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Fast algorithms for nonparametric population modeling of large data sets. (English) Zbl 1154.93440

Summary: Population models are widely applied in biomedical data analysis since they characterize both the average and individual responses of a population of subjects. In the absence of a reliable mechanistic model, one can resort to the Bayesian nonparametric approach that models the individual curves as Gaussian processes. This paper develops an efficient computational scheme for estimating the average and individual curves from large data sets collected in standardized experiments, i.e. with a fixed sampling schedule. It is shown that the overall scheme exhibits a “client-server” architecture. The server is in charge of handling and processing the collective data base of past experiments. The clients ask the server for the information needed to reconstruct the individual curve in a single new experiment. This architecture allows the clients to take advantage of the overall data set without violating possible privacy and confidentiality constraints and with negligible computational effort.

MSC:

93E12 Identification in stochastic control theory
93E03 Stochastic systems in control theory (general)
92D25 Population dynamics (general)
93A30 Mathematical modelling of systems (MSC2010)

Software:

NONMEM
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References:

[1] Anderson, B. D.O.; Moore, J. B., Optimal filtering (1979), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ, USA · Zbl 0758.93070
[2] Basu, R.; Dalla Man, C.; Campioni, M.; Basu, A.; Klee, G.; Jenkins, G., Effect of age and sex on postprandial glucose metabolism: Difference in glucose turnover, insulin secretion, insulin action, and hepatic insulin extraction, Diabetes, 55, 2001-2014 (2006)
[3] Beal, S. L.; Sheiner, L. B., Estimating population kinetics, Critical Reviews in Biomedical Engineering, 8, 3, 195-222 (1982)
[4] Beal, S., & Sheiner, L. (1992). NONMEM user’s guide; Beal, S., & Sheiner, L. (1992). NONMEM user’s guide
[5] Bergman, R. N.; Bowden, C. R.; Cobelli, C., The minimal model approach to quantification of factors controlling glucose disposal in man, (Carbohydrate metabolism (1981), Wiley: Wiley New York)
[6] Bertoldo, A.; Sparacino, G.; Cobelli, C., “Population” approach improves parameter estimation of kinetic models from dynamic PET data, IEEE Transactions on Medical Imaging, 23, 3, 297-306 (2004)
[7] Davidian, M.; Giltinan, D. M., Nonlinear models for repeated measurement data (1995), Chapman and Hall: Chapman and Hall New York
[8] Evgeniou, T.; Micchelli, C. A.; Pontil, M., Learning multiple tasks with kernel methods, Journal of Machine Learning Research, 6, 615-637 (2005) · Zbl 1222.68197
[9] Fattinger, K. E.; Verotta, D., A nonparametric subject-specific population method for deconvolution: I. Description, internal validation, and real data examples, Journal of Pharmacokinetics and Biopharmaceutics, 23, 581-610 (1995)
[10] Ferrazzi, F., Magni, P., & Bellazzi, R. (2003). Bayesian clustering of gene expression time series. In Proceedings of the 3rd international workshop on bioinformatics for the management, analysis and interpretation of microarray data (NETTAB 2003); Ferrazzi, F., Magni, P., & Bellazzi, R. (2003). Bayesian clustering of gene expression time series. In Proceedings of the 3rd international workshop on bioinformatics for the management, analysis and interpretation of microarray data (NETTAB 2003)
[11] Gilks, W. R.; Richardson, S.; Spiegelhalter, D. J., Markov chain Monte Carlo in practice (1996), Chapman and Hall: Chapman and Hall London · Zbl 0832.00018
[12] Ibragimov, I. A.; Khasminskii, R. Z., Statistical estimation: Asymptotic theory (1981), Springer · Zbl 0467.62026
[13] Jacquez, J. A., Compartmental analysis in biology and medicine (1985), University of Michigan Press: University of Michigan Press Ann Arbor · Zbl 0703.92001
[14] Lunn, D. J.; Best, N.; Thomas, A.; Wakefield, J. C.; Spiegelhalter, D., Bayesian analysis of population PK/PD models: General concepts and software, Journal of Pharmacokinetics and Pharmacodynamics, 29, 3, 271-307 (2002)
[15] Magni, P.; Bellazzi, R.; De Nicolao, G.; Poggesi, I.; Rocchetti, M., Nonparametric AUC estimation in population studies with incomplete sampling: A Bayesian approach, Journal of Pharmacokinetics and Pharmacodynamics, 29, 5-6, 445-471 (2002)
[16] Neve, M.; De Nicolao, G.; Marchesi, L., Nonparametric identification of population models via Gaussian processes, Automatica, 43, 1134-1144 (2007) · Zbl 1123.93319
[17] Neve, M.; De Nicolao, G.; Marchesi, L., Nonparametric identification of population models: An MCMC approach, IEEE Transactions on Biomedical Engineering, 55, 41-50 (2008)
[18] Park, K.; Verotta, D.; Blaschke, T. F.; Sheiner, L. B., A semiparametric method for describing noisy population pharmacokinetic data, Journal of Pharmacokinetics and Biopharmaceutics, 25, 615-642 (1997)
[19] Rasmussen, C. E.; Williams, C. K.I., Gaussian processes for machine learning (2006), The MIT Press · Zbl 1177.68165
[20] Sheiner, L. B., The population approach to pharmacokinetic data analysis: Rationale and standard data analysis methods, Drug Metabolism Reviews, 15, 153-171 (1994)
[21] Shiryaev, A. N., Probability (1996), Springer: Springer New York, NY, USA · Zbl 0909.01009
[22] Vicini, P.; Caumo, A.; Cobelli, C., The hot IVGTT two-compartment minimal model: Indexes of glucose effectiveness and insulin sensitivity, American Journal of Physiology, 273, 1024-1032 (1997)
[23] Vicini, P.; Cobelli, C., The iterative two-stage population approach to IVGTT minimal modeling: Improved precision with reduced sampling, American Journal of Physiology Endocrinology and Metabolism, 280, 1, 179-186 (2001)
[24] Vicini, P.; Zachwieja, J. J.; Yarasheski, K. E.; Bier, D. M.; Caumo, A.; Cobelli, C., Glucose production during an IVGTT by deconvolution: Validation with the tracer-to-tracee clamp technique, American Journal of Physiology, 276, 285-294 (1999)
[25] Wahba, G., Spline models for observational data (1990), SIAM: SIAM Philadelphia · Zbl 0813.62001
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