A general approach to confidence regions for optimal factor levels of response surfaces

John J. Peterson, Suntara Cahya, Enrique del Castillo

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

For a response surface experiment, an approximate hypothesis test and an associated confidence region is proposed for the minimizing (or maximizing) factor-level configuration. Carter et al. (1982, Cancer Research 42, 2963-2971) show that confidence regions for optimal conditions provide a way to make decisions about therapeutic synergism. The response surface may be constrained to be within a specified, bounded region. These constraint regions can be quite general. This allows for more realistic constraint modeling and a wide degree of applicability, including constraints occurring in mixture experiments. The usual assumption of a quadratic model is also generalized to include any regression model that is linear in the model parameters. An intimate connection is established between this confidence region and the Box-Hunter (1954, Biometrika 41, 190-199) confidence region for a stationary point. As a byproduct, this methodology also provides a way to construct a confidence interval for the difference between the optimal mean response and the mean response at a specified factor-level configuration. The application of this confidence region is illustrated with two examples. Extensive simulations indicate that this confidence region has good coverage properties.

Original languageEnglish (US)
Pages (from-to)422-431
Number of pages10
JournalBiometrics
Volume58
Issue number2
DOIs
StatePublished - Jan 1 2002

Fingerprint

Confidence Region
Response Surface
Linear Models
Confidence Intervals
Research
Neoplasms
synergism
byproducts
Byproducts
confidence interval
Therapeutics
linear models
Experiments
Mixture Experiments
Synergism
therapeutics
Configuration
neoplasms
Hypothesis Test
Stationary point

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Peterson, John J. ; Cahya, Suntara ; del Castillo, Enrique. / A general approach to confidence regions for optimal factor levels of response surfaces. In: Biometrics. 2002 ; Vol. 58, No. 2. pp. 422-431.
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A general approach to confidence regions for optimal factor levels of response surfaces. / Peterson, John J.; Cahya, Suntara; del Castillo, Enrique.

In: Biometrics, Vol. 58, No. 2, 01.01.2002, p. 422-431.

Research output: Contribution to journalArticle

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