Optimal and Robust Designs for Estimating the Concentration Curve and the AUC

The problem of interest is to estimate the concentration curve and the area under the curve (AUC) by estimating the parameters of a linear regression model with an autocorrelated error process. We introduce a simple linear unbiased estimator of the concentration curve and the AUC. We show that this estimator constructed from a sampling design generated by an appropriate density is asymptotically optimal in the sense that it has exactly the same asymptotic performance as the best linear unbiased estimator. Moreover, we prove that the optimal design is robust with respect to a minimax criterion. When repeated observations are available, this estimator is consistent and has an asymptotic normal distribution. Finally, a simulated annealing algorithm is applied to a pharmacokinetic model with correlated errors.