Geodesic
Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model
Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018) no. 2, pp. 376-391.

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We use a Markov chain Monte Carlo (MCMC) method to quantify uncertainty in parameters of the heterogeneous linear compartmental model of cell population growth, described by a system of ordinary differential equations. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set specifies the following characteristics of the kinetics of human T lymphocyte proliferation assay in vitro: the total number of live cells and dead but not disintegrated cells and the number of cells divided j times. Our goal is to compare results of the MCMC analysis of the uncertainty in the best-fit parameter estimates with the ones obtained earlier, using the variance-covariance approach, the profile-likelihood based approach and the bootstrap technique. We show that the computed posterior probability density functions are Gaussian for most of the model parameters and they are close to Gaussian ones for other parameters except one. We present posterior uncertainty limits for the model solution and new observations. 
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     author = {T. Luzyanina and G. Bocharov},
     title = {Markov chain {Monte} {Carlo} parameter estimation of the {ODE} compartmental cell growth model},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
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T. Luzyanina; G. Bocharov. Markov chain Monte Carlo parameter estimation of the ODE compartmental cell growth model. Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018) no. 2, pp. 376-391. http://geodesic.mathdoc.fr/item/MBB_2018_13_2_a12/

[1] V. Muller, A. F. Maree, R. J. De Boer, “Small variations in multiple parameters account for wide variations in HIV-1 set-points: a novel modelling approach”, Proc. R. Soc. Lond. B, 268 (2001), 235–242 | DOI

[2] R. J. De Boer, A. S. Perelson, “Quantifying T lymphocyte turnover”, J. Theor. Biol., 327 (2013), 45–87 | DOI | MR | Zbl

[3] S. Hross, J. Hasenauer, “Analysis of CFSE time-series data using division-, age- and label-structured population models”, Bioinformatics, 32:15 (2016), 2321–2329 | DOI | MR

[4] Z. R. Kenz, H. T. Banks, R. C. Smith, “Comparison of frequentist and Bayesian confidence analysis methods on a viscoelastic stenosis model”, SIAM/ASA J. on Uncertainty Quantification, 1:1 (2013), 348–369 | DOI | MR | Zbl

[5] B. Ballnus, S. Hug, K. Hatz, L. Grlitz, J. Hasenauer, F. J. Theis, “Comprehensive benchmarking of Markov chain Monte Carlo methods for dynamical systems”, BMC Syst. Biol., 11:63 (2017), 1–18

[6] F. J. Samaniego, A comparison of the Bayesian and frequentist approaches to estimation, Springer Series in Statistics, Springer-Verlag, New York, 2010 | DOI | MR | Zbl

[7] T. Luzyanina, S. Mrusek, J. T. Edward, D. Roose, S. Ehl, G. Bocharov, “Computational analysis of CFSE proliferation assay”, J. of Math. Biology, 54:1 (2007), 57–89 | DOI | MR | Zbl

[8] D. J. Klinke, “An empirical Bayesian approach for model-based inference of cellular signaling networks”, BMC Bioinformatics, 10 (2009), 371–387 | DOI

[9] A. Solonen, P. Ollinaho, M. Laine, H. Haario, J. Tamminen, H. Jarvinen, “Efficient MCMC for climate model parameter estimation: Parallel adaptive chains and early rejection”, Bayesian Analysis, 7:3 (2012), 715–736 | DOI | MR | Zbl

[10] S. Hug, A. Raue, J. Hasenauer, U. Klingmuller, J. Timmer, F. J. Theis, “High-dimensional Bayesian parameter estimation: Case study for a model of JAK2/STAT5 signaling”, Math. Bioscienses, 246 (2013), 293–304 | DOI | MR | Zbl

[11] H. Haario, M. Laine, A. Mira, E. Saksman, “DRAM: Efficient adaptive MCMC”, Stat. Comput., 16 (2006), 539–354 | DOI | MR

[12] Y. Bard, Nonlinear parameter estimation, Academic Press, New York, 1974 | MR | Zbl

[13] D. J. Venzon, S. H. Moolgavkar, “A method for computing profile-likelihood-based confidence intervals”, Appl. Statist., 37:1 (1988), 87–94 | DOI | MR

[14] B. Efron, R. Tibshirani, “Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy”, Stat. Sci., 1:1 (1986), 54–77 | DOI | MR

[15] H. Haario, E. Saksman, J. Tamminen, “An adaptive Metropolis algorithm”, Bernoulli, 7:2 (2001), 223–242 | DOI | MR | Zbl

[16] M. P. Wand, M. C. Jones, Kernel smoothing, Chapman Hall, London, 1995 | MR | Zbl

[17] P. S. Brooks, G. O. Roberts, “Assessing convergence of Markov chain Monte Carlo algorithms”, Stat. Comput., 8 (1998), 319–335 | DOI