Robust C-optimal Design For Estimating Multiple EDps Under The 4-parameter Logistic Model

  • Anqing Zhang North Dakota State University
  • Seung Won Hyun North Dakota State University
DOI: https://doi.org/10.19139/soic.v4i4.254
Keywords: Dose-response Study, Compound Optimal Design, Robust Design, Equivalence Theorem

Abstract

The four-parameter logistic model is often used to describe dose-response functions in many toxicological studies. In this study, under the four-parameter logistic model, optimal designs to estimate the EDp are studied. The EDp is the dose achieving p% of the expected difference between the maximum and the minimum responses. C-optimal design works the best for estimating the EDp, but the best performance is only guaranteed when the goal is for estimating a single EDp. If the c-optimal design for studying a specific EDp is used for studying different EDp values, it may work poorly. This paper shows that the c-optimal design for estimating the EDp truly depends on the value of p under the 4-parameter logistic model. We present a robust c-optimal design that works well for the change in the value of p, so that the design can be used effectively for studying multiple EDp values. In addition, this paper presents a two-stage robust c-optimal design for estimating multiple EDp that is not substantially affected by the mis-specified nominal parameter values.

Author Biographies

Anqing Zhang, North Dakota State University
Department of Statistics
Seung Won Hyun, North Dakota State University
Department of Statistics

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Published
2016-12-07
How to Cite
Zhang, A., & Hyun, S. W. (2016). Robust C-optimal Design For Estimating Multiple EDps Under The 4-parameter Logistic Model. Statistics, Optimization & Information Computing, 4(4), 278-288. https://doi.org/10.19139/soic.v4i4.254
Issue
Vol 4 No 4 (2016)
Section
Research Articles
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