The Annals of Statistics

Universally optimal crossover designs under subject dropout

Wei Zheng

Full-text: Open access

Abstract

Subject dropout is very common in practical applications of crossover designs. However, there is very limited design literature taking this into account. Optimality results have not yet been well established due to the complexity of the problem. This paper establishes feasible, as well as necessary and sufficient conditions for a crossover design to be universally optimal in approximate design theory in the presence of subject dropout. These conditions are essentially linear equations with respect to proportions of all possible treatment sequences being applied to subjects and hence they can be easily solved. A general algorithm is proposed to derive exact designs which are shown to be efficient and robust.

Article information

Source
Ann. Statist., Volume 41, Number 1 (2013), 63-90.

Dates
First available in Project Euclid: 5 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1362493040

Digital Object Identifier
doi:10.1214/12-AOS1074

Mathematical Reviews number (MathSciNet)
MR3059410

Zentralblatt MATH identifier
1347.62168

Subjects
Primary: 62K05: Optimal designs
Secondary: 62J05: Linear regression

Keywords
Crossover designs efficiency robustness subject dropout universal optimality

Citation

Zheng, Wei. Universally optimal crossover designs under subject dropout. Ann. Statist. 41 (2013), no. 1, 63--90. doi:10.1214/12-AOS1074. https://projecteuclid.org/euclid.aos/1362493040


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References

  • Bose, M. and Bagchi, S. (2008). Optimal crossover designs under premature stopping. Util. Math. 75 273–285.
  • Bose, M. and Dey, A. (2009). Optimal Crossover Designs. World Scientific, Hackensack, NJ.
  • Chêng, C. S. and Wu, C.-F. (1980). Balanced repeated measurements designs. Ann. Statist. 8 1272–1283.
  • Godolphin, J. D. (2004). Simple pilot procedures for the avoidance of disconnected experimental designs. J. Roy. Statist. Soc. Ser. C 53 133–147.
  • Hedayat, A. and Afsarinejad, K. (1978). Repeated measurements designs. II. Ann. Statist. 6 619–628.
  • Hedayat, A. S. and Yang, M. (2003). Universal optimality of balanced uniform crossover designs. Ann. Statist. 31 978–983.
  • Hedayat, A. S. and Yang, M. (2004). Universal optimality for selected crossover designs. J. Amer. Statist. Assoc. 99 461–466.
  • Hedayat, A. S. and Zheng, W. (2010). Optimal and efficient crossover designs for test-control study when subject effects are random. J. Amer. Statist. Assoc. 105 1581–1592.
  • Huynh, H. and Feldt, L. S. (1970). Conditions under which mean square ratios in repeated measurements designs have exact $F$-distributions. J. Amer. Statist. Assoc. 65 1582–1589.
  • Jones, B. and Kenward, M. G. (2003). Design and Analysis of Cross-Over Trials, 2nd ed. Chapman & Hall, London.
  • Kiefer, J. (1975). Construction and optimality of generalized Youden designs. In A Survey of Statistical Design and Linear Models (Proc. Internat. Sympos., Colorado State Univ., Ft. Collins, Colo., 1973) (J. N. Srivastava, ed.) 333–353. North-Holland, Amsterdam.
  • Kunert, J. (1984). Optimality of balanced uniform repeated measurements designs. Ann. Statist. 12 1006–1017.
  • Kunert, J. and Martin, R. J. (2000). On the determination of optimal designs for an interference model. Ann. Statist. 28 1728–1742.
  • Kunert, J. and Stufken, J. (2002). Optimal crossover designs in a model with self and mixed carryover effects. J. Amer. Statist. Assoc. 97 898–906.
  • Kushner, H. B. (1997a). Optimality and efficiency of two-treatment repeated measurements designs. Biometrika 84 455–468.
  • Kushner, H. B. (1997b). Optimal repeated measurements designs: The linear optimality equations. Ann. Statist. 25 2328–2344.
  • Kushner, H. B. (1998). Optimal and efficient repeated-measurements designs for uncorrelated observations. J. Amer. Statist. Assoc. 93 1176–1187.
  • Low, J. L., Lewis, S. M. and Prescott, P. (1999). Assessing robustness of crossover designs to subjects dropping out. Statist. Comput. 9 219–227.
  • Majumdar, D., Dean, A. M. and Lewis, S. M. (2008). Uniformly balanced repeated measurements designs in the presence of subject dropout. Statist. Sinica 18 235–253.
  • Matthews, J. N. S. (1988). Recent developments in crossover designs. Internat. Statist. Rev. 56 117–127.
  • Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
  • Ratkowsky, D. A., Evans, M. A. and Alldredge, J. R. (1992). Cross-Over Experiments: Design, Analysis, and Application. Dekker, New York.
  • Senn, S. (2003). Cross-over Trials in Clinical Research, 2nd ed. Wiley, Chichester.
  • Stufken, J. (1991). Some families of optimal and efficient repeated measurements designs. J. Statist. Plann. Inference 27 75–83.
  • Stufken, J. (1996). Optimal crossover designs. In Design and Analysis of Experiments (S. Ghosh and C. R. Rao, eds.). Handbook of Statist. 13 63–90. North-Holland, Amsterdam.
  • Yeh, C.-M. (1986). Conditions for universal optimality of block designs. Biometrika 73 701–706.
  • Zhao, S. and Majumdar, D. (2012). On uniformly balanced crossover designs efficient under subject dropout. J. Stat. Theory Pract. 6 178–189.