Martin Bland and Janet Peacock
Department of Public Health Sciences
St George's Hospital Medical School
These notes are part of a guide to planning a research project for researchers in health care. It is written for applicants for NHS R&D funding in the South East Region, but we hope it will useful for everyone trying to set up healthcare research projects.
Randomisation or random allocation is a method of dividing subjects into groups in such a way that the characteristics of the subject does not affect the group to which they are allocated. To achieve this, we allow chance to decide which group each subject is allocated to. Thus each subject is equally likely to be allocated to any of the available groups and any differences between these groups happens by chance. In a clinical trial randomisation can be used to decide which treatment each subject should receive. For example in a trial of a new treatment versus an existing treatment, randomisation can be used to ensure that each subject has the same chance of receiving either the new or the existing treatment.
Back to top
We can use randomisation in any experimental study where we wish to compare groups receiving different interventions. These can be studies of humans, animals, or some other biological or organisational unit. A typical example where randomisation is used is for a clinical trial comparing individuals receiving one of two treatments. We can also use randomisation when we wish to assign individuals to more than two groups or when we are assigning whole groups of individuals to different intervention groups. An example of this would be assigning whole general practices to receive one of two different interventions. This is known as cluster randomisation (see Section 9)
Back to top
There are three reasons why randomisation is preferred in clinical trials. Firstly, we want to be able to assess the difference between the treatments in an unbiased way. We want to be able to conclude that any differences that we observe between the treatment groups is due to differences in the treatments alone. We do not want differences between the subjects themselves to confound the treatment differences. Without randomisation, treatment comparisons may be prejudiced, whether consciously or not, by selection of participants of a particular kind to receive a particular treatment (CONSORT statement http://www.consort-statement.org). Random allocation does not guarantee that the groups will be identical apart from the treatment given but it does ensure that any differences between them are due to chance alone.
Secondly, randomisation facilitates the concealment of the type of treatment from the researchers and subjects to further reduce bias in treatment comparison. Thirdly, randomisation leads to treatment groups which are random samples of the population sampled and thus makes valid the use of standard statistical tests based on probability theory.
Back to top
Some trials have compared current patients receiving a new treatment with former patients treated with an existing treatment. These patients are not randomly allocated. Historical controls may differ from current patients in many ways and do not provide an unbiased comparison to current patients given a new treatment (ref previous section).
Another common approach is to use a method of systematic allocation. Examples include alternate allocation (A B A B etc) and using date of birth or date of enrolment to study (eg even date=A and odd dates=B). We have seen grant applications and even papers in journals which clearly state that the allocation was performed at random but where the authors have then later indicated that subjects were allocated alternately to treatments. While such schemes are in principle unbiased, problems arise from their openness since it is well known that people with access to the procedure sometimes change the allocation, albeit for altruistic purposes. For these reasons systematic allocation is not recommended unless there is really no alternative.
Back to top
The obvious and most simple way to randomise is to use a physical method. Physical randomisation methods have been in use since the first stone age man cast a couple of knuckle bones. For example, we could toss a coin when a patient is recruited into the trial. Randomisation is usually described in this way on patient information sheets. We do not usually do this in practice, however. The main reason is the lack of an audit trail. We cannot check back to ensure that the random allocation was done correctly. An external observer could not be satisfied that the researchers had not tossed the coin again if they did not like the result, for example. For these reasons` the random allocation should be determined in advance. We could toss the coin in advance and produce a list of allocations before any patients are recruited to the trial. This would be done by someone who will not see any of the trial subjects and the allocation concealed from those recruiting patients into the trial. In a large trial this would be extremely tedious. Instead we use pseudorandom numbers generated by a mathematical process. There are tables of random numbers, usually generated by a computer program, which can used to generate the random sequence. For example, given such a table we could choose a random starting point in it by throwing dice or some other similar method. We then produce a list of allocations by odd number = new treatment, even number = old treatment. Bland (2000) gives examples. However, now that computers are so easily available, we usually cut this stage out and use the computer directly. It is not difficult to write a computer program to carry out random allocation. Our web directory lists some, including our own completely free DOS program Clinstat. Such a program can print out a randomisation list in advance. We think it is very important that the method of randomisation be described in the application. After the randomisation list has been prepared by someone who will not be involved in recruitment to the trial, it must be made available to researchers. This can either be at long range, by telephone from the clinic, or the randomisation can be physically present at the recruitment point. One way to do this is to put the allocation into envelopes. It is important that these envelopes be opaque, as there are well-attested cases of researchers holding envelopes to a lamp in order to read what is written inside. For the same reason these envelopes should be numbered so that the recruiter has to take the next envelope. Shuffling envelope placed in a box is not a good idea. This is a physical method which leaves no audit trail. The researchers should not be given an open randomisation list, so that they know the treatment to which the next potential recruit to the trial will be allocated. This is a really bad idea. It has been shown that the differences in outcome between treatment groups are considerably larger in trials where allocation is open in this way. It produces a clear bias. Long range allocation by telephone is suited to large trials and multi-centre trials in particular. It requires that there be someone in the office to take the call. This may be throughout normal office hours or twenty-four hours a day, depending on the disease being studied. This is difficult for researchers to organise for their own trial, so we usually use a commercial trials office for this. These provide a twenty-four hour phone line, often computer operated, which gives the randomisation. Our web directory lists some service providers and their contact details. It is a good idea to keep track of randomisation. From time to time check that the distribution of variables such as age, sex, important prognostic variables is similar in each treatment group. This is particularly important when a third party is providing randomisation by telephone.
Back to top
If we wish to keep the numbers in each group very close at all times, then we use block randomisation. For example, suppose we have two treatments A and B and we consider subjects in blocks of four at a time. There are six ways of allocating treatments to give two A's and two B's: AABB 2. BBAA 3. ABAB 4. BABA 5. ABBA 6. BAAB If we use combinations of these six ways of allocating treatments then the numbers in the groups can never differ by more than two at any point in the trial recruitment. We can choose blocks at random to create the allocation sequence using random numbers (1 gives AABB, 2 gives BBAA etc and we ignore random numbers other than 1-6). Block allocation can also be done using a computer program. Our web directory lists some, including our own free DOS program Clinstat.
In clinical trials it is best if those giving the treatments do not know how the randomisation sequence was constructed to avoid their deducing in advance which treatment some patients are to be allocated. For this reason larger block sizes of say 20 are sometimes used in large trials. Such block sequences are virtually impossible to guess. A computer is needed to generate such sequences.
Back to top
The aim of randomisation is that the groups of patients receiving different treatments are as similar as possible with respect to features which may affect their prognosis. For example we usually want our groups to have a similar age distribution since prognosis is often related to age. There is however no guarantee that randomisation will give balanced groups, particularly in a small trial. Although any differences will have arisen by chance, they may be inconvenient and lead to doubts being cast as to the reliability of the results. One solution to this problem is to use stratified randomisation at the outset for any variables which are strongly prognostic. Another possible approach is to use minimisation (see Section 8)
In stratified randomisation we produce a separate randomisation list for each subgroup (stratum) so that we get very similar numbers of patients receiving each treatment within each stratum. For example if we were doing a trial of two alternative treatments for breast cancer then we might want to take menopausal status into account. We would then take two separate lists of random numbers and prepare two separate piles of sealed envelopes for premenopausal and postmenopausal women. We may additionally use blocks (see Section 6) to ensure that there is a balance of treatments within each stratum. Stratified randomisation can be extended to two or more stratifying variables. However, we can only have a few strata, otherwise the subgroups produced will be too small.
Back to top
In small studies with several important prognostic variables, random allocation may not provide adequate balance in the groups. In addition, stratified allocation may not be feasible due to there being too few numbers to stratifiy by all important variables. In such studies it is still possible to achieve balance by using a technique called minimisation. This is based on the idea that the next patient to enter the trial is given whichever treatment would minimise the overall imbalance between the groups at any stage of the trial. It is important to specify exactly which prognostic variables are to be used and to say how they are to be grouped. For example just to say that "age" will be used in not sufficient. The actual age groups need to be stated, for example <50 and 50+.
Briefly minimisation works like this. The first patient is randomised to either A or B. When subsequent patients are recruited and their prognostic characteristics noted, their allocation is decided such that the overall balance in the groups at that point is optimised. Further details with a worked example can be found in Pocock (1983).
It is not necessary to minimise individuals in a trial by hand as there are computer programs which will do minimisation for you. Our web-based directory of randomisation software and services provides links to a free program suitable for small trials using minimisation and to providers of minimisation services for larger trials.
Back to top
Sometimes we cannot allocate individuals to treatments, but rather allocate a group of subjects together. For example, in a health promotion study carried out in general practices, we might need to apply the intervention to all the patients in the practice. Publicity may be displayed in the waiting room, for example. For another example, we may need to keep groups of patients separate to avoid contamination. If we are providing a special nurse to patients in a ward, it would be difficult for the nurse to visit some patients and not others. If we are providing training to the patients or their carers, we do not want the subjects receiving training to pass on what they have learned to controls. This might be desirable in general, but not in a trial. For a third case, we may provide an intervention to service providers, clinical guidelines for example. We evaluate the intervention by collecting data from their patients. A group of subjects allocated to a treatment together is called a cluster. Clusters must be taken into account in the design (Kerry and Bland 1998b, Kerry and Bland 1998c, Kerry and Bland 1998d, Kerry and Bland 1998e, Bland 2000) and analysis (Altman and Bland 1997, Bland and Kerry 1997, Kerry and Bland 1998, Kerry and Bland 1998c). The proposal should say how this is to be done. For example, the use of clusters reduces the power of the trial and so requires an increase in sample size
Back to top
Cross over trials are where each patient acts as their own control and thus receives both treatments. The order of treatment should be randomly decided. The randomisation list will look like this: AB AB BA AB BA BA etc.
The same principles apply to within-patient trials where for example different treatments are applied simultaneously to the patient's left and right arms. The choice of which arm gets which treatment should be random.
Back to top
Altman DG, Bland JM. (1997) Statistics Notes. Units of analysis. British Medical Journal 314, 1874.
Bland JM. (2000) Sample size in guidelines trials. Family Practice 17, S17-S20.
Bland M. (2000) An Introduction to Medical Statistics, 3rd Edition. Oxford University Press, Oxford.
Bland JM, Kerry SM. (1997) Statistics Notes. Trials randomized in clusters. British Medical Journal, 315, 600.
Kerry SM, Bland JM. (1998) Statistics Notes. Analysis of a trial randomized in clusters. British Medical Journal 316, 54.
Kerry SM, Bland JM. (1998b) Statistics Notes. Sample size in cluster randomization. British Medical Journal 316, 549.
Kerry SM, Bland JM. (1998c) Trials which randomize practices 1: how should they be analysed? Family Practice 15, 80-83.
Kerry SM, Bland JM. (1998d) Trials which randomize practices 2: sample size. Family Practice 15, 84-87.
Kerry SM, Bland JM. (1998e) Statistics Notes. The intra-cluster correlation coefficient in cluster randomization. British Medical Journal 316, 1455.
Pocock SJ. (1983) Clinical Trials: A Practical Approach. John Wiley and Sons, Chichester.
Directory of randomisation software and services
Public Health Sciences Home Page
St. George's Hospital Medical School Home Page
This page is maintained by
Last updated: [January 7, 2002]
Back to top