D-Optimal Design for a Five-Parameter Logistic Model

Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


We explore the D-optimal design for a five-parameter logistic model, which includes a shape parameter to handle asymmetries, and two threshold parameters to account for situations where the asymptotes are not at 0 and 1. The optimal design is five points, including points at -∞ and ∞ representing the thresholds. We compare the efficiencies of the optimal designs arising from the two- and five- parameter models. We find a significant loss of efficiency when the two-parameter model is used on data generated from the five-parameter model.


Optimal Design Information Matrix Directional Derivative Markov Chain Monte Carlo Method Optimal Design Point 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors thank two excellent referees for their detailed comments. One of the referees found a major mistake, and the authors are deeply appreciative.


  1. Atkinson, A. C., A.N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press.MATHGoogle Scholar
  2. Biedermann, S., H. Dette, and A. Pepelyshev (2006). Some robust design strategies for percentile estimation in binary response models. Canadian Journal of Statistics 34, 603–622.MATHCrossRefMathSciNetGoogle Scholar
  3. Haines, L. M., I. Perevozskaya, and W. F. Rosenberger (2003). Bayesian optimal designs for Phase I clinical trials. Biometrics 59, 591–600.CrossRefMathSciNetGoogle Scholar
  4. Kalish, L. A. and J. L. Rosenberger (1978). Optimal designs for the estimation of the logistic function. Technical Report 33, Pennsylvania State University.Google Scholar
  5. Kiefer, J. and J. Wolfowitz (1960). The equivalence of two extremum problems. Canadian Journal of Mathematics 12, 363–366.MATHMathSciNetGoogle Scholar
  6. Manukyan, Z. (2009). Sequential Designs for Estimating Toxicity and Efficacy in a Dose-Response Setting. Ph. D. thesis, George Mason University.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.The EMMES CorporationRockvilleUSA
  2. 2.Department of StatisticsGeorge Mason UniversityFairfaxUSA

Personalised recommendations