Maths in a minute: Randomised controlled trials
Randomised controlled trials (RCTs) are a way of testing whether a certain intervention, such as a medical drug or treatment, is effective.
To perform an RCT you first find a group of volunteers who are willing to take part in a trial and who are, as a group, broadly representative of the population the intervention is designed for.
Randomised
The trial participants are then randomly allocated to two groups: one group (the study group) is exposed to the intervention you want to test and the other group (the control group) is not. Randomisation is important here: it helps ensure you don't end up with people who are predominantly of a certain age, or gender, or predominantly display other characteristics that might confuse the results of the study.
Controlled
To deal with the famous placebo effect, which has people feeling an effect of a treatment only because they know they have been given it, people in the control group might be given a placebo. Alternatively, if you want to compare a new treatment to an existing one, people in the control group might be given the existing treatment.
The idea is to see whether the intervention that is being tested is more effective than the placebo effect (or the existing intervention) and has no worse side effects.
Blinded
Participants of the trial aren't told whether they are in the study group or the control group. In a double-blinded trial, the people who administer the intervention also don't know whether the person they are administering to is in the study group or the control group. And in a triple-blinded trial, even the scientists doing the statistical analysis of the results don't know who is in which group. Blinding is done to make sure that no form of bias creeps in through a person consciously or unconsciously skewing the outcome into some direction.
Once the people have been exposed to the intervention or the placebo, you see how many register an effect as a result. If outcomes are significantly better in the study group than in the control group, then that's good evidence that the intervention works.
Using statistics
However, there's still the possibility that such a result was a fluke. The intervention may have been more effective in the study group than in the control group by pure chance. Probability theory enables you to work out the chance of seeing an improvement at least as large as the improvement you did see, even if the intervention had no effect (see this article to find out more). If that probability is small — typically the threshold is less than 5% — then you have firmer evidence that the intervention actually does work.
It's very important in any randomised controlled trial (RCT) that the sample size, the number of people taking part in the trial, is large enough: if you only test a drug on four people, then clearly the results won't give you reliable information. Another important number is the effectiveness (or efficacy) of the intervention: the less effective you think it will be, the more people you need to include in your trial. A statistical calculation tells you how big your initial sample needs to be.
To find out more about RCTs, in particular the mathematics involved, see this article.
This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.
