Original articleThe method of minimization for allocation to clinical trials: a review
Introduction
The randomized controlled trial is commonly accepted as the gold standard research method for evaluating health care interventions. Fundamental to its design is that participants are allocated to treatment and control groups at random, thereby controlling selection bias.
In any clinical trial it is desirable not only to achieve similar numbers of patients in each treatment group but also to ensure that patient groups are similar with respect to prognostic factors such as age or stage of disease. Simple (unrestricted) randomization will very often achieve well-balanced groups, especially in larger trials, but there is always a risk that chance imbalances in baseline characteristics will occur. In order to guard against this, stratified randomization has often been employed. This attempts to achieve groups with similar patient characteristics by balancing patient intake into each combination of patient factors, the assignment within strata being made either by simple randomization or by using permuted blocks. However, stratified randomization becomes unworkable as the number of prognostic factors increases, because the number of strata required can quickly exceed the number of patients in the trial [1].
Minimization is a largely nonrandom method of treatment allocation for clinical trials whose use has been recommended by many commentators as a valid alternative to stratified randomization. Our aim was to conduct a systematic literature search on the method of minimization to ascertain the extent of its current use and to determine its advantages and disadvantages compared with other allocation methods.
Section snippets
Methods
An initial search strategy was developed for the MEDLINE database. A selection of papers that had been previously identified opportunistically was used to identify appropriate medical subject headings and text words. The final search strategy was primarily driven by text words, mainly due to the fact that the indexing of methodological papers is less well developed within MEDLINE than that for actual studies. We limited the search to English-language journals published between 1966 and 2000.
Description of minimization
The minimization method was described independently in articles by Taves [2] and Pocock and Simon [3]; Taves' article coined the term “minimization.” Important prognostic factors are identified before the trial starts and assignment of a new patient to a treatment group is determined so as to minimize the differences between the groups in terms of these factors. Unlike stratified randomization, minimization works toward minimizing the total imbalance for all factors together instead of
Advantages and disadvantages of minimization
The primary reason for using minimization is the desire to achieve balanced groups with respect to both the numbers in each treatment arm and the characteristics of each group. The use of minimization can, however, also lead to indirect benefits including increased persuasiveness and credibility by presenting data indicating that prognostic variables are closely balanced within each treatment group [13]. It has also been suggested that planning to use minimization is a good discipline for
Comparison of minimization with other methods
A number of authors have used computer simulations to compare minimization with other allocation methods.
Predictability of next assignment
A strength of simple randomization is that the allocation of future patients to a trial cannot be predicted. The disadvantage of deterministic allocation procedures such as minimization is that in certain cases the next allocation can be predicted with certainty with knowledge of the characteristics of earlier patients. There is therefore a potential for selection bias, which can affect the validity of a trial's results. Even a knowledge of which allocation is more likely to occur next can
Evidence from published papers
In 1982 Pocock and Lagakos conducted a survey of 15 centers conducting trials in cancer [15]. Four centers had used minimization (one always, one in 80% of trials and two in one specific trial), but the most common design was permuted blocks within strata. In 1990 Altman and Doré reviewed 80 reports of randomized clinical trials in four leading journals and found that only one of these trials had used minimization [43]. Vaughan Reed and Wickham stated that since its introduction by Taves in
Recommendations on which allocation method to use
Few authors make unqualified recommendations as to whether minimization should be used in practice in preference to other methods. At least two articles come out wholly in favor of the method, the latter referring to minimization as the platinum standard if randomization is the gold standard 38, 39.
Other authors cite minimization as the method of choice (or one of a number of methods of choice) in smaller trials when it is desirable to achieve balance in a number of prognostic factors 18, 24.
Discussion
While a number of commentators have reviewed specific aspects of minimization techniques, we believe that this is the first comprehensive review of literature in the field, bringing together both statistical and methodological perspectives. We accept that because of the difficulties with the indexing of methodological papers we may have missed some relevant articles from the review; however, the results from the papers that we did locate provided fairly conclusive evidence of the advantages and
Acknowledgements
The Health Services Research Unit is core funded by the Scottish Executive Health Department; however, the views expressed are those of the authors.
References (47)
How many stratification factors are “too many” to use in a randomization plan?
Control Clin Trials
(1993)- et al.
Randomization in clinical trialsconclusions and recommendations
Control Clin Trials
(1988) Adaptive allocation in randomized controlled trials
Control Clin Trials
(1985)- et al.
The impact of treatment allocation procedures on nominal significance levels and bias
Control Clin Trials
(1987) Dynamically allocating treatment when the cost of goods is high and drug supply is limited
Control Clin Trials
(2000)- et al.
Randomisation and baseline comparisons in clinical trials
Lancet
(1990) - et al.
Stratified randomization for clinical trials
J Clin Epidemiol
(1999) Allocation of patients to treatment in clinical trials
Biometrics
(1979)Minimizationa new method of assigning patients to treatment and control groups
Clin Pharmacol Ther
(1974)- et al.
Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial
Biometrics
(1975)
On the use of Pocock and Simon's method for balancing treatment numbers over prognostic factors in the controlled clinical trial
Biometrics
A treatment allocation procedure for sequential clinical trials
Biometrics
Optimum biased coin designs for sequential clinical trials with prognostic factors
Biometrics
Sequential treatment allocation using biased coin designs
J R Statist Soc B
Maximum entropy constrained balance randomization for clinical trials
Biometrics
On constrained balance randomization for clinical trials
Biometrics
Treatment allocation for nonlinear models in clinical trialsthe logistic model
Biometrics
Efficiency of balanced treatment allocation for survival analysis
Biometrics
Dynamic balanced randomization for clinical trials
Stat Med
Commentarytreatment allocation by the method of minimisation
BMJ
Practical experience of randomization in cancer trialsan international survey
Br J Cancer
Treatment allocation methods in clinical trialsa review
Stat Med
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