Evaluation of objective functions for estimation of kinetic parameters

There is growing interest in quantitatively analyzing in vivo image data, as this facilitates objective comparisons and measurement of effect. In this regard, people increasingly turn to pharmacokinetic models and estimation of parameters of such models. In this work several parameter estimation methodologies were compared within the context of the most common pharmacokinetic model used in positron emission tomography imaging to describe glucose metabolism and receptor-ligand interactions at tracer concentrations. Simulated data were generated with 1000 realizations at each of 5 different noise levels. Estimates of the kinetic parameters were made for each realization using seven iterative, nonlinear estimation methodologies: ordinary least squares (OLS), weighted least squares (WLS), penalized weighted least squares (PWLS), iteratively reweighted least squares (IRLS), and variations of extended least squares (ELS0, ELS1, ELS3). Additionally, generalized linear least squares (GLLS) was also used. With relatively noise-free data, the iterative nonlinear estimation methods generally produced low-bias, high-precision parameter estimates, whereas with GLLS the bias was more prominent. Greater distinction between the estimation methods was seen at the higher, more realistic noise levels, with ELS and IRLS methods generally achieving better precision than the other methods. At the high noise levels WLS, GLLS, and PWLS yielded parameter estimates with large bias (>200%) for some kinetic parameters. In general, there are more favorable estimator methodologies than the frequently employed WLS. Methods that determine values of weights based on model output--IRLS, ELS0, ELS1 and ELS3--generally perform better than methods that determine values of weights based directly on the experimental data.