Considerations in the paper by Proschan, Brittain, and Kammerman are not an argument against minimization. In response to Vance W Berger ‘Minimization: not all it’s cracked up to be’, <i>Clin Trials</i> 2011; 8: 443

Kuznetsova, Olga M.

doi:10.1177/1740774512444637

Cited by 4 publications

(3 citation statements)

References 11 publications

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“…However, the shift phenomenon noted by Proschan et al can arise with equal allocation when a conditional randomization test instead of the unconditional randomization test is used to analyze the data . When the allocation results in unequal sizes of the two treatment arms, there are no pairs of twin sequences within the conditional reference set.…”

Section: Introductionmentioning

confidence: 99%

Shift in re‐randomization distribution with conditional randomization test

Kuznetsova

Tymofyeyev

2013

Pharmaceutical Statistics

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Proschan, Brittain, and Kammerman made a very interesting observation that for some examples of the unequal allocation minimization, the mean of the unconditional randomization distribution is shifted away from 0. Kuznetsova and Tymofyeyev linked this phenomenon to the variations in the allocation ratio from allocation to allocation in the examples considered in the paper by Proschan et al. and advocated the use of unequal allocation procedures that preserve the allocation ratio at every step. In this paper, we show that the shift phenomenon extends to very common settings: using conditional randomization test in a study with equal allocation. This phenomenon has the same cause: variations in the allocation ratio among the allocation sequences in the conditional reference set, not previously noted. We consider two kinds of conditional randomization tests. The first kind is the often used randomization test that conditions on the treatment group totals; we describe the variations in the conditional allocation ratio with this test on examples of permuted block randomization and biased coin randomization. The second kind is the randomization test proposed by Zheng and Zelen for a multicenter trial with permuted block central allocation that conditions on the within-center treatment totals. On the basis of the sequence of conditional allocation ratios, we derive the value of the shift in the conditional randomization distribution for specific vector of responses and the expected value of the shift when responses are independent identically distributed random variables. We discuss the asymptotic behavior of the shift for the two types of tests.

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Section: Introductionmentioning

confidence: 99%

Shift in re‐randomization distribution with conditional randomization test

Kuznetsova

Tymofyeyev

2013

Pharmaceutical Statistics

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“…However, there are problems with using minimisation in unequal allocation ratios, including deviation from the target allocation ratio, particularly when the preferred treatment is assigned a probability value that is relatively low [6] and the randomisation distribution does not necessarily have a mean value of 0 [10]. The latter is not necessarily an issue peculiar to minimisation [11]. It is common to all unequal allocation procedures for which the allocation ratio varies from allocation to allocation [11].…”

Section: Discussionmentioning

confidence: 99%

“…The latter is not necessarily an issue peculiar to minimisation [11]. It is common to all unequal allocation procedures for which the allocation ratio varies from allocation to allocation [11]. This paper proposes a new minimisation procedure for unequal treatment allocation.…”

Section: Discussionmentioning

confidence: 99%

Sequence balance minimisation: minimising with unequal treatment allocations

Madurasinghe¹

2017

Trials

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BackgroundMinimisation ensures excellent balance between groups for several prognostic factors, even in small samples. However, its use with unequal allocation ratios has been problematic. This paper describes a new minimisation scheme named sequence balance minimisation for unequal treatment allocations.MethodsTreatment- and factor-balancing properties were assessed in simulation studies for two- and three-arm trials with 1:2 and 1:2:3 allocation ratios. Sample sizes were set 30, 60 and 120. The number of prognostic factors on which to achieve balance was ranged from zero (treatment totals only) to ten with two levels occurring in equal probabilities. Random elements were set at 0.95, 0.9, 0.85, 0.80, 0.7, 0.6 and 0.5. Characteristics of the randomisation distributions and the impact of changing the block size while maintaining the allocation ratio were also examined.ResultsSequence balance minimisation has good treatment- and factor-balancing capabilities, and the randomisation distribution was centred at zero for all scenarios. The mean and median number of allocations achieved were the same as the number expected in most scenarios, and including additional factors (up to ten) in the minimisation scheme had little impact on treatment balance. Treatment balance tended to depart from the target as the random element was lowered. The variability in allocations achieved increased slightly as the number of factors increased, as the random element was decreased and as the sample size increased. The mean and median factor imbalance remained tightly around zero even when the chosen factor was not included in the minimisation scheme, though the variability was greater. The variability in factor imbalance increased slightly as the random element decreased, as well as when the number of prognostic factors and sample size increased. Increasing block size while maintaining the allocation ratio improved treatment balance notably with little impact on factor imbalance.ConclusionsSequence balance minimisation has good treatment- and factor-balancing properties and is particularly useful for small trials seeking to achieve balance across several prognostic factors.Electronic supplementary materialThe online version of this article (doi:10.1186/s13063-017-1942-3) contains supplementary material, which is available to authorized users.

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Randomization Challenges in Adaptive Design Studies

Kuznetsova

2014

Practical Considerations for Adaptive Trial Design and Implementation

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Considerations in the paper by Proschan, Brittain, and Kammerman are not an argument against minimization. In response to Vance W Berger ‘Minimization: not all it’s cracked up to be’, Clin Trials 2011; 8: 443

Cited by 4 publications

References 11 publications

Shift in re‐randomization distribution with conditional randomization test

Shift in re‐randomization distribution with conditional randomization test

Sequence balance minimisation: minimising with unequal treatment allocations

Randomization Challenges in Adaptive Design Studies

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