1097-0258/asset/SIM_left.gif?v=1&s=1b631772c3897aa95941da3609d901cd1d389e83)
1097-0258/asset/olbannerright.gif?v=1&s=6d257623b3308a7485294c87b3b5e1e665484099)
Research Article
The k-in-a-row up-and-down design, revisited
Article first published online: 17 APR 2009
DOI: 10.1002/sim.3590
Copyright © 2009 John Wiley & Sons, Ltd.
1097-0258/asset/cover.gif?v=1&s=64ebf4a6597e744f418c952845cddf175ccc795f "Statistics in Medicine")
Additional Information
How to Cite
Oron, A. P. and Hoff, P. D. (2009), The k-in-a-row up-and-down design, revisited. Statistics in Medicine, 28: 1805–1820. doi: 10.1002/sim.3590
Publication History
- Issue published online: 7 MAY 2009
- Article first published online: 17 APR 2009
- Manuscript Accepted: 25 FEB 2009
- Manuscript Received: 7 MAY 2008
- Abstract
- References
- Cited By
Keywords:
- up-and-down;
- staircase methods;
- Phase I;
- sensory studies;
- adaptive designs;
- anesthesiology;
- percentile finding
Abstract
The percentile-finding experimental design known variously as ‘forced-choice fixed-staircase’, ‘geometric up-and-down’ or ‘k-in-a-row’ (KR) was introduced by Wetherill four decades ago. To date, KR has been by far the most widely used up-and-down (U&D) design for estimating non-median percentiles; it is implemented most commonly in sensory studies. However, its statistical properties have not been fully documented, and the existence of a unique mode in its asymptotic treatment distribution has been recently disputed.
Here we revisit the KR design and its basic properties. We find that KR does generate a unique stationary mode near its target percentile, and also displays better operational characteristics than two other U&D designs that have been studied more extensively. Supporting proofs and numerical calculations are presented. A recent experimental example from anesthesiology serves to highlight some of the ‘up-and-down’ design family's properties and advantages. Copyright © 2009 John Wiley & Sons, Ltd.