Elsevier

Controlled Clinical Trials

Volume 23, Issue 6, December 2002, Pages 662-674
Controlled Clinical Trials

Original article
The method of minimization for allocation to clinical trials: a review

https://doi.org/10.1016/S0197-2456(02)00242-8Get rights and content

Abstract

Minimization is a largely nonrandom method of treatment allocation for clinical trials. We conducted a systematic literature search to determine its advantages and disadvantages compared with other allocation methods. Minimization was originally proposed by Taves and by Pocock and Simon. The latter paper introduces a family of allocation methods of which Taves' method is the simplest example. Minimization aims to ensure treatment arms are balanced with respect to predefined patient factors as well as for the number of patients in each group. Further extensions of the method have also been proposed by other authors. Simulation studies show that minimization provides better balanced treatment groups when compared with restricted or unrestricted randomization and that it can incorporate more prognostic factors than stratified randomization methods such as permuted blocks within strata. Some more computationally complex methods may give an even better performance. Concerns over the use of minimization have centered on the fact that treatment assignments may be predicted with certainty in some situations and on the implications for the analysis methods used. It has been suggested that adjustment should always be made for minimization factors when analyzing trials where minimization is the allocation method used. The use of minimization may sometimes result in added organizational complexity compared with other methods. Minimization has been recommended by many commentators for use in clinical trials. Despite this it is still rarely used in practice. From the evidence presented in this review, we believe minimization to be a highly effective allocation method and recommend its wider adoption in the conduct of randomized controlled trials.

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)

  • L.S Freedman et al.

    On the use of Pocock and Simon's method for balancing treatment numbers over prognostic factors in the controlled clinical trial

    Biometrics

    (1976)
  • C.B Begg et al.

    A treatment allocation procedure for sequential clinical trials

    Biometrics

    (1980)
  • A.C Atkinson

    Optimum biased coin designs for sequential clinical trials with prognostic factors

    Biometrics

    (1982)
  • R.L Smith

    Sequential treatment allocation using biased coin designs

    J R Statist Soc B

    (1984)
  • J.H Klotz

    Maximum entropy constrained balance randomization for clinical trials

    Biometrics

    (1978)
  • D.M Titterington

    On constrained balance randomization for clinical trials

    Biometrics

    (1983)
  • C.B Begg et al.

    Treatment allocation for nonlinear models in clinical trialsthe logistic model

    Biometrics

    (1984)
  • L.A Kalish et al.

    Efficiency of balanced treatment allocation for survival analysis

    Biometrics

    (1988)
  • D.F Signorini et al.

    Dynamic balanced randomization for clinical trials

    Stat Med

    (1993)
  • Brown BW. Statistical controversies in the design of clinical trials. Technical Report No. 37. 1978. Division of...
  • S Day

    Commentarytreatment allocation by the method of minimisation

    BMJ

    (1999)
  • S.J Pocock et al.

    Practical experience of randomization in cancer trialsan international survey

    Br J Cancer

    (1982)
  • L.A Kalish et al.

    Treatment allocation methods in clinical trialsa review

    Stat Med

    (1985)
  • Cited by (521)

    View all citing articles on Scopus
    View full text