Comparison of ED, EID, and API criteria for the robust optimization of sampling times in pharmacokinetics

Optimization of the sampling schedule can be used in pharmacokinetic (PK) experiments to increase the accuracy and the precision of parameter estimation or to reduce the number of samples required. Several optimization criteria that formally incorporate prior parameter uncertainty have been proposed earlier. These criteria consist in finding the sampling schedule that maximizes the expectation (over a given parameter distribution) of det F (ED-optimality) or Log(det F) (API-optimality), or minimizes the expectation of 1/det F (EID-optimality), where F is the Fisher information matrix. The precision and the accuracy of parameter estimation after having fitted a PK model to a small number of optimal data points (determined according to D, ED, EID, and API criteria) or to a naive sampling schedule were compared in a Monte Carlo simulation study. A one-compartment model with first-order absorption rate (3 parameters) and a two-compartment model with zero-order infusion rate (4 parameters) were considered. Data were simulated for 300 subjects with both structural models, combined with several residual error models (homoscedastic, heteroscedastic with constant or variable coefficient of variation). Interindividual variabilities in PK parameters ranged from 25-66%. ED-, EID-, and API-optimal sampling times were calculated using the software OSP-Fit. Three or five samples were allowed for parameter estimation by extended least-squares. Performances of each design criterion were evaluated in terms of mean prediction error, root mean squared error, and number of acceptable estimates (i.e., with a SE less than 30%). Compared to the D-optimal design, the EID and API designs reduced the bias and the imprecision of the estimation of the parameters having a large interindividual variability. Moreover, the API design resulted in some cases in a higher number of acceptable estimates.