Statistics and Computing

, Volume 24, Issue 1, pp 101–109 | Cite as

The construction of optimal designs for dose-escalation studies

Article

Abstract

Methods for the construction of A-, MV-, D- and E-optimal designs for dose-escalation studies are presented. Algebraic results proved elusive and explicit expressions for the requisite optimal designs are only given for a restricted class of traditional designs. Recourse to numerical procedures and heuristics is therefore made. Complete enumeration of all possible designs is discussed but is, as expected, highly computer intensive. Two exchange algorithms, one based on block exchanges and termed the Block Exchange Algorithm and the other a candidate-set-free algorithm based on individual exchanges and termed the Best Move Algorithm, are therefore introduced. Of these the latter is the most computationally effective. The methodology is illustrated by means of a range of carefully selected examples.

Keywords

Dose-escalation studies A-, MV-, D- and E-optimal designs Complete enumeration Exchange algorithms 

References

  1. Atkinson, A.C., Donev, A.N., Tobias, R.D.: Optimum Experimental Designs, with SAS. Oxford University Press, Oxford (2007) MATHGoogle Scholar
  2. Bailey, R.A.: Designs for dose-escalation trials with quantitative responses. Stat. Med. 28, 3721–3738 (2009) CrossRefMathSciNetGoogle Scholar
  3. Clark, A.E., Haines, L.M.: Work in progress (2012) Google Scholar
  4. Fisher, N.I., Hall, P.: Bootstrap algorithms for small samples. J. Stat. Plan. Inference 27, 157–169 (1991) CrossRefMathSciNetGoogle Scholar
  5. GAUSS Programming Language. Aptech Systems, Inc. (2011) Google Scholar
  6. Goos, P.: The Optimal Design of Blocked and Split-Plot Experiments. Springer, New York (2002) CrossRefMATHGoogle Scholar
  7. Hastie, T.J., Tibshirani, R.J., Friedman, J.: The Elements of Statistical Learning, 2nd edn. Springer, New York (2009) CrossRefMATHGoogle Scholar
  8. John, J.A., Williams, E.R.: Cyclic and Computer Generated Designs, 2nd edn. Chapman & Hall, London (1995) CrossRefMATHGoogle Scholar
  9. Jones, B., Goos, P.: A candidate-set-free algorithm for generating D-optimal split-plot designs. Appl. Stat. 56, 347–364 (2007) MathSciNetGoogle Scholar
  10. Le Tourneau, C., Lee, J.J., Siu, L.L.: Dose escalation methods in phase I cancer clinical trials. J. Natl. Cancer Inst. 101, 708–720 (2009) CrossRefGoogle Scholar
  11. Mathematica, Version 8.0, Wolfram Research, Inc., Champaign, IL (2011) Google Scholar
  12. Meyer, R.K., Nachtsheim, C.J.: The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37, 60–69 (1995) CrossRefMATHMathSciNetGoogle Scholar
  13. Nijenhuis, A., Wilf, H.S.: Combinatorial Algorithms for Computers and Calculators. Academic Press, New York (1978) MATHGoogle Scholar
  14. O’Neill, B.: A-optimal continuous designs and statistical issues in clinical trials. M.Sc. thesis, Queen Mary University of London (2011) Google Scholar
  15. Pringle, R.M., Rayner, A.A.: Generalized Inverse Matrices with Applications to Statistics. Griffin, London (1971) MATHGoogle Scholar
  16. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2011). ISBN 3-900051-07-0, URL http://www.R-project.org/ Google Scholar
  17. Senn, S., Amin, D., Bailey, R.A., Bird, S.M., Bogacka, B., Colman, P., Garrett, A., Grieve, A., Lachmann, P.: Statistical issues in first-in-man studies. J. R. Stat. Soc. A 170, 517–579 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Statistical SciencesUniversity of Cape TownRondeboschSouth Africa

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