Abstract
A multiple-objective optimal design is useful for dose-response studies because it can incorporate several objectives at the design stage. Objectives can be of varying interests and a properly constructed multiple-objective optimal design can provide user-specified efficiencies, delivering higher efficiencies for the more important objectives. In this work, we introduce the VNM package written in R for finding 3-objective locally optimal designs for the 4-parameter logistic (4PL) model widely used in education, bioscience and in the manufacturing industry. The package implements the methodology to construct multipleobjective optimal designs in Hyun and Wong (2015). As illustrative examples, we focus on a biomedical application where our objectives are to estimate: (1) the shape of the dose-response curve, (2) the median effective dose level (ED50) and (3) the minimum effective dose level (MED) in the 4PL model. Our VNM package uses a state-of-theart algorithm to generate multiple-objective optimal designs that meet the user-specified efficiency requirement for each objective, provides tools for calculating the efficiency of the generated design under each objective and also a plot for confirming optimality of the VNM-generated design. The package can also be used to determine an optimal scheme for allocating subjects to the various doses when the number and doses of the drug are fixed in advance.
Highlights
Optimal designs are getting more attention nowadays because of rising experimental cost and the desire to use minimum resources without sacrificing statistical precision in the inference making process
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
We describe the VNM package for finding 3-objective optimal designs to estimate the shape of dose-response, the ED50 and the minimum effective dose level (MED) for the 4PL model
Summary
Optimal designs are getting more attention nowadays because of rising experimental cost and the desire to use minimum resources without sacrificing statistical precision in the inference making process. The objectives typically have different levels of interest in the study and it is desirable to have a multiple-objective optimal design that provides user-specified efficiency under each criterion, with higher efficiencies for the more important objectives. Numerous researches have attempted to tackle design problems with multiple objectives. Some used ad-hoc or numerical methods and a few found dual-objective optimal designs using theory. A limited number of 3-objective optimal designs has recently shown up in a non dose-response set up where the design space is discrete. The optimal choices depend on the given design criterion, the statistical model and the range of plausible doses for the study.
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