Up‐and‐Down Designs

Up-and-down designs are useful for evaluating and comparing the toxicity of pesticides and other chemical compounds. In particular, the primary goal of an up-and-down design in toxicity studies is to estimate the dose having a prespecified toxicity rate Γ,0 < Γ < 1. A secondary goal is to limit the experimental subjects that are given highly toxic exposure. Up-and-down designs can be sequential or group sequential.

[1]  Nancy Flournoy,et al.  Up-and-down designs. I. Stationary treatment distributions , 1995 .

[2]  Georg v. Békésy,et al.  A New Audiometer , 1947 .

[3]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[4]  Alessandra Giovagnoli,et al.  Properties of frequency distributions induced by general ‘up-and-down’ methods for estimating quantiles , 1998 .

[5]  S C Choi,et al.  Interval estimation of the LD50 based on an up-and-down experiment. , 1990, Biometrics.

[6]  A. Lichtman,et al.  The up-and-down method substantially reduces the number of animals required to determine antinociceptive ED50 values. , 1998, Journal of pharmacological and toxicological methods.

[7]  S. Durham,et al.  A random walk rule for phase I clinical trials. , 1997, Biometrics.

[8]  Charles Natanson,et al.  Anthrax lethal and edema toxins produce different patterns of cardiovascular and renal dysfunction and synergistically decrease survival in canines. , 2010, The Journal of infectious diseases.

[9]  B. Treutwein.  Adaptive psychophysical procedures , 1995, Vision Research.

[10]  Nancy Flournoy,et al.  Group up-and-down designs for dose-finding , 2006 .

[11]  S. D. Durham,et al.  A sequential design for maximizing the probability of a favourable response , 1998 .

[12]  Alessandra Giovagnoli,et al.  Up-and-down experiments of first and second order , 2005 .

[13]  Nancy Flournoy,et al.  Dose Finding Using the Biased Coin Up‐and‐Down Design and Isotonic Regression , 2002, Biometrics.

[14]  R. Tsutakawa,et al.  Random Walk Design in Bio-Assay , 1967 .

[15]  K. A. Brownlee,et al.  The Up-and-Down Method with Small Samples , 1953 .

[16]  Nathan L Pace,et al.  Advances in and Limitations of Up-and-down Methodology: A Précis of Clinical Use, Study Design, and Dose Estimation in Anesthesia Research , 2007, Anesthesiology.

[17]  Alexander M. Mood,et al.  A Method for Obtaining and Analyzing Sensitivity Data , 1948 .

[18]  J. Kingman.  A FIRST COURSE IN STOCHASTIC PROCESSES , 1967 .

[19]  Assaf P Oron,et al.  The k‐in‐a‐row up‐and‐down design, revisited , 2009, Statistics in medicine.

[20]  P. Diaconis,et al.  Geometric Bounds for Eigenvalues of Markov Chains , 1991 .

[21]  H. D. Brunk,et al.  Statistical inference under order restrictions : the theory and application of isotonic regression , 1973 .

[22]  C. D. Kershaw.  A comparison of estimators of the ED50 in up-and-down experiments , 1987 .

[23]  G. B. Wetherill,et al.  Sequential Estimation of Quantal Response Curves , 1963 .

[24]  M. Warne,et al.  Use of the Up-and-Down Acute Toxicity Test Procedure to Generate LC50 Data for Fish , 2004, Bulletin of environmental contamination and toxicology.

[25]  W. Dixon.  The Up-and-Down Method for Small Samples , 1965 .

[26]  Nancy Flournoy,et al.  Technical Report No. 2000-2: A New Approach to Dose Finding for Phase I Clinical Trials (AU-CAS-MathStats) , 2014 .

[27]  Giorgio Capogna,et al.  Minimum Analgesic Dose of Epidural Sufentanil for First-stage Labor Analgesia: A Comparison between Spontaneous and Prostaglandin-induced Labors in Nulliparous Women , 2001, Anesthesiology.

[28]  M. García-Pérez,et al.  Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties , 1998, Vision Research.

[29]  Choi Sc.  An investigation of Wetherill's method of estimation for the up-and-down experiment. , 1971 .

[30]  Michael Proschan,et al.  Estimating the probability of toxicity at the target dose following an up‐and‐down design , 2003, Statistics in medicine.

[31]  Nancy Flournoy,et al.  UP-AND-DOWN DESIGNS II: EXACT TREATMENT MOMENTS , 1995 .

[32]  Cyrus Derman,et al.  Non-Parametric Up-and-down Experimentation , 1957 .

[33]  N. Flournoy,et al.  An Optimizing Up-and-Down Design , 2001 .

[34]  M. Silvapulle.  On the Existence of Maximum Likelihood Estimators for the Binomial Response Models , 1981 .

[35]  Nancy Flournoy,et al.  Random Walks for Quantile Estimation , 1994 .

[36]  Alessandra Giovagnoli,et al.  Randomized group up and down experiments , 2008 .

[37]  N. Flournoy.  Adaptive Designs , 2001 .

[38]  Christopher D. Kershaw.  Asymptotic Properties of $\bar{w}$, an Estimator of the ED50 Suggested for Use in Up-and-Down Experiments in Bio-Assay , 1985 .

[39]  F. T. Wright,et al.  Order restricted statistical inference , 1988 .

[40]  William F. Rosenberger,et al.  Adaptive Designs (Lecture Notes Monograph Series, Vol. 25). , 1997 .

[41]  J. Keilson,et al.  Some Results for Discrete Unimodality , 1971 .