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Published in Filomena Pereira-Maxwell, Medical Statistics, 2018
resulting in treatment groups with equal sample sizes. A randomized block design is a parallel trial in which restricted randomization, rather than simple randomization, is employed. Biased coin allocation is used to the same aim as block randomization. See also complete block design, incomplete block design. Further details are given by ALTMAN (1991), POCOCK (1983) and FLEISS (1999), and also under randomized block design.
Evolution of Restricted Randomization with Maximum Tolerated Imbalance
Published in Vance W. Berger, Randomization, Masking, and Allocation Concealment, 2017
The primary goal of restricted randomization is to control the treatment distribution imbalance. It is a natural strategy to alter the treatment allocation probability according to the observed treatment distribution. A restricted randomization procedure can be classified as a Markov process if the treatment assignment for the next subject depends solely on the current treatment distribution, not on the treatment assignment sequences that preceded it.8 Consider a two-arm trial with equal allocation, let ni,A and ni,B be the number of subjects previously assigned to arms A and B, respectively, among the i subjects being randomized into the study. Let pi,A and pi,B be the conditional allocation probability for assigning subject i to arms A and B, respectively, and Ri be the random number with uniform distribution on (0,1) for the randomization of subject i. The conditional allocation probability for a restricted randomization takes a general format as below:
Statistics in medical research
Published in Douglas G. Altman, Practical Statistics for Medical Research, 1990
Randomized blocks can be of any size, but using a multiple of the number of treatments is more logical. Large blocks are best avoided as they control balance less well. In clinical trials it is highly desirable for the randomization sequence to be kept hidden from those actually giving the treatments. This is often achieved by creating a pile of opaque numbered sealed envelopes each containing the allocation for one patient. Even so, with the knowledge that restricted randomization is being used, it is possible to deduce in advance the treatment to be given to every fourth patient. For this reason it is better for the users of the random numbers not to know how the sequence was constructed, and it may also be desirable to vary the block length, again at random, perhaps using a mixture of blocks of size 2, 4, or 6. A similar approach is used when there are more than two treatments. For example, blocks of size 3, 6, or 9 can be used for three treatments. Obviously these considerations do not apply to experiments on animals or laboratory experiments on human samples.
A practitioner's guide to conducting and analysing embedded randomized single-case experimental designs
Published in Neuropsychological Rehabilitation, 2023
This set-up allowed the authors to assess two different interventions (massed versus distributed practice) within and between six participants and to assess whether effects fade when treatment is withdrawn (i.e., including baseline phases). Randomization was implemented in a restricted manner: The child rolled a die before the first weekly session to determine which condition would be presented first in that session; the following session would have the reverse order. Thus, the order of conditions was counterbalanced by week but randomized across weeks, and each condition was presented an equal number of times. (Maas et al., 2019, p. 3167)For data analysis, the authors performed visual analysis combined with d-statistic calculations (Busk & Serlin, 1992). It would also have been possible to conduct a randomization test following the restricted randomization used in the design. An alternative or additional way of incorporating randomization would have been the random determination of phase change moments or the random assignment of participants to predetermined phase lengths.
Dealing with Possible Baseline Inequalities Between Experimental Groups – The Case of Motor Learning
Published in Journal of Motor Behavior, 2020
Gal Ziv, Ronnie Lidor, Yael Netz
However, in small samples (<200; Lachin, 1988), simple randomization may fail to prevent selection bias and may lead to imbalances in certain variables between groups (Broglio, 2018). Therefore, a number of restricted randomization procedures have been proposed for small samples. Among these procedures are several forms of covariate-adaptive randomization (e.g., minimization and dynamic hierarchical randomization) (Lin, Zhu, & Su, 2015). Covariate-adaptive randomization can be used when there are several covariates that may strongly affect the endpoint variable (Lin et al., 2015). In minimization, for example, allocation to experimental groups is performed for each new participant in such a way that it minimizes imbalances across several covariates at baseline (Lin et al., 2015).
Design and analysis considerations for comparing dynamic treatment regimens with binary outcomes from sequential multiple assignment randomized trials
Published in Journal of Applied Statistics, 2018
Kelley M. Kidwell, Nicholas J. Seewald, Qui Tran, Connie Kasari, Daniel Almirall
The ‘weighted and replicated’ estimation method weights and replicates observations to account for the restricted randomization by design. Many SMART designs include restricted randomization by only randomizing some of the trial participants to specific intervention options (e.g. in design II only non-responders are re-randomized to receive intensified or additional therapy), unequal randomization between interventions at the first and/or second stage, or randomization to different numbers of interventions (for example, non-responders could receive one of three possible interventions, whereas responders could receive one of two possible interventions) [35]. When any of these three scenarios occur, there is under- or over-representation of certain groups of individuals due to the design of the trial. To account for this, inverse-probability-of-treatment weighting is used [17]. Each observation is weighted inversely proportional to its probability of receiving its own DTR. The weights are known; they are obtained from the assigned randomization probability to the first- and second-stage intervention options.