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This web page provides a brief overview over different ways of randomly allocate subjects to different groups. It also discusses the purpose of including confounding variables as well as the hot topic “should you check for baseline differences?“.
You will understand this page best if you first have read the pages Study design and Sampling Strategies and Data Collection.
Introduction to randomization
This page does not talk about random sampling but rather allocation of participants into groups. This is commonly used in experimental studies. The advantages of using random allocation to groups are :
- Elimination of selection bias.
This is the most important advantage since it eliminates a type I error (“hallucinating” seeing things that are not there). A type I error means you have a difference between groups in one confounding variable influencing the outcome. - Permits using statistical tests relying on probability theory.
You may assume that any differences between groups are random or caused by an effect of the intervention but not by a systematic error. - May facilitate blinding
Using random allocation usually also facilitates the use of blinding
Successful randomisation requires a random allocation sequence that is concealed until actual group allocation occurs .
Types of randomization
The main types are “Simple randomization” and “Restricted randomization” . Every new participant has an equal chance of being allocated to the available groups in simple randomisation. Simple randomization may sometimes allocate almost all participants to one group and almost none to the other. This is rare but can happen. One of the oldest forms of simple randomization is to toss a coin. However, that method is not recommended any more. It seems that tossing a coin may not be as random as we think . It is much better to use random numbers generated by Excel or by another software. Anything else than simple randomization is labelled restricted randomisation. The most common types of restricted randomisation are:
- Block randomisation
Ensures the allocation to groups results in almost equal numbers in each group. This can be done even if you only have a one factor design but is especially useful if you do a two or three factor design. - Stratified randomization
This is sometimes used to ensure groups are matched at baseline in all important characteristics (could be that they must have similar gender, study site or level of blood pressure). The procedure is to first create all subsets (pairs if you allocate to two groups) and ensure they are similar in relevant characteristics. Then perform a randomisation to groups within each subset. - Minimisation
This is an extension of stratified randomisation where more effort is put into ensuring that each group becomes very similar in multiple baseline characteristics. It is common to use computer programs to ensure this. Minimization has received some critique for not being a true random process.
Baseline differences
A handy side effect of randomisation is that groups often become similar and comparable. This is not an aim of the randomisation but a natural consequence. However, sometimes groups differ at baseline. Do they differ by pure chance or due to other factors? Previously it was argued that it was an important part of the analysis of data to compare groups at baseline. The main purpose was to:
- check if the randomization seems to have worked.
- identify variables that need to be adjusted for in the statistical analysis.
Check if randomization worked as intended
Previously it was considered important to check that the randomization worked by comparing baseline differences. A more modern approach is to say that this is not required anymore for the following reasons:
- It is enough that you describe the randomization and group allocation procedure in the methods section . No testing of baseline differences are required if that is a clear description of a true random group allocation.
- It would not be unreasonable to get at least one variable at baseline differing statistically between groups with a p-value <0.05 just by pure chance if you analyze a number of variables. Hence, one problem is that there is no clear cut off as to when you should reject the randomisation and group allocation as being flawed .
Does a perfect description of a seemingly trustworthy randomization and concealment ensure that it was a true random group allocation? Yes according to CONSORT . If in doubt an analysis of baseline differences might sometimes give a clue. As mentioned above a reasonably small statistical difference in baseline (p>0.001?) might occur by chance and as such might be OK but a larger statistical difference (p<0.001?) may suggest that the intended random group allocation may not have worked as intended. In a randomized controlled trial including 11,018 patients the two groups had different blood pressure at baseline :
| Mean values at baseline | Captopril group (n=5,492) | Conventional treatment group (n=5,493) | P-value when comparing groups at baseline |
|---|---|---|---|
| Systolic blood pressure | 161.8 (19.9) | 159.6 (20.1) | 8.4 * 10-9 = 0.0000000084 |
| Diastolic blood pressure | 99.8 (9.9) | 98.1 (10.1) | 6.0 * 10-19 = 0.00000000000000000060 |
| Proportion having diabetes | 5.62% (309) | 4.79% (263) | 0.053 |
The two groups were similar in other variables but differed for blood pressure. The difference in blood pressure may be perceived as small from a clinical point of view. However, the major question here is not if the difference in blood pressure could have influenced the outcome. The main question is if this absurdly low p-value (unlikely to happen by chance) may indicate that the group allocation did not work as intended in reality and that there is an unknown selection bias at play. If that would be the case it would also open up for the possibility that there might be other confounding factors at play that have not been adjusted for and we can’t for certain rule out the possibility of a type I error. Please note that this study published in 1999 is not necessarily better or worse than other studies. It is merely used as an example. The point is that with the new recommendations a baseline comparison may not be done and we will never know if there might be a potential problem despite describing a proper random allocation procedure.
It can be debated if refraining from checking for baseline differences (as currently recommended) is a good practice. As with much else there is no given truth, only opinions, choices and consequences.
Identify variables that need to be adjusted for
Adjusting for factors correlating to the outcome of the study is likely to provide a better estimate of the true effect of the intervention . Please note that this is something else than checking if randomisation worked as intended.
Variables likely to influence outcome should be selected well before data collection (and described in the study protocol). This choice of predefined confounding variables is made without the knowledge of any baseline differences and they are included in the statistical analysis even if there are no baseline differences on group level .
Analysing data from randomized trials
There are a few different pathways to statistically analyse the effect size investigated in randomized trials. Read more about this on the page Intention to treat / Per protocol.