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# Re-randomization in clinical trials

We saw in a previous post that sample size is very important. The sample should be the right size, neither more nor less. If too large, we are wasting resources, something to keep in mind in modern times. If we use a small sample we will save money, but lose statistical power. This means that it may happen that there is a difference in effect between the two interventions tested in a clinical trial and not be able to recognize it, which we will be just throwing good money equally.

## When sample size is out of our reach

The problem is that sometimes it can be very difficult to get an adequate sample size, needing excessively long periods of time to get the desired size. Well, for these cases, someone with commercial mentality has devised a method that is to include the same participant many times in the trial. It’s like in bars. Better to have a regular clientele who comes many times to the establishment, always easier than to have a very busy parish (which is also desirable).

There are times when the same patient needs the same treatment in repeated occasions. Consider, for example, asthmatics that need bronchodilator treatment repeatedly, or couples undergoing a process of in vitro fertilization, which requires several cycles to succeed.

## Re-randomization in clinical trials

Although the usual standard in clinical trials is randomizing participants, in these cases we can randomize each participant independently whenever he needs treatment. For example, if we are testing two bronchodilators, we can randomize the same subject to one of two every time he has an asthma attack and needs treatment. This procedure is known as re-randomization and consists, as we have seen, in randomizing situations rather than participants.

This trick is quite correct from a methodological point of view, provided that certain conditions discussed below are met.

The participant enters the trial the first time in the usual way, being randomly assigned to one of two arms of the trial. Subsequently he is followed-up during the appropriate period and the results of the study variables are collected. Once the follow-up period is finished, if the patient requires new treatment, and continues to meet the inclusion criteria of the trial, he is randomized again, repeating this cycle as necessary to achieve the desired sample size.

This mode of recruiting situations instead of participants achieves getting the sample size with a smaller number of participants. For example, if we need 500 participants, we can randomize 500 once, 250 twice, or 200 once and 50 six times. The important thing is that the number of randomizations of each participant cannot be specified previously, but must depend on the need of treatment in every time.

## Three conditions

To apply this method correctly you need to meet three requirements. First, patients can only be re-randomized when they have fully completed the follow-up period of the previous procedure. This is logical because, otherwise, the effects of the two treatments would overlap and a biased measure of the effect of the intervention would be obtained.

Second, each new randomization in the same participant should be done independently of the others. In other words, the probability of assignment to each intervention should not depend on previous assignments. Some authors are tempted to use reallocations to balance the two groups, but this can bias comparisons between the two groups.

Third, the participant should receive the same benefit of each intervention. Otherwise, we get a biased estimate of treatment effect.

We see, then, that this is a good way to reach more easily the sample size we want. The problem with this type of design is that the analysis of the results is more complex than that of conventional clinical trial.

Basically, without going into details, there are two methods of analysis of results. The simplest is the unadjusted analysis, in which all interventions, even if they belong to the same participant are treated independently. This model, which is usually expressed by a linear regression model, does not take into account the effect that participants can have on the results.

The other method is adjusted for the effect of patients, which takes into account the correlation between observations of the same participants.

## We’re leaving…

And here we leave for today. We have not talked anything about the mathematical treatment of the adjusted method to avoid burning the reader’s neurons. Suffice it to say that there are several models that have to do with using generalized linear models and mixed-effects models. But that is another story…