Dr. Edgar Brunner

Department of Medical Statistics

University of Göttingen, Germany

Title: " Rank Procedures for Repeated Measures "

Repeated Measures appear in many biological as well as preclinical and clinical medical trials and studies. Appropriate statistical modeling and analysis require taking into account the dependency of the observations within the subjects. An additional difficulty appears if different factors have an impact on the observed outcome, i.e. if the design has a factorial structure. If the underlying distributions of the data cannot be assumed to be multivariate normal, nonparametric methods are necessary. In particular rank procedures have been developed for the analysis of such complicated designs. They can be applied to metric data as well as to ordered categorical data. Since there are no parameters involved in the statistical models, the hypotheses to be tested are formulated by means of the distribution functions.

In this talk, I will explain the underlying methodology and properties of some existing rank procedures. In particular approximations for small samples are discussed along with some asymptotic results. Also confidence intervals are presented for the relative effects on which the rank procedures are based.

The methodology is motivated and presented by means of a clinical trial involving time curves of ordered categorical data (shoulder-tip pain trial, Lumley, 1996).

Further applications of the method developed are discussed at the end of the talk. Such applications are the analysis of ROC-curves in imaging diagnostic trials involving a factorial structure to separate the impact of the readers of the images from the impact of the diagnostic medium (ultra-sound, X-ray, MRT ? with or without a contrast medium). Adjusting for covariates and the new upcoming method of multiple contrast tests (Bretz et al, 2001) are briefly mentioned to indicate the ideas of some new research projects.


BATHKE, A. and BRUNNER, E. (2003). A Nonparametric Alternative to Analysis of Covariance. In Recent Advances and Trends in Nonparametric Statistics (Eds. M.G. Akritas and D.N. Politis), 109-120.

BRETZ, F., GENZ, A. and HOTHORN, L.A. (2001). On the Numerical Availability of Multiple Comparison Procedures. Biometrical Journal 43, 645-656.

BRUNNER, E., MUNZEL, U. AND PURI, M. L. (1999). Rank-Score Tests in Factorial Designs with Repeated Measures. J. Mult. Analysis 70, 286-317.

KAUFMANN, J., WERNER, C., and BRUNNER, E. (2005). Nonparametric methods for analyzing the accuracy of diagnostic tests with multiple readers. Statistical Methods in Medical Research 14, 129-146.

KONIETSCHKE, F., BATHKE, A.C., HOTHORN, L.A., and BRUNNER, E. (2010). Testing and Estimation of purely nonparametric effects in repeated measures designs. Computational Statistics and Data Analysis 53, 730-741.

LUMLEY, T. (1996). Generalized estimating equations for ordinal data: A note on working correlation structures. Biometrics 52, 354-361.