin

Moustafa

2020

Series in BioEngineering

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Tumor growth modeling: Parameter estimation with Maximum Likelihood methods

Abstract: Using nonstandard, problem specific techniques can improve the estimation accuracy and best exploit the available data.

Cited by 18 publications

References 37 publications

A comparison between Nonlinear Least Squares and Maximum Likelihood estimation for the prediction of tumor growth on experimental data of human and rat origin

A comparison between Nonlinear Least Squares and Maximum Likelihood estimation for the prediction of tumor growth on experimental data of human and rat origin

Development of a Model to Estimate the Association Between Delay in Cancer Treatment and Local Tumor Control and Risk of Metastases

Time Series Data to Mathematical Model

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