The k-in-a-row up-and-down design, revisited.
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.
Department of Statistics, University of Washington, Seattle, WA 98195-4322, U.S.A. assaf.oron@gmail.com
Assaf P
AP
Oron
Peter D
PD
Hoff
D000776:Anesthesiology / Q000706:statistics & numerical data; D018686:Anesthetics, Intravenous / Q000008:administration & dosage / Q000009:adverse effects; D001699:Biometry / Q000379:methods*; D017321:Clinical Trials, Phase I as Topic / Q000706:statistics & numerical data; D006801:Humans; D008390:Markov Chains; D015233:Models, Statistical; D010146:Pain / Q000139:chemically induced / Q000517:prevention & control; D015742:Propofol / Q000008:administration & dosage / Q000009:adverse effects; D013874:Thiopental / Q000008:administration & dosage
D018686:Anesthetics, Intravenous; D013874:Thiopental; D015742:Propofol