Methodology of Adaptive Randomization
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Abstract Simple randomization consists of allocating treatments to patients with equal probability. Attempts to improve over simple randomization stem from the desire (i) to ensure that a prespecified number of patients is enrolled in each treatment arm, (ii) to ensure balance with respect to important baseline prognostic factors across all treatment arms, or (iii) to favor (i.e., allocate with higher probability) the treatment arm that is currently faring better. These objectives can be fulfilled, respectively, by use of treatment‐adaptive randomization, covariate‐adaptive randomization, and outcome‐adaptive randomization. Treatment‐adaptive randomization can be implemented as a restricted randomization through randomly permuted blocks or as a dynamic method using a biased coin. Similarly, covariate‐adaptive randomization can use randomly permuted blocks within strata or minimization. Outcome‐adaptive randomization remains controversial because of it produces only modest gains in terms of total number of failures at the cost of increased complexity, a risk of accrual bias, and the potential for ethical concerns.Keywords:
Restricted randomization
Randomization is a key step in reducing selection bias during the treatment allocation phase in randomized clinical trials. The process of randomization follows specific steps, which include generation of the randomization list, allocation concealment, and implementation of randomization. The phenomenon in the dental and orthodontic literature of characterizing treatment allocation as random is frequent; however, often the randomization procedures followed are not appropriate. Randomization methods assign, at random, treatment to the trial arms without foreknowledge of allocation by either the participants or the investigators thus reducing selection bias. Randomization entails generation of random allocation, allocation concealment, and the actual methodology of implementing treatment allocation randomly and unpredictably. Most popular randomization methods include some form of restricted and/or stratified randomization. This article introduces the reasons, which make randomization an integral part of solid clinical trial methodology, and presents the main randomization schemes applicable to clinical trials in orthodontics.
Restricted randomization
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Abstract A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.
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Planning cluster randomized studies requires special attention due to their specific design. To achieve balance on a cluster level as well as on individual level, it is necessary to apply randomization techniques which involve restricted randomization. Objective: Determine randomization techniques as well as their frequency in protocols for cluster randomized trials. Materials and method: Searching the MEDLINE bibliographic database, there were 1020 bibliographic units, the analysis included only the protocols for cluster randomized trials, which was a total of 169 trials. Data on randomization techniques, units of randomization and publication years of protocols were extracted. Results: The randomization technique with most frequency was stratification (35.9%). After stratification the most frequent was simple randomization (13.5%), followed by a combination of block and stratification (10%), block randomization (9.4%) and matching (9.4%). The most frequent units of randomization were health facilities (52%). The number of published protocols statistically increases during time (p<0.01). Conclusion: The most frequent randomization technique used by researchers is restricted randomization.
Restricted randomization
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In most clinical trials, patients are randomized with equal probability among treatments to obtain an unbiased estimate of the treatment effect. Response-adaptive randomization (RAR) has been proposed for ethical reasons, where the randomization ratio is tilted successively to favor the better performing treatment. However, the substantial disagreement regarding bias due to time-trends in adaptive randomization is not fully recognized. The type-I error is inflated in the traditional Bayesian RAR approaches when a time-trend is present. In our approach, patients are assigned in blocks and the randomization ratio is recomputed for blocks rather than traditional adaptive randomization where it is done per patient. We further investigate the design with a range of scenarios for both frequentist and Bayesian designs. We compare our method with equal randomization and with different numbers of blocks including the traditional RAR design where randomization ratio is altered patient by patient basis. The analysis is stratified if there are two or more patients in each block. Small blocks should be avoided due to the possibility of not acquiring any information from the $\mu_i$. On the other hand, RAR with large blocks has a good balance between efficiency and treating more subjects to the better-performing treatment, while retaining blocked RAR's unique unbiasedness.
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In general, randomization can be classified as follows: simple randomization; permuted block randomization; stratified randomization; and adaptive randomization (AR). In a two-arm randomized study, the biased coin design (BCD) can be used to sequentially allocate patients between the two treatments. The play-the-winner rule is a simple response-adaptive design. Similar to the play-the-winner rule, the drop-the-loser rule also assigns more patients to a better treatment. The drop-the-loser rule may produce a less variable proportion during patients' allocation to treatment groups. The doubly adaptive biased coin design allows the randomization probability to explicitly depend on both the observed allocation proportion and the estimated target allocation ratio. Although various AR procedures are available, the conventional fixed randomization (FR) remains its dominant role in clinical trials. Controlled Vocabulary Terms permutation test; randomization
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This chapter outlines the basic steps in determining an appropriate randomization procedure to use, generating the randomization sequence, and implementing the randomization in the clinical trial. It reviews important characteristics of the restricted randomization procedures. The basic issue is a trade-off between the desire to promote or guarantee balance in the numbers of treatment assignments versus the susceptibility to either selection bias or accidental covariate imbalances. The restricted randomization procedures have only been compared with respect to an individual criterion separately. Trade-off plots are useful in comparing restricted randomization procedures, and they can facilitate the appropriate selection of procedures for different criteria. While each trial has its own unique considerations, and some criteria may be more important than others, there are some interesting observations that can be made based on the limited investigations the authors have conducted.
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Though therapeutic clinical trials are often categorized as using either "randomization" or "historical controls" as a basis for treatment evaluation, pure random assignment of treatments is rarely employed. Instead various restricted randomization designs are used. The restrictions include the balancing of treatment assignments over time and the stratification of the assignment with regard to covariates that may affect response. Restricted randomization designs for clinical trials differ from those of other experimental areas because patients arrive sequentially and a balanced design cannot be ensured. The major restricted randomization designs and arguments concerning the proper role of stratification are reviewed here. The effect of randomization restrictions on the validity of significance tests is discussed.
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This paper attempts to strengthen faith in randomization, first by defining it in general and second by showing how it is the fundamental means, in many experiments, of generating the probability space. It is defined by the natural structure of the experimental units (E.U.'s) not by a particular experimental design imposed on that structure. Three examples are given, with the same design but different E.U. structures and randomizations, to show that models developed from experimental designs are superficial, but that their randomization is fundamental.
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Often experimental scientists employ a Randomized Complete Block Design (RCBD) to study the effect of treatments on different subjects. Under a 'complete randomization', the order of the apparatus setups within each block, including all replications of each treatment across all subjects, is completely randomized. However, in many experimental settings complete randomization is impractical due to the cost involved in re-adjusting the device to administer a new treatment. One typically resorts to a type of 'restricted randomization', in which multiple subjects are tested under each treatment before the apparatus is re-adjusted. The order of the treatments as well as the assignment of subjects to each block are random. If the data obtained under any type of restricted randomization are treated as if the data were collected under an RCBD with complete randomization within each block, then there is potential to increase the risk of false positives (Type I error). This is of concern to animal orientation studies and other areas such as chemical ecology where it is impractical to reset the experimental device for each subject tested. The goal of the research presented in this article is twofold: (1) to demonstrate the consequences of constructing an F-statistic based on a mean square error for testing the significance of treatment effects under the restricted randomization; (2) to describe an alternative method, based on split-plot analysis of variance, to analyze designed experiments that yield better power under the restricted randomization. The statistical analyses of simulated experiments and data involving virgin male Periplaneta americana substantiate the benefits of the alternative approach under the restricted randomization. The methodology and analysis employed for the simulated experiment is equally applicable to any organism or artificial agent tested under a restricted randomization protocol.
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In most clinical trials, patients are randomized with equal probability among treatments to obtain an unbiased estimate of the treatment effect. Response-adaptive randomization (RAR) has been proposed for ethical reasons, where the randomization ratio is tilted successively to favor the better performing treatment. However, the substantial disagreement regarding bias due to time-trends in adaptive randomization is not fully recognized. The type-I error is inflated in the traditional Bayesian RAR approaches when a time-trend is present. In our approach, patients are assigned in blocks and the randomization ratio is recomputed for blocks rather than traditional adaptive randomization where it is done per patient. We further investigate the design with a range of scenarios for both frequentist and Bayesian designs. We compare our method with equal randomization and with different numbers of blocks including the traditional RAR design where randomization ratio is altered patient by patient basis. The analysis is stratified if there are two or more patients in each block. Small blocks should be avoided due to the possibility of not acquiring any information from the $\mu_i$. On the other hand, RAR with large blocks has a good balance between efficiency and treating more subjects to the better-performing treatment, while retaining blocked RAR's unique unbiasedness.
Restricted randomization
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