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Bayesian analysis of a one-compartment kinetic model used in medical imaging

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  • Peter Malave
  • Arkadiusz Sitek

Abstract

Kinetic models are used extensively in science, engineering, and medicine. Mathematically, they are a set of coupled differential equations including a source function, otherwise known as an input function. We investigate whether parametric modeling of a noisy input function offers any benefit over the non-parametric input function in estimating kinetic parameters. Our analysis includes four formulations of Bayesian posteriors of model parameters where noise is taken into account in the likelihood functions. Posteriors are determined numerically with a Markov chain Monte Carlo simulation. We compare point estimates derived from the posteriors to a weighted non-linear least squares estimate. Results imply that parametric modeling of the input function does not improve the accuracy of model parameters, even with perfect knowledge of the functional form. Posteriors are validated using an unconventional utilization of the χ-super-2-test. We demonstrate that if the noise in the input function is not taken into account, the resulting posteriors are incorrect.

Suggested Citation

  • Peter Malave & Arkadiusz Sitek, 2015. "Bayesian analysis of a one-compartment kinetic model used in medical imaging," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 98-113, January.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:1:p:98-113
    DOI: 10.1080/02664763.2014.934666
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    References listed on IDEAS

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    1. Yan Zhou & John Aston & Adam Johansen, 2013. "Bayesian model comparison for compartmental models with applications in positron emission tomography," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 993-1016.
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