Up-and-down design

Up-and-down designs (UDDs) are a family of statistical experiment designs used in dose-finding experiments in science, engineering, and medical research. Dose-finding experiments have binary responses: each individual outcome can be described as one of two possible values, such as success vs. failure or toxic vs. non-toxic. Mathematically the binary responses are coded as 1 and 0. The goal of dose-finding experiments is to estimate the strength of treatment (i.e., the "dose") that would trigger the "1" response a pre-specified proportion of the time. This dose can be envisioned as a percentile of the distribution of response thresholds. An example where dose-finding is used is in an experiment to estimate the LD50 of some toxic chemical with respect to mice.

Simulated experiments from three different UDDs. 0 and 1 responses are marked by o and x, respectively. Top to bottom: the original "simple" UDD that targets the median, a Durham-Flournoy biased-coin UDD targeting approximately the 20.6% percentile, and a k-in-a-row / "transformed" UDD targeting the same percentile.

Dose-finding designs are sequential and response-adaptive: the dose at a given point in the experiment depends upon previous outcomes, rather than be fixed a priori. Dose-finding designs are generally more efficient for this task than fixed designs, but their properties are harder to analyze, and some require specialized design software. UDDs use a discrete set of doses rather than vary the dose continuously. They are relatively simple to implement, and are also among the best understood dose-finding designs. Despite this simplicity, UDDs generate random walks with intricate properties.[1] The original UDD aimed to find the median threshold by increasing the dose one level after a "0" response, and decreasing it one level after a "1" response. Hence the name "up-and-down". Other UDDs break this symmetry in order to estimate percentiles other than the median, or are able to treat groups of subjects rather than one at a time.

UDDs were developed in the 1940s by several research groups independently.[2][3][4] The 1950s and 1960s saw rapid diversification with UDDs targeting percentiles other than the median, and expanding into numerous applied fields. The 1970s to early 1990s saw little UDD methods research, even as the design continued to be used extensively. A revival of UDD research since the 1990s has provided deeper understanding of UDDs and their properties,[5] and new and better estimation methods.[6][7]

UDDs are still used extensively in the two applications for which they were originally developed: psychophysics where they are used to estimate sensory thresholds and are often known as fixed forced-choice staircase procedures,[8] and explosive sensitivity testing, where the median-targeting UDD is often known as the Bruceton test. UDDs are also very popular in toxicity and anesthesiology research.[9] They are also considered a viable choice for Phase I clinical trials.[10]

  1. ^ Durham, SD; Flournoy, N. "Up-and-down designs. I. Stationary treatment distributions.". In Flournoy, N; Rosenberger, WF (eds.). IMS Lecture Notes Monograph Series. Vol. 25: Adaptive Designs. pp. 139–157.
  2. ^ Dixon, WJ; Mood, AM (1948). "A method for obtaining and analyzing sensitivity data". Journal of the American Statistical Association. 43 (241): 109–126. doi:10.1080/01621459.1948.10483254.
  3. ^ von Békésy, G (1947). "A new audiometer". Acta Oto-Laryngologica. 35 (5–6): 411–422. doi:10.3109/00016484709123756.
  4. ^ Anderson, TW; McCarthy, PJ; Tukey, JW (1946). 'Staircase' method of sensitivity testing (Technical report). Naval Ordnance Report. 65-46.
  5. ^ Flournoy, N; Oron, AP. "Up-and-Down Designs for Dose-Finding". In Dean, A (ed.). Handbook of Design and Analysis of Experiments. CRC Press. pp. 858–894.
  6. ^ Stylianou, MP; Flournoy, N (2002). "Dose finding using the biased coin up-and-down design and isotonic regression". Biometrics. 58 (1): 171–177. doi:10.1111/j.0006-341x.2002.00171.x. PMID 11890313. S2CID 8743090.
  7. ^ Oron, AP; Flournoy, N (2017). "Centered Isotonic Regression: Point and Interval Estimation for Dose-Response Studies". Statistics in Biopharmaceutical Research. 9 (3): 258–267. arXiv:1701.05964. doi:10.1080/19466315.2017.1286256. S2CID 88521189.
  8. ^ Leek, MR (2001). "Adaptive procedures in psychophysical research". Perception and Psychophysics. 63 (8): 1279–1292. doi:10.3758/bf03194543. PMID 11800457.
  9. ^ Pace, NL; Stylianou, MP (2007). "Advances in and Limitations of Up-and-down Methodology: A Precis of Clinical Use, Study Design, and Dose Estimation in Anesthesia Research". Anesthesiology. 107 (1): 144–152. doi:10.1097/01.anes.0000267514.42592.2a. PMID 17585226.
  10. ^ Oron, AP; Hoff, PD (2013). "Small-Sample Behavior of Novel Phase I Cancer Trial Designs". Clinical Trials. 10 (1): 63–80. arXiv:1202.4962. doi:10.1177/1740774512469311. PMID 23345304. S2CID 5667047.