Statistical Science

Nonparametric Approaches to the Analysis of Crossover Studies

Mary E. Putt and Vernon M. Chinchilli

Full-text: Open access

Abstract

We illustrate nonparametric, and particularly rank-based analyses of crossover studies, designs in which each subject receives more than one treatment over time. Principles involved in using the Wilcoxon rank sum test in the simple two-period, two-treatment crossover are described through theory and example. We then extend the ideas to two-treatment designs with more than two periods and to three-treatment, three-period designs. When more than one nonparametric approach is available, we consider the issue of statistical power in choosing an appropriate test.

Article information

Source
Statist. Sci., Volume 19, Number 4 (2004), 712-719.

Dates
First available in Project Euclid: 18 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.ss/1113832735

Digital Object Identifier
doi:10.1214/088342304000000611

Mathematical Reviews number (MathSciNet)
MR2196197

Zentralblatt MATH identifier
1100.62568

Keywords
Crossover clinical trials nonparametrics rank-based statistics

Citation

Putt, Mary E.; Chinchilli, Vernon M. Nonparametric Approaches to the Analysis of Crossover Studies. Statist. Sci. 19 (2004), no. 4, 712--719. doi:10.1214/088342304000000611. https://projecteuclid.org/euclid.ss/1113832735


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References

  • Bellavance, F. and Tardif, S. (1995). A nonparametric approach to the analysis of three-treatment three-period crossover designs. Biometrika 82 865--875.
  • Bellavance, F., Tardif, S. and Stephens, M. A. (1996). Tests for the analysis of variance of crossover designs with correlated errors. Biometrics 52 607--612.
  • Carriere, K. C. (1994). Crossover designs for clinical trials. Statistics in Medicine 13 1063--1069.
  • Chinchilli, V. M. and Esinhart, J. D. (1996). Design and analysis of intrasubject variability in cross-over experiments. Statistics in Medicine 15 1619--1634.
  • Correa, J. A. and Bellavance, F. (2001). Power comparison of robust approximate and nonparametric tests for the analysis of cross-over trials. Statistics in Medicine 20 1185--1196.
  • Craig, T. J., Teets, S., Lehman, E. B., Chinchilli,V. M. and Zwillich, C. (1998). Nasal congestion secondary to allergic rhinitis as a cause of sleep disturbance and daytime fatigue and the response to topical nasal corticosteroids. J. Allergy and Clinical Immunology 101 633--637.
  • Everitt, B. S. (1979). A Monte Carlo investigation of the robustness of Hotelling's one- and two-sample $T^2$ tests. J. Amer. Statist. Assoc. 74 48--51.
  • Freeman, P. R. (1989). The performance of the two-stage analysis of two-treatment, two-period cross-over trials. Statistics in Medicine 8 1421--1432.
  • Good, P. I. (2000). Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd ed. Springer, New York.
  • Hettmansperger, T. (1991). Statistical Inference Based on Ranks. Krieger, Malabar, FL.
  • Hollander, M. and Wolfe, D. A. (1999). Nonparametric Statistical Methods, 2nd ed. Wiley, New York.
  • Koch, G. (1972). The use of nonparametric methods in the statistical analysis of the two-period change-over design. Biometrics 28 577--584.
  • Lagakos, S. (2003). Clinical trials and rare diseases. New England J. Medicine 348 2455--2456.
  • Öhrvik, J. (1998). Nonparametric methods in crossover trials. Biometrical J. 40 771--789.
  • Putt, M. E. and Chinchilli, V. M. (2000). A robust analysis of crossover designs using multisample generalized $L$-statistics. J. Amer. Statist. Assoc. 95 1256--1262.
  • Putt, M. E. and Ravina, B. (2002). Randomized, placebo-controlled, parallel group versus crossover study designs for the study of dementia in Parkinson's disease. Controlled Clinical Trials 23 111--126.
  • Senn, S. (2002). Cross-over Trials in Clinical Research, 2nd ed. Wiley, New York.
  • Tudor, G. and Koch, G. G. (1994). Review of nonparametric methods for the analysis of crossover studies. Statistical Methods in Medical Research 3 345--381.
  • Vonesh, E. F. and Chinchilli, V. M. (1997). Linear and Nonlinear Models for the Analysis of Repeated Measurements. Dekker, New York.