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GMDS 2012: 57. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e. V. (GMDS)

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie

16. - 20.09.2012, Braunschweig

Two-stage adaptive designs with test statistics with arbitrary dependence structure based on the inverse normal method

Meeting Abstract

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  • Rene Schmidt - WWU/UKM Münster, Deutschland
  • Joachim Gerß - Westfälische Wilhelms-Universität Münster, Deutschland
  • Andreas Faldum - WWU/UKM Münster, Deutschland

GMDS 2012. 57. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS). Braunschweig, 16.-20.09.2012. Düsseldorf: German Medical Science GMS Publishing House; 2012. Doc12gmds149

DOI: 10.3205/12gmds149, URN: urn:nbn:de:0183-12gmds1498

Published: September 13, 2012

© 2012 Schmidt et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( You are free: to Share – to copy, distribute and transmit the work, provided the original author and source are credited.



Adaptive designs were originally developed for independent test statistics. This is true for example if the data for each stage come from different units and are normally distributed with known variance. Another possibility to get independent test statistics is to exploit the independent increment structure of some statistical models. Sometimes it may not be possible to satisfy these conditions or to check whether they are satisfied. In these cases, the test statistics and p-values of each stage may be dependent. Depending on the design parameters and on the true dependence structure between the p-values of the stages, the decisions can become conservative as well as anticonservative. In general, there will be uncountable dependence structures. For example, the joint distribution of the test statistics from the stages need not be bivariate normal even if the test statistics of each stage are univariate normal. We investigate the type I error of two-stage adaptive designs if any dependence structure between the test statistics from the stages is assumed to be admissible (worst case scenario). For this purpose, we perform analytical considerations under the restriction that the conditional error function is given according to the inverse normal method. We discuss how the significance level of the unweighted inverse normal design is inflated in the worst case as compared to the situation of independent stages. On this basis the decision boundary for the second stage can be modified so that the type I error is controlled in the worst case and thus for any dependence structure.