Model selection for time-activity curves: the corrected Akaike information criterion and the F-test

Data analysis often requires a multi model approach, i.e. the best model or models are selected from a well chosen set of candidate models and subsequent parameter inference is conducted. The selection of the model or models which are best supported by the data can be accomplished using various criteria. The present work focuses on the comparison of two approaches namely the corrected Akaike information criterion (AICc) and the F-test for sparse data sets, which are common in medical research. The selection of the true model and the determination of relevant pharmacokinetic parameters as the clearance, the volume of distribution and the mean residence time are examined using Monte Carlo simulations with 10000 replications. The data (N = 10 per replication) are generated from a sum of two exponentials, which parameters were determined by fitting to time-concentration data of 111In labelled anti-CD66 antibody in blood serum. Four different normal distributed multiplicative statistical errors (0.05, 0.1, 0.15, 0.2) were examined. The set of candidate models consists of sums of up to 3 exponentials. Comparisons with two different model set sizes were conducted. All candidate models are fitted to the generated data and selected according to the AICc and the F-test. Both selection criteria perform well for our data. The selection frequency of functions of lower dimension increases proportionally to the statistical error for both criteria, while for higher errors, the AICc tends to choose a model of lower dimension more frequently than the F-test. In addition, the overfitted fraction decreases proportionally to the statistical error for both methods but selection frequency of function of higher dimension is larger using the F-test. The choice of the adequate model set is important for the positive effect of model averaging concerning the bias and the variability of the estimated parameters. It is in general assumed and has been confirmed in this study that parameter estimation using the AICc has clear advantages over the F-test.