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23
Design issues for generalized linear models: A review
 Statistical Science
, 2006
"... Abstract. Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and bui ..."
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Abstract. Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs. Key words and phrases: Bayesian design, dependence on unknown parameters, locally optimal design, logistic regression, response surface methodology, quantal dispersion graphs, sequential design. 1.
Bayesian Optimal Design in Population Models of Hematologic Data
 Statistics in Medicine
, 1995
"... We introduce a population model to design optimal apheresis schedules to collect blood stem cells from cancer patients. Blood stem cells are collected prior to the patient undergoing highdose chemoradiotherapy and are returned after this treatment to enable reconstitution of the white blood cell co ..."
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We introduce a population model to design optimal apheresis schedules to collect blood stem cells from cancer patients. Blood stem cells are collected prior to the patient undergoing highdose chemoradiotherapy and are returned after this treatment to enable reconstitution of the white blood cell components. Maximizing the number of cells collected in as few aphereses as possible is desirable. We use a longitudinal data model with random effects to describe profiles of individual patients. A hierarchical prior model introduces common mean profiles for patients undergoing different treatments. The optimal apheresis schedule for a new patient is found by minimizing an expected loss over the posterior predictive distribution of the patient's predicted CD34 profile. Estimation of the model and solution of the optimal design problem are implemented by a simulation approach, which allows us to accommodate arbitrary shapes for the profiles and realistic loss functions which include relative p...
MultipleObjective Optimal Designs For The Logit Model
 Comm. Stat. Theory Methods
, 1998
"... The toxicity and efficiency of a drug must be determined before it is approved for general use. Quantal doseresponse experiments are routinely conducted to examine the response rates at dose levels of interest. Multipleobjective optimal designs for such studies are found and compared with the popu ..."
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Cited by 7 (5 self)
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The toxicity and efficiency of a drug must be determined before it is approved for general use. Quantal doseresponse experiments are routinely conducted to examine the response rates at dose levels of interest. Multipleobjective optimal designs for such studies are found and compared with the popular equal allocation rules.
Experimental Design: A Bayesian Perspective
"... Introduction Experimentation plays an integral part in the scientific method. Conjectures and hypotheses are put forth based on the current state of knowledge. Experimental data may be collected to address unknown aspects of the problem. Int. Encyc. Social and Behavioral Sciences 4 April 2001 2 Fin ..."
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Introduction Experimentation plays an integral part in the scientific method. Conjectures and hypotheses are put forth based on the current state of knowledge. Experimental data may be collected to address unknown aspects of the problem. Int. Encyc. Social and Behavioral Sciences 4 April 2001 2 Finally, analysis of experimental results may lead to one hypothesis being favored over others or may lead to new questions and investigations, so that the process is repeated, with the accumulation of additional knowledge about the scientific process under investigation. In some fields of scientific inquiry, physical models can be used to describe the outcome of an experiment given certain inputs with complete certainty. In the majority of applications, one cannot describe the scientific phenomena perfectly, leading to a distribution on possible outcomes, which can be described by probability models. For example, in comparing a new therapy to an existing treatment, ind
Constrained optimal discriminating designs for Fourier regression models. Annals of Statistical Mathematics
, 2007
"... Abstract In this article, the problem of constructing efficient discrimination designs in a Fourier regression model is considered. We propose designs which maximize the power of the Ftest, which discriminates between the two highest order models, subject to the constraints that the tests that disc ..."
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Abstract In this article, the problem of constructing efficient discrimination designs in a Fourier regression model is considered. We propose designs which maximize the power of the Ftest, which discriminates between the two highest order models, subject to the constraints that the tests that discriminate between lower order models have at least some given relative power. A complete solution is presented in terms of the canonical moments of the optimal designs, and for the special case of equal constraints even more specific formulae are available.
Designing observation times for interval censored data. Sankyha A
, 1998
"... SUMMARY. This paper studies the optimal choice of observation times for duration data, presenting necessary conditions for the optimality of a sequence of observation times under two alternative criteria, and characterizing the form of the solution in special cases. A corollary of these results is a ..."
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SUMMARY. This paper studies the optimal choice of observation times for duration data, presenting necessary conditions for the optimality of a sequence of observation times under two alternative criteria, and characterizing the form of the solution in special cases. A corollary of these results is a simple expression for the binary partition of a continuous random variable that is most informative for learning about an unknown parameter in its distribution. 1.
Constrained Design Strategies for Improving Normal Approximations in Nonlinear Regression Problems
"... this paper, in contrast, is how the experimental design influences the normal approximation in nonlinear regression. Design criteria that reflect the primary goal of an experiment are reviewed in Section 1.2. In Section 2 methods are given for calculating the Bates and Watts (1980) curvature arrays ..."
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this paper, in contrast, is how the experimental design influences the normal approximation in nonlinear regression. Design criteria that reflect the primary goal of an experiment are reviewed in Section 1.2. In Section 2 methods are given for calculating the Bates and Watts (1980) curvature arrays in terms of design measures. A new notation for representing curvature arrays is introduced in Section 2 and explained further in Appendix A. Appendix B presents some theoretical results on designs that minimize intrinsic curvature. In Section 3 it is argued that a good design procedure is one where a primary design criterion is maximized subject to constraints based on summaries of the curvature measures (Appendix C) that help ensure the accuracy of the normal approximation. The constraints, and hence the designs, depend on the sample size. Examples are given in Sections 4, 5, 6 and 7 of 1
Timing Medical Examinations via Intensity Functions
, 1996
"... This article considers a decision theoretic method for timing medical examinations. The specific model is motivated by screening that is examining asymptomatic individuals for hidden disease or riskincreasing conditions. Ideas and strategies may be applied more broadly to problems in which a sto ..."
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This article considers a decision theoretic method for timing medical examinations. The specific model is motivated by screening that is examining asymptomatic individuals for hidden disease or riskincreasing conditions. Ideas and strategies may be applied more broadly to problems in which a stochastic process is monitored over time with a costly and possibly faulty data collection procedure. From a technical viewpoint, the approach of this article is based on modeling the decision space as a space of functions, termed screening intensity functions. Results include explicit rules for deciding whether or not an individual of given age and risk factors should be screened for a disease, and for deciding when an individual examined today should be examined again. For example, in a special case, the optimal frequency of examinations is proportional to the square root of the incidence of the disease. Results are illustrated using data on breast cancer screening. Some key words: Design, ...
Supplement to “Multiobjective optimal designs in comparative clinical trials with covariates: The reinforced doublyadaptive biased coin design.” DOI:10.1214/12AOS1007SUPP
, 2012
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Controlled Optimal Design Program for the Logit Dose Response Model
"... The assessment of doseresponse is an integral component of the drug development process. Parallel doseresponse studies are conducted, customarily, in preclinical and phase 1, 2 clinical trials for this purpose. Practical constraints on dose range, dose levels and dose proportions are intrinsic iss ..."
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The assessment of doseresponse is an integral component of the drug development process. Parallel doseresponse studies are conducted, customarily, in preclinical and phase 1, 2 clinical trials for this purpose. Practical constraints on dose range, dose levels and dose proportions are intrinsic issues in the design of dose response studies because of drug toxicity, efficacy, FDA regulations, protocol requirements, clinical trial logistics, and marketing issues. We provide a free online software package called Controlled Optimal Design 2.0 for generating controlled optimal designs that can incorporate prior information and multiple objectives, and meet multiple practical constraints at the same time. Researchers can either run the webbased design program or download its standalone version to construct the desired multipleobjective controlled Bayesian optimal designs. Because researchers often adopt adhoc design schemes such as the equal allocation rules without knowing how efficient such designs would be for the design problem, the program