Multiple-Objective Optimal Designs for Studying the Dose Response Function and Interesting Dose Levels

Abstract

We construct an optimal design to simultaneously estimate three common interesting features in a dose-finding trial with possibly different emphasis on each feature. These features are (1) the shape of the dose-response curve, (2) the median effective dose and (3) the minimum effective dose level. A main difficulty of this task is that an optimal design for a single objective may not perform well for other objectives. There are optimal designs for dual objectives in the literature but we were unable to find optimal designs for 3 or more objectives to date with a concrete application. A reason for this is that the approach for finding a dual-objective optimal design does not work well for a 3 or more multiple-objective design problem. We propose a method for finding multiple-objective optimal designs that estimate the three features with user-specified higher efficiencies for the more important objectives. We use the flexible 4-parameter logistic model to illustrate the methodology but our approach is applicable to find multiple-objective optimal designs for other types of objectives and models. We also investigate robustness properties of multiple-objective optimal designs to mis-specification in the nominal parameter values and to a variation in the optimality criterion. We also provide computer code for generating tailor made multiple-objective optimal designs.

VNM: An R Package for Finding Multiple-Objective Optimal Designs for the 4-Parameter Logistic Model

“…This is generally a laborious task even though the time required to determine the sought multiple-objective optimal design is now much reduced using our current package. An alternative and likely more effective way of using this package to generate multiple-objective optimal designs is described in Hyun and Wong (2015). Of course, if the demands are too stringent, a multiple objective optimal design may not be found.…”

“…Given the multiple objectives, a multipleobjective optimal design can help to identify the optimal number of dose levels to use, where these optimal dose levels are and the optimal distribution of subjects over the selected dose levels for attaining the objectives most efficiently. Hyun and Wong (2015) recently constructed optimal designs for estimating three interesting features in a 4-parameter logistic model and each of these objectives may have different degrees of interest to the researcher. Their approach is systematic and can be directly applied to search for other types of multiple-objective optimal designs in other models.…”

“…We describe here our VNM package that implements the method from Hyun and Wong (2015) for generating one, two or three-objective optimal designs for the 4-parameter logistic (4PL) model. This package is available from the Comprehensive R Archive Network at https://CRAN.R-project.org/package=VNM.…”

Optimal designs based on the maximum quasi-likelihood estimator

“…For example, when working with an inhibitory drug, it may be desirable to estimate the dose that would shrink the tumor size by some user-specified δ units. It is straightforward to show that for the 4PL model, ED 50 = − θ 3 /θ 2 and $\mathit{MED}(\delta )=\{\mathit{log}(\frac{-\delta }{{\theta }_1+\delta })-{\theta }_3\}/{\theta }_2$ if θ 2 > 0 or $\mathit{MED}(\delta )=\{\mathit{log}(\frac{{\theta }_1-\delta }{\delta })-{\theta }_3\}/{\theta }_2$ if θ 2 < 0, where 0 < | δ | < θ 1 and δ must have an opposite sign from θ 2 (Hyun and Wong, 2015). …”

Robust C-optimal Design For Estimating Multiple EDps Under The 4-parameter Logistic Model

“…The ED 50 is a common interesting dose level because it provides a reasonable expectation of the drug effect. Other dose levels such as ED 10 or ED 90 are also interesting dose levels sometimes.…”