Methods of Robust Design of Nonlinear Models with an Application to Pharmacokinetics

Abstract

Optimal design methods for nonlinear models are dependent on the true but unknown parameter values. Criteria for developing designs that are robust to the choice of parameter values such as ED optimality have been proposed. However, these criteria are computationally intensive and can perform poorly at extremes of the prior parameter distribution. Two different criteria are proposed. Both involve evaluation of the determinant of the Fisher information matrix over models formed at various combinations of the 2.5th and 97.5th percentiles of the parameter space. The performance of the proposed optimality criteria is compared to two existing robust optimal design criteria.

Comparison of Robust Criteria for D-Optimal Designs

“…It is also noted that in the current investigation the local design lnD was optimal under the prior parameter distribution, but this is not always the case and should not be construed to mean that D-optimal design are robust across all sets of parameter vectors (see Foo and Duffull, 2010, for examples where this is not the case).…”

“…In contrast, the HClnD-optimality criterion involves considerably fewer evaluations of the Fisher information matrix compared to ElnD or ED. Recent work indicates that HClnD is expected to be in the order of at least 100-fold less computationally intensive than ED (Foo and Duffull, 2010).…”

“…The HClnD-optimality criterion (Foo and Duffull, 2010) maximizes the summation of the scaled logarithm of the determinant of the Fisher information matrix for component models formed by parameter values assumed at different percentile of the prior parameter distribution. For a model with q parameters there will be m = 2 q component models; that is, there are two component models for a one-parameter model where a component model is formed at each of the lower and upper percentile of the prior parameter distribution.…”

“…However, since PKPD models are generally nonlinear, the D-optimal design is dependent on the true but unknown parameter values. Robust designs, for example, ED (Walter and Pronzato, 1987), EID (Walter and Pronzato, 1987), API (D' Argenio, 1990), and HCD (Foo and Duffull, 2010), were introduced to address this dependency issue by incorporating the prior information of the parameter values in the form of probability distributions.…”

“…In another comparison (Tod and Rocchisani, 1996) in which the precision and accuracy of parameter estimation was compared for a one-compartment and two-compartment PK model it was found that API and EID gave a higher percentage of acceptable parameter estimates and higher precision and accuracy in parameter estimates than ED. Foo and Duffull (2010) examined four robust designs, namely, HCD, MaxiMin, ED, and DE. They found that all four optimality criteria appeared to perform similarly in terms of D-efficiency, while HCD provided a 100-fold improvement in the speed of computation compared to ED and DE.…”