Studywise minimization: A treatment allocation method that improves balance among treatment groups and makes allocation unpredictable

ObjectivesIn randomized controlled trials with many potential prognostic factors, serious imbalance among treatment groups regarding these factors can occur. Minimization methods can improve balance but increase the possibility of selection bias. We described and evaluated the performance of a new method of treatment allocation, called studywise minimization, that can avoid imbalance by chance and reduce selection bias.Study Design and SettingThe studywise minimization algorithm consists of three steps: (1) calculate the imbalance for all possible allocations, (2) list all allocations with minimum imbalance, and (3) randomly select one of the allocations with minimum imbalance. We carried out a simulation study to compare the performance of studywise minimization with three other allocation methods: randomization, biased-coin minimization, and deterministic minimization. Performance was measured, calculating maximal and average imbalance as a percentage of the group size.ResultsIndependent of trial size and number of prognostic factors, the risk of serious imbalance was the highest in randomization and absent in studywise minimization. The largest differences among the allocation methods regarding the risk of imbalance were found in small trials.ConclusionStudywise minimization is particularly useful in small trials, where it eliminates the risk of serious imbalances without generating the occurrence of selection bias.     

Preserving the allocation ratio at every allocation with biased coin randomization and minimization in studies with unequal allocation

The demand for unequal allocation in clinical trials is growing. Most commonly, the unequal allocation is achieved through permuted block randomization. However, other allocation procedures might be required to better approximate the allocation ratio in small samples, reduce the selection bias in open-label studies, or balance on baseline covariates. When these allocation procedures are generalized to unequal allocation, special care is to be taken to preserve the allocation ratio at every allocation step. This paper offers a way to expand the biased coin randomization to unequal allocation that preserves the allocation ratio at every allocation. The suggested expansion works with biased coin randomization that balances only on treatment group totals and with covariate-adaptive procedures that use a random biased coin element at every allocation. Balancing properties of the allocation ratio preserving biased coin randomization and minimization are described through simulations. It is demonstrated that these procedures are asymptotically protected against the shift in the rerandomization distribution identified for some examples of minimization with 1:2 allocation. The asymptotic shift in the rerandomization distribution of the difference in treatment means for an arbitrary unequal allocation procedure is explicitly derived in the paper.     

Generalized multidimensional dynamic allocation method

Dynamic allocation has received considerable attention since it was first proposed in the 1970s as an alternative means of allocating treatments in clinical trials which helps to secure the balance of prognostic factors across treatment groups. The purpose of this paper is to present a generalized multidimensional dynamic allocation method that simultaneously balances treatment assignments at three key levels: within the overall study, within each level of each prognostic factor, and within each stratum, that is, combination of levels of different factors Further it offers capabilities for unbalanced and adaptive designs for trials. The treatment balancing performance of the proposed method is investigated through simulations which compare multidimensional dynamic allocation with traditional stratified block randomization and the Pocock–Simon method. On the basis of these results, we conclude that this generalized multidimensional dynamic allocation method is an improvement over conventional dynamic allocation methods and is flexible enough to be applied for most trial settings including Phases I, II and III trials. Copyright © 2012 John Wiley & Sons, Ltd.     

Studies with group treatments required special power calculations, allocation methods, and statistical analyses

ObjectiveIn some trials, the intervention is delivered to individuals in groups, for example, groups that exercise together. The group structure of such trials has to be taken into consideration in the analysis and has an impact on the power of the trial. Our aim was to provide optimal methods for the design and analysis of such trials.Study Design and SettingWe described various treatment allocation methods and presented a new allocation algorithm: optimal batchwise minimization (OBM). We carried out a simulation study to evaluate the performance of unrestricted randomization, stratification, permuted block randomization, deterministic minimization, and OBM. Furthermore, we described appropriate analysis methods and derived a formula to calculate the study size.ResultsStratification, deterministic minimization, and OBM had considerably less risk of imbalance than unrestricted randomization and permuted block randomization. Furthermore, OBM led to unpredictable treatment allocation. The sample size calculation and the analysis of the study must be based on a multilevel model that takes the group structure of the trial into account.ConclusionTrials evaluating interventions that are carried out in subsequent groups require adapted treatment allocation, power calculation, and analysis methods. From the perspective of obtaining overall balance, we conclude that minimization is the method of choice. When the number of prognostic factors is low, stratification is an excellent alternative. OBM leads to better balance within the batches, but it is more complicated. It is probably most worthwhile in trials with many prognostic factors. From the perspective of predictability, a treatment allocation method, such as OBM, that allocates several subjects at the same time, is superior to other methods because it leads to the lowest possible predictability.     

New algorithm for treatment allocation reduced selection bias and loss of power in small trials

OBJECTIVE: In clinical trials, patients become available for treatment sequentially. Especially in trials with a small number of patients, loss of power may become an important issue, if treatments are not allocated equally or if prognostic factors differ between the treatment groups. We present a new algorithm for sequential allocation of two treatments in small clinical trials, which is concerned with the reduction of both selection bias and imbalance. STUDY DESIGN AND SETTING: With the algorithm, an element of chance is added to the treatment as allocated by minimization. The amount of chance depends on the actual amount of imbalance of treatment allocations of the patients already enrolled. The sensitivity to imbalance may be tuned. We performed trial simulations with different numbers of patients and prognostic factors, in which we quantified loss of power and selection bias. RESULTS: With our method, selection bias is smaller than with minimization, and loss of power is lower than with pure randomization or treatment allocation according to a biased coin principle. CONCLUSION: Our method combines the conflicting aims of reduction of bias by predictability and reduction of loss of power, as a result of imbalance. The method may be of use in small trials.     

Validity and power considerations on hypothesis testing under minimization

Minimization, a dynamic allocation method, is gaining popularity especially in cancer clinical trials. Aiming to achieve balance on all important prognostic factors simultaneously, this procedure can lead to a substantial reduction in covariate imbalance compared with conventional randomization in small clinical trials. While minimization has generated enthusiasm, some controversy exists over the proper analysis of such a trial. Critics argue that standard testing methods that do not account for the dynamic allocation algorithm can lead to invalid statistical inference. Acknowledging this limitation, the International Conference on Harmonization E9 guideline suggests that ‘the complexity of the logistics and potential impact on analyses be carefully evaluated when considering dynamic allocation’. In this article, we investigate the proper analysis approaches to inference in a minimization design for both continuous and time‐to‐event endpoints and evaluate the validity and power of these approaches under a variety of scenarios both theoretically and empirically. Published 2016. This article is a U.S. Government work and is in the public domain in the USA     

Dynamic randomization and a randomization model for clinical trials data

Randomization models are useful in supporting the validity of linear model analyses applied to data from a clinical trial that employed randomization via permuted blocks. Here, a randomization model for clinical trials data with arbitrary randomization methodology is developed, with treatment effect estimators and standard error estimators valid from a randomization perspective. A central limit theorem for the treatment effect estimator is also derived. As with permuted‐blocks randomization, a typical linear model analysis provides results similar to the randomization model results when, roughly, unit effects display no pattern over time. A key requirement for the randomization inference is that the unconditional probability that any patient receives active treatment is constant across patients ; when this probability condition is violated, the treatment effect estimator is biased from a randomization perspective. Most randomization methods for balanced, 1 to 1, treatment allocation satisfy this condition. However, many dynamic randomization methods for planned unbalanced treatment allocation, like 2 to 1, do not satisfy this constant probability condition, and these methods should be avoided. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison of stratification and adaptive methods for treatment allocation in an acute stroke clinical trial

Achieving balance on prognostic factors between treatment groups in a clinical trial is important to ensure that any observed treatment effect may be attributed to the treatment itself. Improving the balance on prognostic factors also potentially increases the statistical power attained in a trial. Substantial imbalances may occur by chance if simple randomization is used. Allocation of the treatment according to stratified random blocks based on clinical features is the conventional approach to obtain treatment groups that are as similar as possible. An alternative approach, known as minimization (or more generally as adaptive stratification), has also been proposed. We assessed the feasibility of adaptive stratification in the context of a clinical trial of insulin to control plasma glucose level following acute stroke. We determined suitable settings for the parameters in the adaptive stratification procedure by simulation studies. Specifically, we assessed: the optimal probability for allocating a patient to the preferred (leading to least imbalance on prognostic factors) treatment group; the number of variables that could be incorporated in the adaptive stratification algorithm; the weighting that should be given to each variable; and whether interactions between variables should be included. We then compared the statistical power, across a range of simulated treatment effects, between trials where treatments were allocated by stratified random blocks and by adaptive stratification. Finally, we considered the importance of the method of analysis in realizing the gain in power which may potentially be achieved by allocating treatments using stratified random blocks or adaptive stratification.     

Dynamic balanced randomization for clinical trials

Common methods of treatment allocation for multi-centre and/or stratified randomized clinical trials can result in substantial differences between the number of patients allocated to each treatment arm. This can occur in the overall trial for a permuted block design or within individual institutions/strata when using a minimization scheme. This may lead to a bias in the result. Also, these procedures can be predictable, with the possibility of an investigator-introduced selection bias. An easily implemented method of randomization is proposed which attempts to overcome these problems by balancing treatment allocations both within strata and across the trial as a whole. The method keeps a running tally on total treatment allocation numbers at all stratification levels. When a patient accrues a hierarchical decision rule is applied, and the allocation is deterministic if certain pre-defined limits are exceeded, and random otherwise. The method is an extension of the big stick design of Soares and Wu, and is related to both Zelen's key number randomization methods and the schemes of Nordle and Brantmark. Simulation studies are used to demonstrate that major imbalances possible with other schemes do not occur using this method, and that the potential for selection bias is much reduced.     

Approaches to expanding the two‐arm biased coin randomization to unequal allocation while preserving the unconditional allocation ratio

The paper discusses three methods for expanding the biased coin randomization (BCR) to unequal allocation while preserving the unconditional allocation ratio at every step. The first method originally proposed in the contexts of BCR and minimization is based on mapping from an equal allocation multi‐arm BCR. Despite the improvement proposed in this paper to ensure tighter adherence to the targeted unequal allocation, this method still distributes the probability mass at least as wide as the permuted block randomization (PBR). This works for smaller block sizes, but for larger block sizes, a tighter control of the imbalance in the treatment assignments is desired. The second method, which has two versions, allows to tighten the distribution of the imbalance compared with that achieved with the PBR. However, the distribution of the imbalance remains considerably wider than that of the brick tunnel randomization – the unequal allocation procedure with the tightest possible imbalance distribution among all allocation ratio preserving procedures with the same allocation ratio. Finally, the third method, the BCR with a preset proportion of maximal forcing, mimics the properties of the equal allocation BCR. With maximum forcing, it approaches the brick tunnel randomization, similar to how 1:1 BCR approaches 1:1 PBR with the permuted block size of 2 (the equal allocation procedure with the lowest possible imbalance) when the bias approaches 1. With minimum forcing, the BCR with a preset proportion of maximal forcing approaches complete randomization (similar to 1:1 BCR). Copyright © 2017 John Wiley & Sons, Ltd.