Least-squares fitting of compartmental model (or function) to measured data provides the model (function) parameters, and the sum-of-squares (SS) as an estimate of the goodness of the fit, but not the errors on the estimated model (function) parameters. With the means of classical statistics we could estimate the confidence intervals (CI), if the measurement errors of the data were normally distributed, with a known variance. Usually, this not the case, and most certainly not regarding the PET data. However, Monte Carlo simulation based bootstrap method allows estimation of the errors on the estimated model (function) parameters without knowing the distribution and variance of the errors in the data.
In the bootstrap method the model is fitted to the data as usual, but the residuals for the individual data points are stored, and randomly picked to generate synthetic datasets. The synthetic datasets are then fitted using the same method, each dataset fit providing us a set of bootstrapped parameter estimates. From these we can estimate confidence intervals for the model parameters.
Bootstrap method can be combined with AIC in model selection (Burnham & Anderson, 2002). Spectral analysis can be used in combination with bootstrapping (Turkheimer et al., 1998).
Bootstrap approach has been validated for estimation of the statistical properties of PET and SPECT reconstructed images, including variance and noise correlation (Buvat, 2002; Dahlbom, 2002).
Patient movement during the PET scan can be detected using bootstrap method, if list-mode data is saved (Huang et al., 2011).
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Ikoma Y, Ito H, Yamaya T, Kitamura K, Takano A, Toyama H, Suhara T. Evaluation of error on parameter estimates in the quantitative analysis of receptor studies with positron emission tomography. IEEE Nuc Sci Sym Con. 2005: 2683-2685. doi: 10.1109/NSSMIC.2005.1596889.
Ikoma Y, Shidahara M, Ito H, Seki C, Suhara T, Kanno I. Evaluation of optimal scan time by bootstrap approach for quantitative analysis in PET receptor study. positron emission tomography. IEEE Nuc Sci Sym Con. 2006. doi: 10.1109/NSSMIC.2006.354335.