Exact linear rank tests for two-sample equivalence problems with continuous data
Article first published online: 23 JUN 2010
© 2010 The Authors. Statistica Neerlandica © 2010 VVS
Volume 64, Issue 4, pages 482–504, November 2010
How to Cite
Janssen, A. and Wellek, S. (2010), Exact linear rank tests for two-sample equivalence problems with continuous data. Statistica Neerlandica, 64: 482–504. doi: 10.1111/j.1467-9574.2010.00466.x
- Issue published online: 23 JUN 2010
- Article first published online: 23 JUN 2010
- Received: August 2008. Revised: April 2010.
- equivalence test;
- proportional hazards;
- testing statistical functionals;
- Wilcoxon test;
- Savage test
The present paper introduces a methodology for the semiparametric or non-parametric two-sample equivalence problem when the effects are specified by statistical functionals. The mean relative risk functional of two populations is given by the average of the time-dependent risk. This functional is a meaningful non-parametric quantity, which is invariant under strictly monotone transformations of the data. In the case of proportional hazard models, the functional determines just the proportional hazard risk factor. It is shown that an equivalence test of the type of the two-sample Savage rank test is appropriate for this functional. Under proportional hazards, this test can be carried out as an exact level α test. It also works quite well under other semiparametric models. Similar results are presented for a Wilcoxon rank-sum test for equivalence based on the Mann–Whitney functional given by the relative treatment effect.