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

A multiple-objective optimal design is useful for dose-response studies because it canincorporate several objectives at the design stage. Objectives can be of varying interestsand a properly constructed multiple-objective optimal design can provide user-specifiedefficiencies, 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 designsfor the 4-parameter logistic (4PL) model widely used in education, bioscience and in themanufacturing industry. The package implements the methodology to construct multipleobjectiveoptimal designs in Hyun and Wong (2015). As illustrative examples, we focuson a biomedical application where our objectives are to estimate: (1) the shape of thedose-response curve, (2) the median effective dose level (ED50) and (3) the minimumeffective dose level (MED) in the 4PL model. Our VNM package uses a state-of-theartalgorithm to generate multiple-objective optimal designs that meet the user-specifiedefficiency requirement for each objective, provides tools for calculating the efficiency ofthe generated design under each objective and also a plot for confirming optimality of theVNM-generated design. The package can also be used to determine an optimal schemefor allocating subjects to the various doses when the number and doses of the drug arefixed in advance.