Randomized Trials
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How Many Stratification Factors Is Too Many" to Use in a Randomization
How many Strati cation Factors is \Too Many" to Use in a Randomization Plan? Terry M. Therneau, PhD Abstract The issue of strati cation and its role in patient assignment has gen- erated much discussion, mostly fo cused on its imp ortance to a study [1,2] or lack thereof [3,4]. This rep ort fo cuses on a much narrower prob- lem: assuming that strati ed assignment is desired, how many factors can b e accomo dated? This is investigated for two metho ds of balanced patient assignment, the rst is based on the minimization metho d of Taves [5] and the second on the commonly used metho d of strati ed assignment [6,7]. Simulation results show that the former metho d can accomo date a large number of factors 10-20 without diculty, but that the latter b egins to fail if the total numb er of distinct combinations of factor levels is greater than approximately n=2. The two metho ds are related to a linear discriminant mo del, which helps to explain the results. 1 1 Intro duction This work arose out of my involvement with lung cancer studies within the North Central Cancer Treatment Group. These studies are small, typically 100 to 200 patients, and there are several imp ortant prognostic factors on whichwe wish to balance. Some of the factors, such as p erformance or Karnofsky score, are likely to contribute a larger survival impact than the treatment under study; hazards ratios of 3{4 are not uncommon. In this setting it b ecomes very dicult to interpret study results if any of the factors are signi cantly out of balance. -
Harmonizing Fully Optimal Designs with Classic Randomization in Fixed Trial Experiments Arxiv:1810.08389V1 [Stat.ME] 19 Oct 20
Harmonizing Fully Optimal Designs with Classic Randomization in Fixed Trial Experiments Adam Kapelner, Department of Mathematics, Queens College, CUNY, Abba M. Krieger, Department of Statistics, The Wharton School of the University of Pennsylvania, Uri Shalit and David Azriel Faculty of Industrial Engineering and Management, The Technion October 22, 2018 Abstract There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in advance and subjects can be divided optimally into two groups based on a criterion of homogeneity or \imbalance" between the two groups. These designs are far from random. This paper seeks to understand the benefits and the costs over classic randomization in the context of different performance criterions such as Efron's worst-case analysis. In the criterion that we motivate, randomization beats optimization. However, the optimal arXiv:1810.08389v1 [stat.ME] 19 Oct 2018 design is shown to lie between these two extremes. Much-needed further work will provide a procedure to find this optimal designs in different scenarios in practice. Until then, it is best to randomize. Keywords: randomization, experimental design, optimization, restricted randomization 1 1 Introduction In this short survey, we wish to investigate performance differences between completely random experimental designs and non-random designs that optimize for observed covariate imbalance. We demonstrate that depending on how we wish to evaluate our estimator, the optimal strategy will change. We motivate a performance criterion that when applied, does not crown either as the better choice, but a design that is a harmony between the two of them. -
Some Restricted Randomization Rules in Sequential Designs Jose F
This article was downloaded by: [Georgia Tech Library] On: 10 April 2013, At: 12:48 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Communications in Statistics - Theory and Methods Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/lsta20 Some Restricted randomization rules in sequential designs Jose F. Soares a & C.F. Jeff Wu b a Federal University of Minas Gerais, Brazil b University of Wisconsin Madison and Mathematical Sciences Research Institute, Berkeley Version of record first published: 27 Jun 2007. To cite this article: Jose F. Soares & C.F. Jeff Wu (1983): Some Restricted randomization rules in sequential designs, Communications in Statistics - Theory and Methods, 12:17, 2017-2034 To link to this article: http://dx.doi.org/10.1080/03610928308828586 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-and-conditions This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. -
Stratification Trees for Adaptive Randomization in Randomized
Stratification Trees for Adaptive Randomization in Randomized Controlled Trials Max Tabord-Meehan Department of Economics Northwestern University [email protected] ⇤ (Click here for most recent version) 26th October 2018 Abstract This paper proposes an adaptive randomization procedure for two-stage randomized con- trolled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimize the variance of an estimator for the average treatment e↵ect (ATE). We consider selection from a class of stratified randomization procedures which we call stratification trees: these are procedures whose strata can be represented as decision trees, with di↵ering treatment assignment probabilities across strata. By using the first wave to estimate a stratification tree, we simultaneously select which covariates to use for stratification, how to stratify over these covariates, as well as the assign- ment probabilities within these strata. Our main result shows that using this randomization procedure with an appropriate estimator results in an asymptotic variance which minimizes the variance bound for estimating the ATE, over an optimal stratification of the covariate space. Moreover, by extending techniques developed in Bugni et al. (2018), the results we present are able to accommodate a large class of assignment mechanisms within strata, including stratified block randomization. We also present extensions of the procedure to the setting of multiple treatments, and to the targeting of subgroup-specific e↵ects. In a simulation study, we find that our method is most e↵ective when the response model exhibits some amount of “sparsity” with respect to the covariates, but can be e↵ective in other contexts as well, as long as the first-wave sample size used to estimate the stratification tree is not prohibitively small. -
Pragmatic Cluster Randomized Trials Using Covariate Constrained Randomization: a Method for Practice-Based Research Networks (Pbrns)
SPECIAL COMMUNICATION Pragmatic Cluster Randomized Trials Using Covariate Constrained Randomization: A Method for Practice-based Research Networks (PBRNs) L. Miriam Dickinson, PhD, Brenda Beaty, MSPH, Chet Fox, MD, Wilson Pace, MD, W. Perry Dickinson, MD, Caroline Emsermann, MS, and Allison Kempe, MD, MPH Background: Cluster randomized trials (CRTs) are useful in practice-based research network transla- tional research. However, simple or stratified randomization often yields study groups that differ on key baseline variables when the number of clusters is small. Unbalanced study arms constitute a potentially serious methodological problem for CRTs. Methods: Covariate constrained randomization with data on relevant variables before randomization was used to achieve balanced study arms in 2 pragmatic CRTs. In study 1, 16 counties in Colorado were randomized to practice-based or population-based reminder recall for vaccinating children ages 19 to 35 months. In study 2, 18 primary care practices were randomized to computer decision support plus practice facilitation versus computer decision support alone to improve care for patients with stage 3 and 4 chronic kidney disease. For each study, a set of optimal randomizations, which minimized differ- ences of key variables between study arms, was identified from the set of all possible randomizations. Results: Differences between study arms were smaller in the optimal versus remaining randomiza- tions. Even for the randomization in the optimal set with the largest difference between groups, study arms did not differ significantly on any variable for either study (P > .05). Conclusions: Covariate constrained randomization, which restricts the full randomization set to a subset in which differences between study arms are minimized, is a useful tool for achieving balanced study arms in CRTs. -
Random Allocation in Controlled Clinical Trials: a Review
J Pharm Pharm Sci (www.cspsCanada.org) 17(2) 248 - 253, 2014 Random Allocation in Controlled Clinical Trials: A Review Bolaji Emmanuel Egbewale Department of Community Medicine, Ladoke Akintola University of Technology, Ogbomoso, Nigeria Received, February 16, 2014; Revised, May 23, 2014; Accepted, May 30, 2014; Published, June 2, 2014. ABSTRACT- PURPOSE: An allocation strategy that allows for chance placement of participants to study groups is crucial to the experimental nature of randomised controlled trials. Following decades of the discovery of randomisation considerable erroneous opinion and misrepresentations of its concept both in principle and practice still exists. In some circles, opinions are also divided on the strength and weaknesses of each of the random allocation strategies. This review provides an update on various random allocation techniques so as to correct existing misconceptions on this all important procedure. METHODS: This is a review of literatures published in the Pubmed database on concepts of common allocation techniques used in controlled clinical trials. RESULTS: Allocation methods that use; case record number, date of birth, date of presentation, haphazard or alternating assignment are non-random allocation techniques and should not be confused as random methods. Four main random allocation techniques were identified. Minimisation procedure though not fully a random technique, however, proffers solution to the limitations of stratification at balancing for multiple prognostic factors, as the procedure makes treatment groups similar in several important features even in small sample trials. CONCLUSIONS: Even though generation of allocation sequence by simple randomisation procedure is easily facilitated, a major drawback of the technique is that treatment groups can by chance end up being dissimilar both in size and composition of prognostic factors. -
In Pursuit of Balance
WPS4752 POLICY RESEA R CH WO R KING PA P E R 4752 Public Disclosure Authorized In Pursuit of Balance Randomization in Practice Public Disclosure Authorized in Development Field Experiments Miriam Bruhn David McKenzie Public Disclosure Authorized The World Bank Public Disclosure Authorized Development Research Group Finance and Private Sector Team October 2008 POLICY RESEA R CH WO R KING PA P E R 4752 Abstract Randomized experiments are increasingly used in emerge. First, many researchers are not controlling for the development economics, with researchers now facing method of randomization in their analysis. The authors the question of not just whether to randomize, but show this leads to tests with incorrect size, and can result how to do so. Pure random assignment guarantees that in lower power than if a pure random draw was used. the treatment and control groups will have identical Second, they find that in samples of 300 or more, the characteristics on average, but in any particular random different randomization methods perform similarly in allocation, the two groups will differ along some terms of achieving balance on many future outcomes of dimensions. Methods used to pursue greater balance interest. However, for very persistent outcome variables include stratification, pair-wise matching, and re- and in smaller sample sizes, pair-wise matching and randomization. This paper presents new evidence on stratification perform best. Third, the analysis suggests the randomization methods used in existing randomized that on balance the re-randomization methods common experiments, and carries out simulations in order to in practice are less desirable than other methods, such as provide guidance for researchers. -
Week 10: Causality with Measured Confounding
Week 10: Causality with Measured Confounding Brandon Stewart1 Princeton November 28 and 30, 2016 1These slides are heavily influenced by Matt Blackwell, Jens Hainmueller, Erin Hartman, Kosuke Imai and Gary King. Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 1 / 176 Where We've Been and Where We're Going... Last Week I regression diagnostics This Week I Monday: F experimental Ideal F identification with measured confounding I Wednesday: F regression estimation Next Week I identification with unmeasured confounding I instrumental variables Long Run I causality with measured confounding ! unmeasured confounding ! repeated data Questions? Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 2 / 176 1 The Experimental Ideal 2 Assumption of No Unmeasured Confounding 3 Fun With Censorship 4 Regression Estimators 5 Agnostic Regression 6 Regression and Causality 7 Regression Under Heterogeneous Effects 8 Fun with Visualization, Replication and the NYT 9 Appendix Subclassification Identification under Random Assignment Estimation Under Random Assignment Blocking Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 3 / 176 Lancet 2001: negative correlation between coronary heart disease mortality and level of vitamin C in bloodstream (controlling for age, gender, blood pressure, diabetes, and smoking) Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 4 / 176 Lancet 2002: no effect of vitamin C on mortality in controlled placebo trial (controlling for nothing) Stewart (Princeton) Week 10: Measured Confounding November 28 and 30, 2016 4 / 176 Lancet 2003: comparing among individuals with the same age, gender, blood pressure, diabetes, and smoking, those with higher vitamin C levels have lower levels of obesity, lower levels of alcohol consumption, are less likely to grow up in working class, etc. -
Randomized Complete Block Designs
1 2 RANDOMIZED COMPLETE BLOCK DESIGNS Randomization can in principal be used to take into account factors that can be treated by blocking, but Introduction to Blocking blocking usually results in smaller error variance, hence better estimates of effect. Thus blocking is Nuisance factor: A factor that probably has an effect sometimes referred to as a method of variance on the response, but is not a factor that we are reduction design. interested in. The intuitive idea: Run in parallel a bunch of Types of nuisance factors and how to deal with them experiments on groups (called blocks) of units that in designing an experiment: are fairly similar. Characteristics Examples How to treat The simplest block design: The randomized complete Unknown, Experimenter or Randomization block design (RCBD) uncontrollable subject bias, order Blinding of treatments v treatments Known, IQ, weight, Analysis of (They could be treatment combinations.) uncontrollable, previous learning, Covariance measurable temperature b blocks, each with v units Known, Temperature, Blocking Blocks chosen so that units within a block are moderately location, time, alike (or at least similar) and units in controllable (by batch, particular different blocks are substantially different. choosing rather machine or (Thus the total number of experimental units than adjusting) operator, age, is n = bv.) gender, order, IQ, weight The v experimental units within each block are randomly assigned to the v treatments. (So each treatment is assigned one unit per block.) 3 4 Note that experimental units are assigned randomly RCBD Model: only within each block, not overall. Thus this is sometimes called a restricted randomization. -
How to Do Random Allocation (Randomization) Jeehyoung Kim, MD, Wonshik Shin, MD
Special Report Clinics in Orthopedic Surgery 2014;6:103-109 • http://dx.doi.org/10.4055/cios.2014.6.1.103 How to Do Random Allocation (Randomization) Jeehyoung Kim, MD, Wonshik Shin, MD Department of Orthopedic Surgery, Seoul Sacred Heart General Hospital, Seoul, Korea Purpose: To explain the concept and procedure of random allocation as used in a randomized controlled study. Methods: We explain the general concept of random allocation and demonstrate how to perform the procedure easily and how to report it in a paper. Keywords: Random allocation, Simple randomization, Block randomization, Stratified randomization Randomized controlled trials (RCT) are known as the best On the other hand, many researchers are still un- method to prove causality in spite of various limitations. familiar with how to do randomization, and it has been Random allocation is a technique that chooses individuals shown that there are problems in many studies with the for treatment groups and control groups entirely by chance accurate performance of the randomization and that some with no regard to the will of researchers or patients’ con- studies are reporting incorrect results. So, we will intro- dition and preference. This allows researchers to control duce the recommended way of using statistical methods all known and unknown factors that may affect results in for a randomized controlled study and show how to report treatment groups and control groups. the results properly. Allocation concealment is a technique used to pre- vent selection bias by concealing the allocation sequence CATEGORIES OF RANDOMIZATION from those assigning participants to intervention groups, until the moment of assignment. -
Guideline on Adjustment for Baseline Covariates' (EMA/CHMP/295050/2013)
26 February 2015 EMA/40143/2014 CHMP Biostatistics Working Party (BSWP) Overview of comments received on 'Guideline on adjustment for baseline covariates' (EMA/CHMP/295050/2013) Interested parties (organisations or individuals) that commented on the draft document as released for consultation. Stakeholder no. Name of organisation or individual 1 Alisa J. Stephens, University of Pennsylvania, USA; Eric J. Tchetgen Tchetgen, Harvard University, USA; Victor De Gruttola, Harvard University, USA. 2 European Federation of Statisticians in the Pharmaceutical Industry (EFSPI) 3 Merck Sharp & Dohme (MSD) 4 F. Hoffmann – la Roche Ltd. 5 The European Federation of Pharmaceutical Industries and Associations (EFPIA) 6 Teva Pharmaceutical Ltd 7 Ablynx (Heidi Wouters en Katrien Verschueren) 8 IDeAl (Integrated Design and AnaLysis of small population group trials) FP7 Consortium 9 SciencePharma (Poland) 30 Churchill Place ● Canary Wharf ● London E14 5EU ● United Kingdom Telephone +44 (0)20 3660 6000 Facsimile +44 (0)20 3660 5555 Send a question via our website www.ema.europa.eu/contact An agency of the European Union © European Medicines Agency, 2015. Reproduction is authorised provided the source is acknowledged. 1. General comments – overview Stakeholder no. General comment (if any) Outcome (if applicable) 1 1. Introduction The proposed EMA guidelines highlight important issues surrounding covariate adjustment in the analysis and interpretation of results from randomized trials. As the guidelines state, proper covariate adjustment can enhance precision in the estimation of treatment effects; however, doing so in practice raises several important issues, including interpretation of the estimated effects, evaluation of the impact of model misspecification, and the consequences of inclusion of postrandomization covariates. -
A General Overview of Adaptive Randomization Design for Clinical Trials
tri ome cs & Bi B f i o o l s t a a n t r i s u t i o c J s Journal of Biometrics & Biostatistics Lin et al., J Biom Biostat 2016, 7:2 ISSN: 2155-6180 DOI: 10.4172/2155-6180.1000294 Review Article Open Access A General Overview of Adaptive Randomization Design for Clinical Trials Jianchang Lin1*, Li-An Lin2 and Serap Sankoh1 1Takeda Pharmaceutical Company Limited, Cambridge, MA, USA 2Merck Research Laboratories, Whitehouse Station, New Jersey , USA *Corresponding author: Jianchang Lin, Takeda Pharmaceutical Company Limited, Cambridge, MA, USA, Tel: +1-617-679-7000; E-mail: [email protected] Rec date: March 25, 2016; Acc date: April 14, 2016; Pub date: April 21, 2016 Copyright: © 2016 Lin J, et al.This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abstract With the recent release of FDA draft guidance (2010), adaptive designs, including adaptive randomization (e.g. response-adaptive (RA) randomization) has become popular in clinical trials because of its advantages of flexibility and efficiency gains, which also have the significant ethical advantage of assigning fewer patients to treatment arms with inferior outcomes. In this paper, we presented a general overview of adaptive randomization designs for clinical trials, including Bayesian and frequentist approaches as well as response-adaptive randomization. Examples were used to demonstrate the procedure for design parameters calibration and operating characteristics. Both advantages and disadvantages of adaptive randomization were discussed in the summary from practical perspective of clinical trials.