A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models. (January 2017)

• Record Type: Journal Article
• Authors: Casero-Alonso, V.; López-Fidalgo, J.; Torsney, B.
• Is Part Of: Computer methods and programs in biomedicine. Volume 138(2017)
• Page Start: 105
• Page End: 115
• Publication Date: 2017-01
• Subjects: Applet -- c-optimality -- Equivalence theorem -- Equal variance optimality -- Fisher information matrix -- Optimal design; Medicine -- Computer programs -- Periodicals; Biology -- Computer programs -- Periodicals; Computers -- Periodicals; Medicine -- Periodicals; Médecine -- Logiciels -- Périodiques; Biologie -- Logiciels -- Périodiques; Biology -- Computer programs; Medicine -- Computer programs; Periodicals; Electronic journals; 610.28
• DOI: 10.1016/j.cmpb.2016.10.009
• Languages: English
• ISSNs: 0169-2607

Abstract

Highlights: A user-friendly applet to compute MV-optimal designs is provided. The applet is applied to binary response and weighted linear regression models, for several standard weight functions. The methodology for obtaining MV-optimal designs in a general compact interval design space is given. Optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. Illustrative examples shows a representation of MV-optimal designs in the plane defined by the extremes of the design space. Abstract: Background and objective: Binary response models are used in many real applications. For these models the Fisher information matrix (FIM) is proportional to the FIM of a weighted simple linear regression model. The same is also true when the weight function has a finite integral. Thus, optimal designs for one binary model are also optimal for the corresponding weighted linear regression model. The main objective of this paper is to provide a tool for the construction of MV-optimal designs, minimizing the maximum of the variances of the estimates, for a general design space. Methods: MV-optimality is a potentially difficult criterion because of its nondifferentiability at equal variance designs. A methodology for obtaining MV-optimal designs where the design space is a compact interval [ a, b ] will be given for several standard weight functions. Results: The methodology will allow us to build a user-friendly computer tool based on Mathematica to compute MV-optimal designs. Some illustrative examples will show a representation of MV-optimal designs in the Euclidean plane, taking a and b as the axes. The applet will be explained using two relevant models. In the first one the case of a weighted linear regression model is considered, where the weight function is directly chosen from a typical family. In the second example a binary response model is assumed, where the probability of the outcome is given by a typical probability distribution. Conclusions: Practitioners can use the provided applet to identify the solution and to know the exact support points and design weights.