Robust D-optimal Design of Nonlinear Fixed Effects Pharmacokinetic Model

Background: D-optimality is often used to design an optimum experiment for the purpose of parameter estimation. When the model is nonlinear, D-optimal designs depend on the nominal parameter values in the model, which are unknown. In order to address this dependency issue, various robust optimal design methods have been introduced [1, 2]. These methods utilize prior information of the parameter distribution. However, most of these robust design criteria (e.g. ED-optimality where the Expectation of the Determinant is taken over the prior parameter values) invoke significant computational burden. This study proposes to compare the Hypercube D-optimal design (HCD) and GD optimal design to commonly used existing methods such as ED and DE.

Aim: To develop and evaluate a robust optimal design criterion for D-optimal design of pharmacokinetic models.

Methods: Linear IV Bolus and Bateman pharmacokinetic models were considered in this study. For each model, one thousand parameter values were simulated from a multivariate log normal distribution. The optimal designs of different optimal criteria (ED, DE, GD and HCD) were found using simulated annealing algorithm. Comparisons were made in terms of (1) D-efficiency, (2) parameter relative standard error and (3) the time taken to locate D-optimal design.

Results: Result from our empirical study showed that HCD and GD optimal design appeared to be cost efficient and perform equally well as compared to ED and DE optimal design for nonlinear models. HCD-optimal design showed comparable or even better D-efficiency values compared to ED optimal design when evaluated at different nominal parameter values. The time taken to locate HCD optimal design was more than 100 times faster than to locate ED optimal design.

Conclusion: HCD optimal design is a rational choice to design optimum experiment for the purpose of parameter estimation for nonlinear models.


  1. Walter E, Pronzato L. Optimal experiment design for nonlinear models subject to large prior uncertainties. Am. J. Physiol. Regul. Integr. Comp. Physiol 1987; 253: R530-R534.
  2. D’Argenio DZ. Incorporating prior parameter uncertainty in the design of sampling schedules forpharmacokinetic parameter estimation experiments. Mathematical Biosciences 1990; 99: 105-118.