Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 178–189 | Cite as

On Uniformly Balanced Crossover Designs Efficient Under Subject Dropout

  • Shi ZhaoEmail author
  • Dibyen Majumdar


Design selection is examined for crossover studies under the situation that subjects may terminate prior to fulfilling the treatment sequences. Construction and efficiency of a class of designs, called Uniformly Balanced Designs Balanced for Loss, is examined.

AMS Subject Classification

62K05 05B15 


Crossover study Latin square Precision loss Repeated measurement design Subject dropout Universal optimality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bose, M., and S. Bagchi. 2008. Crossover design allowing for premature stopping. Util. Math., 75, 273–285.MathSciNetzbMATHGoogle Scholar
  2. Dudeney, H. E. 1958. Amusements in mathematics. New York, Dover Publications.Google Scholar
  3. Godolphin, J. D. 2004. Simple pilot procedures for the avoidance of disconnected experimental designs. Appl. Stat., 53, 133–147.MathSciNetzbMATHGoogle Scholar
  4. Hedayat, A. S., and K. Afsarinejad. 1978. Repeated measurements designs II. Ann. Stat., 6, 619–628.MathSciNetCrossRefGoogle Scholar
  5. Hedayat, A. S., and W. Zhao. 1990. Optimal two-period repeated measurements designs. Ann. Stat., 18, 1805–1816.MathSciNetCrossRefGoogle Scholar
  6. Hedayat, A. S., and M. Yang. 2003. Universal optimality of balanced uniform crossover designs. Ann. Stat., 31, 978–983.MathSciNetCrossRefGoogle Scholar
  7. Hedayat, A. S., and M. Yang. 2004. Universal optimality for selected crossover designs. J. Am. Stat. Assoc., 99, 461–466.MathSciNetCrossRefGoogle Scholar
  8. Jones, B., and M. G. Kenwood. 2003. Design and analysis of cross-over trials. London, CRC Press.CrossRefGoogle Scholar
  9. Kiefer, J. 1975. Construction and optimality of generalized Youden designs. In A survey of statistical design and linear models, ed. J. N. Srivastava, 333–353. Amsterdam, North Holland.Google Scholar
  10. Kushner, H. B., 1997. Optimal repeated measurements designs: The linear optimality equations. Ann. Stat., 25, 2328–2344. Corr. (1998) 26, 2081.MathSciNetCrossRefGoogle Scholar
  11. Low, J. L., S. M. Lewis, and P. Prescott, 1999. Assessing robustness of crossover designs to subjects dropping out. Stat. Comput., 9, 219–227.CrossRefGoogle Scholar
  12. Majumdar, D., A. M. Dean, and S. M. Lewis, 2008. Uniformly balanced repeated measurements designs in the presence of subject dropout. Stat. Sin., 18, 235–253.MathSciNetzbMATHGoogle Scholar
  13. Ratkowsky, D. A., M. A. Evans, and J. R. Alldredge. 1992. Cross-over experiments: Design, analysis and application. New York, Marcel Dekker.Google Scholar
  14. Senn, S. 2002. Cross-over trials in clinical research. New York, Wiley.CrossRefGoogle Scholar
  15. Stufken, J. 1991. Some families of optimal and efficient repeated measurements designs. J. Stat. Plan. Inference, 27, 75–83.MathSciNetCrossRefGoogle Scholar
  16. Stufken, J. 1996. Optimal crossover designs. In Design and analysis of experiments. Handbook of statistics 13, ed. S. Ghosh and C. R. Rao, 63–90. Amsterdam, North Holland.MathSciNetCrossRefGoogle Scholar
  17. Williams, E. J. 1949. Experimental designs balanced for the estimation of residual effects of treatments. Austr. J. Sci. Res. Ser. A Phys. Sci., 2, 149–168.MathSciNetGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Xerox Innovation GroupWebsterUSA
  2. 2.Department of Mathematics, Statistics, and Computer ScienceUniversity of IllinoisChicagoUSA

Personalised recommendations