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Rapid Responses: Rapid Responses published:
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Randomisation
- Sue Richards (4 February 1999)
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Minimisation and the randomised block design
- Tom Treasure, Kenneth D MacRae (4 February 1999)
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Minimisation: the platinum standard for trials?
- Vaughan Reed (15 February 1999)
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Advantages of Minimized Block Designs
- Donald R Taves (5 April 1999)
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Sue Richards
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Dear Editor, I think that the letter from N Ross1 on the topic of randomised block design versus minimisation suggests that there is a lack of understanding about the term minimisation. The editorial which brought up this issue2 did not fully explain it. It is simply explained by an example: Suppose age and sex are two important factors which we wish to be similarly distributed within two randomised treatment groups. We can divide the age into groups such as <40, 40-59, 60+. When a new patient is to be allocated a treatment, we first determine their age group and sex. Suppose they are male, aged 45. Then we count the number of male patients, regardless of age, who have been allocated treatment A (mA) and the number who have been allocated treatment B (mB). Similarly we count the number in the 40-59 age group, regardless of sex, who have been allocated treatment A (nA) and the number who have been allocated treatment B (nB). We then calculate mA - mB + nA – nB. Allocation is then determined by the sign of this quantity: if negative, allocate A, if positive, allocate B, if zero, randomise between A and B. The advantage of this method is that if a relatively large number of variables are thought to be important, they can all be used in the balancing. The danger in using blocked randomisation, often called stratified randomisation, is that there may be some blocks with very few patients in them and it is possible for this to result in an overall imbalance in some factors. This is especially likely if there are many factors or many groups used within some factors. I have used the minimisation method for treatment allocation for some years now and have found it simple to apply and satisfactory in practice. 1 Ross N. Randomised block design is more powerful than minimisation. BMJ 1999;318;263-264 2 Treasure T, MacRae KD. Minimisation: the platinum standard for trials? BMJ 1998;317:362-3 Yours sincerely Dr. Sue Richards Senior Research Fellow |
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Tom Treasure , Kenneth D MacRae
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In commenting on our editorial (1), Ross (2) suggests that the randomised block design is similar to minimisation, but has even more power. We are unaware of any publication which demonstrates that this is the case. He also states that these two methods have the same disadvantage, namely, that assignment to a block becomes a major undertaking. In fact, minimisation does not have the problem of assignment to a block that the randomised block design has, and this is precisely why minimisation was invented. In the context of clinical trials, the randomised block design is referred to as stratified randomisation - for example, the males and females each have their own random allocation series - and if stratified randomisation is feasible, it is indeed an excellent method for obtaining balanced treatment groups. However, stratified allocation becomes unweildy and eventually impossible as the number of relevant patient characteristics increases. Ross mentions age, sex, or number of pack years smoked as patient characteristics that could be used in stratified allocation, but he does not consider what would happen if one wished to balance the treatment assignment for all three of these characteristics. Suppose we have 3 age groups and 4 groupings of pack years smoked, plus, of course, 2 sexes. This gives 24 strata, and the randomised block design would therefore have to have 24 separate random allocation series. This might just be manageable in a large trial, but many trials have considerably more than three patient characteristics which relate to prognosis. For example, Lee et al (3) compared their patient groups at baseline on 14 `selected' dichotomised characteristics, which in combination give 2 to the power 14 = 16,384 strata. Minimisation could handle treatment allocation in such a situation with ease, but the randomised block design would be in some difficulty! Tom Treasure MD MS FRCS Professor of Cardiothoracic Surgery St George's Hospital Medical School London SW17 0QT Kenneth D MacRae MA PhD FIS Medical Statistician 5 Northcroft Terrace London W13 9SP 1. Treasure T, MacRae KD. Minimisation: the platinum standard for trials? BMJ 1998; 317: 362-363 (8 August). 2. Ross N. Randomised block design is more powerful than minimisation. BMJ 1999; 318: 263 (23 January). 3. Lee KL, McNeer F, Starmer F, Harris PJ, Rosati RA. Clinical judgment and statistics: lessons from a simulated randomized trial in coronary artery disease. Circulation 1980; 61(3): 508-515 (March). |
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Vaughan Reed
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EDITOR - The letter by Ross rather misses the point.1 Minimisation was introduced precisely to overcome the practical problems of methods such as the one he describes, which is essentially stratification under another name.2 The biggest problem with stratification is the overage of expensive trial medication which has to be prepared in order to cope with unknown numbers of patients in every possible combination. To stratify for the factors which Ross lists for just three ranges of age, three levels of cigarette consumption and the two sexes would require medication to be supplied for up to 18 strata. Such a study would be prohibitively expensive and a nightmare to run. Using minimisation there is no need for overage in the trial materials. Assignment to a treatment group is not the major undertaking Ross describes - with a computer program, the entire process of allocation can be performed over the telephone by a good secretary in a matter of minutes.3 With minimisation, the use of several levels for factors such as age and cigarette consumption is possible, whereas with stratification it is not practicable. This means that a closer matching of the treatment groups is possible with minimisation than with stratification. We have now used minimisation for some 20 years in a variety of settings. It works well and avoids the disaster of an expensive trial not being analysable because of serious imbalance of either the main parameter or other confounding factors. We remain puzzled and bemused at the lengths to which some workers in the clinical trial field and even registration authorities will go, to raise objections to its routine use. To answer Treasure and MacRae's original question, "Yes - minimisation is the Platinum Standard". Vaughan Reed Freelance Statistician Anne Wickham Pharmaceutical Physician, Medical Input, PO Box 246, Canterbury, Kent 1 Ross N. Randomised block design is more powerful than minimisation. BMJ 1999;318:263-4. (23 January) 2 Taves DR. Minimization: a new method of assigning patients to treatment and control groups. Clin Pharmacol Ther 1974;15:443-53. 3 Reed JV, Wickham EA. Practical experience of minimisation in clinical trials. Pharmaceut Med 1988;3:349-59 |
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Donald R Taves Redmond, WA,98052
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EDITOR--While Ross1 agrees with Treasure and MacRae2 that minimization3 is
more powerful than randomization, he claims that randomized block designs
are more powerful than minimization. He misses the fact that minimized
block designs are more powerful than randomized block designs. The
substitution of minimization for randomization in block designs decreases
the imbalance of the other variates, thus increasing the power. An
additional advantage is gained from the proper analysis of minimized block
designs.
Clinical trials are vulnerable to selection bias in the analysis stage because data are commonly available on 100 or more variates4. With so many, several can be expected to be unbalanced or correlated with the outcome by chance alone. Investigators, being human, will look harder for these aberrant covariates when the results are not what they expect, thus introducing bias. The neglected rule in classical statistics that the analysis must follow the design5 seeks to prevent this. Selecting covariates post hoc undoubtedly accounts for some of the non repeatable clinical trials. Clinical trials using a large number of variates for minimization are more vulnerable to this bias because data are collected on a computer where it is easy to ransack. An additional problem for minimized designs is the lack of data showing whether minimization produces the desired normal curve of the difference in means. Both problems can be solved by splitting the analysis into two stages. The primary analysis uses only covariates which determine the blocks. The secondary analyses use any selection of variates. Probability statements from each require limiting signs, less than for the primary analysis and greater than for the secondary analyses. If any variate is found to be important, post hoc, the secondary p-value will be decreased and form a lower limit. Two advantages, increased power and control of selection bias in the analysis phase, make minimized block designs superior to designs in current use. DR Taves, M.D., M.P.H., Ph.D. 1. Ross N. Randomised block design is more powerful than minimisation. BMJ 1999;318:263(23 January) 2. Treasure T, MacRae KD. Minimisation: the platinum standard for trials? BMJ 1998;317: 362-363 (8 August) 3. Taves DR. Minimization: A new method of assigning patients to treatment and control groups. Clin Pharmacol & Ther. 1974;15:443-453. 4. Beach ML, Meier P. Choosing covariates in the analysis of clinical trials. Controlled Clin Trials 1989;10:161S-175S. 5. Kimball AW. Discussion of: "Recent methodological contributions to clinical trials." Am J Epidemiol. 1976;104:422-424. |
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