Balance and randomness in sequential clinical trials: the dominant biased coin design

2014 ◽  
Vol 13 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Alessandro Baldi Antognini ◽  
Maroussa Zagoraiou
Keyword(s):  
Clinical Trials ◽  
Biased Coin Design ◽  
Biased Coin

Generalized Efron's biased coin design and its theoretical properties

2016 ◽  
Vol 53 (2) ◽  
pp. 327-340 ◽  
Author(s):  
Yanqing Hu
Keyword(s):  
Clinical Trials ◽  
General Theory ◽  
Convergence Rate ◽  
Biased Coin Design ◽  
Target Ratio ◽  
Allocation Ratio ◽  
Target Allocation ◽  
Biased Coin

Abstract In clinical trials with two treatment arms, Efron's biased coin design, Efron (1971), sequentially assigns a patient to the underrepresented arm with probability p > ½. Under this design the proportion of patients in any arm converges to ½, and the convergence rate is n-1, as opposed to n-½ under some other popular designs. The generalization of Efron's design to K ≥ 2 arms and an unequal target allocation ratio (q1, . . ., qK) can be found in some papers, most of which determine the allocation probabilities ps in a heuristic way. Nonetheless, it has been noted that by using inappropriate ps, the proportion of patients in the K arms never converges to the target ratio. We develop a general theory to answer the question of what allocation probabilities ensure that the realized proportions under a generalized design still converge to the target ratio (q1, . . ., qK) with rate n-1.

scholarly journals Merged block randomisation: A novel randomisation procedure for small clinical trials

2019 ◽  
Vol 16 (3) ◽  
pp. 246-252 ◽  
Author(s):  
Stéphanie L van der Pas
Keyword(s):  
Clinical Trials ◽  
Simple Procedure ◽  
Good Choice ◽  
Main Concern ◽  
Treatment Groups ◽  
Biased Coin Design ◽  
Block Randomisation ◽  
Number Of Patients ◽  
Single Centre Study ◽  
Small Clinical Trials

Background/Aims: Randomisation in small clinical trials is a delicate matter, due to the tension between the conflicting aims of balanced groups and unpredictable allocations. The commonly used method of permuted block randomisation has been heavily criticised for its high predictability. This article introduces merged block randomisation, a novel and conceptually simple restricted randomisation design for small clinical trials (less than 100 patients per stratum). Merged block randomisation is a simple procedure that can be carried out without need for a computer. Merged block randomisation is not restricted to 1:1 randomisation, but is readily applied to unequal target allocations and to more than two treatment groups. Methods: The position of merged block randomisation on the spectrum of balance and predictability is investigated in a simulation study, in two common situations: a single-centre study and a multicentre study (with sampling stratified per centre). Methods included for comparison were permuted block randomisation, Efron’s biased coin design, the maximal procedure, the block urn design and the big stick design. Results: Compared to permuted block randomisation with blocks of size 4, merged block randomisation has the same maximum tolerated imbalance and is thus as impervious to chronological bias, with the added benefit of being less predictable. Each method in the study takes a different position on the balance/determinism spectrum, and none was uniformly best. Merged block randomisation was either less predictable or more balanced than the other methods, in all simulation settings. Conclusion: Merged block randomisation is a versatile restricted randomisation method that outperforms permuted block randomisation and is a good choice for small clinical trials where imbalance is a main concern, especially in multicentre trials where the number of patients per centre may be small.

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