Estimation of kinetic parameters in graphical analysis of PET imaging data

Positron emission tomography (PET) imaging is a useful tool for quantifying various aspects of the distribution of neuroreceptors throughout the human brain in vivo. A typical analysis consists of applying a pharmacokinetic model to the data, estimating the parameters of the model using non-linear least squares methods, then taking the appropriate function of estimated model parameters as a final estimate of the parameter(s) of interest. As an alternative for fitting these models, it has been shown previously that taking a particular transformation of the data results in two variables that have a linear relationship, and that the slope of this linear relationship is the parameter of primary interest. However, estimating the slope using ordinary least squares (OLS) regression results in a large negative bias. By rearranging the terms in the relationship, the problem may be reformed to allow direct application of standard estimation principles. Estimators resulting from this approach are shown via simulation to have better estimation properties as compared to the OLS estimators.