Casero-Alonso, V., López-Fidalgo, J. and Torsney, B.
(2017)
A computer tool for a minimax criterion in binary response and heteroscedastic simple linear regression models.
*Computer Methods and Programs in Biomedicine*, 138,
pp. 105-115.
(doi: 10.1016/j.cmpb.2016.10.009)
(PMID:27886709)

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## 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.

Item Type: | Articles |
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Additional Information: | Casero-Alonso and López-Fidalgo have been sponsored by Ministerio de Economía y Competitividad and fondos FEDER MTM2013-47879-C2-1-P and the Grant GI20163415 from UCLM. |

Status: | Published |

Refereed: | Yes |

Glasgow Author(s) Enlighten ID: | Torsney, Dr Bernard |

Authors: | Casero-Alonso, V., López-Fidalgo, J., and Torsney, B. |

College/School: | College of Science and Engineering > School of Mathematics and Statistics > Statistics |

Journal Name: | Computer Methods and Programs in Biomedicine |

Publisher: | Elsevier |

ISSN: | 0169-2607 |

ISSN (Online): | 1872-7565 |

Published Online: | 27 October 2016 |

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