Someone always does not do what he’s told. No matter how simple the approach of a clinical trial seems to be regarding to its participants. They are randomly assigned to one of the two arms of the trial and some have to take the pill A whereas other have to take B, so we can test which one of both is better.
However, there’s always someone who does not do what he has to and takes the pill that not correspond, or doesn’t take any pill at all, or takes it wrong, or withdraws it ahead of the proper time, etc., etc., etc.
Types of analysis
And what do we do when it comes to analyzing the results? Common sense tells us that if a participant has been wrong with the assigned treatment we should include him in the group of the pill he actually took (this is called to make a per protocol analysis). Other option is to forget that participant who doesn`t take the treatment. But this attitude is not correct if we want to make an unbiased analysis of the results. If participants begin to change from one group to the other we lose the benefit we obtained by distributing them randomly, and the result can be the come into play of confounding or modifying variables that were balanced between the two groups during randomization.
To avoid this, the right thing is to respect the initial intention of group assignment and analyze the results of the subject being mistaken as if he had taken the treatment correctly assigned. It is what is known as the intention to treat analysis, the only preserving the advantages of randomization.
There’re several reasons why a participant in a trial cannot receive the assigned treatment, in addition to a poor compliance by its part. Here are some.
Sometimes it may be the researcher who makes an erroneous inclusion of the participant in the treatment group. Imagine that, after randomization, we realize that some participants are not eligible for the intervention, either because they have the disease or because we discover that there is a contraindication to surgery, for example. If we are strict, we should include them in the analysis group to which they were assigned, although they have not received the intervention. However, it may be reasonable to exclude them if the causes of exclusion are previously specified in the trial protocol. However, it is important that this is performed by someone who does not know the allocation and results, so participants of both arms of the trial are managed similarly. Anyway, if we want more security, we can do a sensitivity analysis with and without these subjects to see how the results change.
Another problem of this type can result of missing data. The results of all variables, and especially the principal, should be present for all participants, but this is not always the case, so we have to decide what to do with the subjects with any missing data.
Most statistical programs operate with complete data analysis excluding those records of subjects with missing data. This reduces the effective sample size and may bias the results, in addition to reducing the power of the study. Some models, such as mixed longitudinal or Cox regression handle the records with some missing data, but no one can do anything if all the information of a subject is missing. In these cases we can use data imputation in all of its forms, so that we fill the gaps to take advantage of the overall sample according to the intention to treat.
When data imputation is not convenient, one thing we can do is what is called an analysis of extreme cases. This is done by assigning the gaps the best and worst possible outcomes and sees how the results change. So, we’ll get an idea of the maximum potential impact of missing data on the results of the study. In any case, there is no doubt that the best strategy will be to design the study so that the missing data are kept to a minimum.
Anyway, there’s always someone who is mistaken and mess the performance of the trial. What can we do?
Variations of intention-to-treat analysis
One possibility is to use an intention to treat modified analysis. It includes everyone in the assigned group, but it’s allowed to exclude participants like those who never started treatment or who were not considered suitable for the study. The problem is that this opens a door to mask the data as we are interested in and bias the results to our advantage. Therefore, we must be suspicious when these changes were not specified in the trial protocol and are a post hoc decision.
The other possibility is to make the analysis according to treatment received (per protocol analysis). The problem, as we have said, is that the balance of randomization is lost. Also, if those who have been mistaken have some special feature the results of the study may be biased. Moreover, the advantage of analyzing the facts as the really have happened is that we can get a better idea of how treatment can work in real life.
Finally, perhaps the safest thing to do is to perform both analyzes, the per protocol and the intention to treat, and compared the results obtained with each. In these cases it may be that we detect an effect with the per protocol analysis and not with the intention to treat analysis. This may be due to two main causes. First, per protocol analysis may create spurious associations by the lack of the balance of confounders guaranteed by randomization. Second, the intention to treat analysis favors the null hypothesis, so it has less power than the per protocol analysis. Of course, if we detect a significant effect, we will be strengthened if the analysis was by intention to treat.
And here we end for today. We have seen how try to control errors in the assignment to groups in the trial and how we can impute the missing data, which is a fancy way of saying that we invent data where they’re missing. Of course, we can only do that if some conditions are fulfilled. But that’s another story…