Optimum Dose Levels when Males and Females Differ in Response

Atkinson, Anthony C.; Demétrio, Clarice Garcia Borges; Zocchi, Silvio Sandoval

doi:10.2307/2986346

Cited by 22 publications

(16 citation statements)

References 18 publications

(17 reference statements)

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“…In this paper, it is proposed the use of canonical forms to solve a problem non-standard of optimal experimental designs laid out by Atkinson et al (1995) [1] upon calculating the optimum dose of a fly insecticide. The main difficulty arises by adding uncertainty about gender since they differ in the response and the experiment only senses applied on the whole population.…”

Section: Discussionmentioning

confidence: 99%

“…Denoting η as the probability of death, x as the logarithm of dose (in micrograms per millilitre) and y as the number of deaths, it must be: [1]. A wide range of dichotomous response-mechanisms can be expressed in terms of the previous model.…”

Section: Introductionmentioning

confidence: 99%

“…The parameter estimates were obtained in Atkinson et al (1995) [1]. The last step will be to calculate the value of the original variables through inverse change…”

mentioning

confidence: 99%

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The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

Gutiérrez¹,

Martín²

2014

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Logistic regression models for binary response problems are present in a wide variety of industrial, biological, social and medical experiments; therefore, optimum designs are a valuable tool for experimenters, leading to estimators of parameters with minimum variance. Our interest in this contribution is to provide explicit formulae for the D-optimal designs as a function of the unknown parameters for the logistic model ( )

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

Gutiérrez¹,

Martín²

2014

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“…In the following sections, we will focus on determining D-and A-optimal designs for and 1 2 and E-optimal design for the testing problem of the form H 0 = 0 against both-sided alternatives. It is worth mentioning that Atkinson et al (1995) studied design optimality in a similar experimental situation when males and females differ in response in the sense of m = f . However, the model admitted m = f to start with.…”

Section: Effect Of a Qualitative Classifiermentioning

confidence: 99%

Optimal Designs for Binary Logistic Regression with a Qualitative Classifier with Independent Levels

Nandy

Helle

Liski

et al. 2010

Communications in Statistics - Simulation and Computation

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Dose response studies arise in many medical applications. Often, such studies are considered within the framework of binary-response experiments such as successfailure. In such cases, popular choices for modeling the probability of response are logistic or probit models. Design optimality has been well studied for the logistic model with a continuous covariate. A natural extension of the logistic model is to consider the presence of a qualitative classifier. In this work, we explore D-, A-, and E-optimal designs in a two-parameter, binary logistic regression model after introducing a binary, qualitative classifier with independent levels.

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“…There are three main approaches: sequential experimentation [5,6], maximin designs [7] and Bayesian designs [8]. More recent work [9] has used computer intensive optimisation methods to find designs for several variables which are robust to misspecification of the parameter values. In addition, use of the optimum-in-average (or compromise) criterion by Woods et al [10] has allowed designs to be found that are also robust to the choice of link function and form of the linear predictor (see also [11]).…”

Section: Introductionmentioning

confidence: 99%

Robust designs for binary data: applications of simulated annealing

Woods

2010

Journal of Statistical Computation and Simulation

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When the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for Doptimality under a GLM is presented which improves the computational efficiency of the search.Robust designs for binary data: applications of simulated annealingSouthampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK AbstractWhen the aim of an experiment is the estimation of a Generalised Linear Model (GLM), standard designs from linear model theory may prove inadequate. This paper describes a flexible approach for finding designs for experiments to estimate GLMs through the use of D-optimality and a simulated annealing algorithm. A variety of uncertainties in the model can be incorporated into the design search, including the form of the linear predictor, through use of a robust design selection criterion and a postulated model space. New methods appropriate for screening experiments and the incorporation of correlations between possible model parameters are described through examples. An updating formula for D-optimality under a GLM is presented which improves the computational efficiency of the search.

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Optimum Dose Levels when Males and Females Differ in Response

Cited by 22 publications

References 18 publications

The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

The Construction of Locally D-Optimal Designs by Canonical Forms to an Extension for the Logistic Model

Optimal Designs for Binary Logistic Regression with a Qualitative Classifier with Independent Levels

Robust designs for binary data: applications of simulated annealing

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