Advances in and Limitations of Up-And-Down Methodology a Pre´Cis of Clinical Use, Study Design, and Dose Estimation in Anesthesia Research Nathan L
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Ⅵ REVIEW ARTICLE David C. Warltier, M.D., Ph.D., Editor Anesthesiology 2007; 107:144–52 Copyright © 2007, the American Society of Anesthesiologists, Inc. Lippincott Williams & Wilkins, Inc. Advances in and Limitations of Up-and-down Methodology A Pre´cis of Clinical Use, Study Design, and Dose Estimation in Anesthesia Research Nathan L. Pace, M.D., M.Stat.,* Mario P. Stylianou, Ph.D.† Sequential design methods for binary response variables of the patient can be observed immediately.1 The earliest exist for determination of the concentration or dose associated use by the anesthesia research community of one partic- with the 50% point along the dose–response curve; the up-and- ular sequential design—the up-and-down method down method of Dixon and Mood is now commonly used in anesthesia research. There have been important developments (UDM)—seems to have been in studies of the effective in statistical methods that (1) allow the design of experiments concentration for a 50% response (EC50 or minimum for the measurement of the response at any point (quantile) alveolar concentration) of inhalation anesthestics.2,3 along the dose–response curve, (2) demonstrate the risk of Columb and Lyons4 used the same design and reported certain statistical methods commonly used in literature reports, the EC —labeled by them the minimum local analgesic (3) allow the estimation of the concentration or dose—the tar- 50 get dose—associated with the chosen quantile without the as- concentration (MLAC)—of epidural bupivacaine and li- sumption of the symmetry of the tolerance distribution, and (4) docaine for pain relief during labor. The use of this set bounds on the probability of response at this target dose. experimental design is now commonly seen in studies of This article details these developments, briefly surveys current intrathecal local anesthestics,5 intrathecal opioids,6 intra- use of the up-and-down method in anesthesia research, reana- 7 ␣ 8 venous opioids, intravenous 2 agonists, intravenous lyzes published reports using the up-and-down method for the 9 10 study of the epidural relief of pain during labor, and discusses anesthetics, and inhalation anesthetics —all studies de- appropriate inferences from up-and-down method studies. termining the concentration or dose (EC50 or ED50)of these drugs. A DRUG tolerance distribution is the distribution Since the first reported use of the UDM in the anesthe- among a number of subjects of the critical level of sia literature, there have been important developments intensity (dose or concentration) at which the drug will in statistical methods that (1) allow the design of exper- just produce or just prevent a reaction in each subject. iments for the measurement of the response at any point Experiments may be designed to characterize all or part (quantile g) along the dose–response curve, (2) demon- of the tolerance distribution. Experimental methods for strate the risk of certain statistical methods commonly binary response variables exist for determination of the used in literature reports, (3) allow the estimation of the dose associated with the 50% point along the dose– concentration or dose associated with the chosen quan- response curve or tolerance distribution if the response tile g (ECg or EDg) without the assumption of the sym- metry of the tolerance distribution, and (4) set bounds on the probability of response at the EC or ED . This This article is accompanied by an Editorial View. Please see: g g ᭜ Fisher D: What if half of your patients moved (or remembered article will detail these developments, briefly survey cur- or did something else bad) at incision? ANESTHESIOLOGY 2007; rent use of the UDM in anesthesia research, reanalyze 107:1–2. published reports of MLAC for epidural relief of pain during labor to demonstrate newer methods, and discuss appropriate inferences from UDM studies. * Professor of Anesthesiology, University of Utah. † Mathematical Statistician, Office of Biostatistics Research, National Heart, Lung, and Blood Institute, Na- tional Institutes of Health. Received from the Department of Anesthesiology, University of Utah, Salt Lake Materials and Methods City, Utah, and the Office of Biostatistics Research, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland. Submitted for Experimental Design publication July 19, 2006. Accepted for publication January 24, 2007. Dr. Pace The following notation and nomenclature will be used. A received salary support from the Department of Anesthesiology, University of Utah, and Dr. Stylianou received salary support from the Office of Biostatistics study uses K ordered dose or concentration levels that are Research, National Heart, Lung, and Blood Institute, National Institutes of Health. denoted by the set ⍀ ϭ {x Ͻ x Ͻ ...Ͻ x Ͻ ...Ͻ x }; e.g., Presented in part at the Annual Meeting of the American Society of Anesthesiol- x 1 2 k K ogists, Atlanta, Georgia, October 25, 2005. if five concentrations of bupivacaine (0.07, 0.08, 0.09, 0.10, ⍀ ϭ Address correspondence to Dr. Pace: University of Utah, Department of 0.11) are used, then x {0.07, 0.08, 0.09, 0.10, 0.11}. The Anesthesiology, 30 North 1900 East, 3C444, Salt Lake City, Utah 84132-2304. purpose of the study is to determine the dose level that has a [email protected]. This article may be accessed for personal use at no charge ⌫ through the Journal Web site, www.anesthesiology.org. probability of effect ; most commonly the EC50 or ED50 is Anesthesiology, V 107, No 1, Jul 2007 144 ADVANCES IN AND LIMITATIONS OF UP-AND-DOWN METHODOLOGY 145 desired, and thus the assignment ⌫ϭ0.5 is made so that a ogously; if a positive response is observed, the dose is response is produced in 100 ϫ⌫ϭ50% of the target popu- stepped down; if no response is observed, the next lation. This will be denoted the target dose. N denotes the patient is randomized with probability B to the next total sample size, Nk and Rk are the number of subjects and higher dose and with probability 1 – B to the same ϭ the number of responses at dose level xk, and Rk /Nk dose. Intervals between doses do not have to be equal ϭ pˆ(xk) pˆk denotes the observed response rate at the dose in the BCD. The BCD is optimal among the general xk; the observed response rate pˆk is an estimator of the true class of up-and-down designs in the sense that the ϭ probability of response p(xk) pk at dose xk. Let X(i) distribution of administered doses is most peaked denote the dose level administered to the ith patient. The around .At⌫ϭ0.5, the BCD reduces to the Dixon target dose is designated —with ˆ being the estimator of and Mood UDM. No studies in the anesthesia literature . The probability of effect at ˆ is p(ˆ); the estimator of have attempted to study other quantiles on the dose– p(ˆ) will be denoted pˆ(ˆ). response curve using a sequential design. The first description of the performance of a UDM experiment is attributed to Dixon and Mood.11 To Graphical Display perform the study at the quantile ⌫ϭ0.5, the K dose An ingenious graphical display is now almost univer- levels are chosen, the sample size of patients from a sal in reports using the UDM; the first report of UDM target population is selected, and the definition of a methodology by Dixon and Mood11 included this positive response is specified; the K doses are chosen graphical display. It simultaneously displays the doses/ ⍀ with a fixed, constant interval between levels. The concentrations administered ( x), the sequencing of first patient is exposed to one of the K dose levels; at administered doses (X(i)), and the positive or negative the discretion of the investigators, this may be chosen response for each subject at their assigned dose/con- to be the lowest dose, may be the dose thought to be centration. As all experimental data are displayed, a closest to , or may be selected arbitrarily. The re- reanalysis is easily possible. (Reanalysis is also possible sponse of the first patient determines the dose level from a tabular plotting of dose, number of events, and for the second patient. If the first patient has a positive number treated.) Figure 1 shows a replotting of data from two published UDM studies.14,15 Each study re- response at dose xk, then the second patient is ex- ported the MLAC from two UDM experiments—one posed to the next lower dose xkϪ1. If the first patient experiment performed for levobupivacaine and one has a negative response at dose xk, then the second experiment performed for ropivacaine. (If two drugs patient is exposed to the next higher dose xkϩ1. Suc- cessive patients are assigned a dose similarly by the are being compared in the same study, patients should response of the previous patient. At the lowest and be randomly allocated to the one or the other drug.) ⍀ Long sequences of steadily increasing or decreasing highest doses of k, appropriate adjustments for the next dose keep all doses within the specified dose doses with repeated ineffective or effective responses range. Although Dixon proposed a modified UDM for are common. In such circumstances, some assigned very small samples (N Յ 6),12 anesthesia trials using doses or concentrations must vary considerably from the UDM typically have 20–40 patients. the underlying true EDg or ECg. While there are several types of sequential designs for determining the target dose, all outperform nonsequen- Target Dose Estimation tial designs by having a smaller mean square error (MSE) Besides the goal of estimating ˆ from a UDM study, for the same sample size1; often a nonsequential design it is also necessary to specify the precision of ˆ with will require two to three times as many patients to have a 95% confidence interval (CI).