In a factorial trial, two (or more) intervention comparisons are carried out simultaneously. Thus, for example, participants may be randomized to receive aspirin or placebo, and also randomized to receive a behavioural intervention or standard care. Most factorial trials have two ‘factors’ in this way, each of which has two levels; these are called 2×2 factorial trials. Occasionally 3×2 trials may be encountered, or trials that investigate three, four, or more interventions simultaneously. Often only one of the comparisons will be of relevance to any particular review. The following remarks focus on the 2×2 case but the principles extend to more complex designs.
In most factorial trials the intention is to achieve ‘two trials for the price of one’, and the assumption is made that the effects of the different active interventions are independent, that is, there is no interaction (synergy). Occasionally a trial may be carried out specifically to investigate whether there is an interaction between two treatments. That aspect may more often be explored in a trial comparing each of two active treatments on its own with both combined, without a placebo group. Such trials are not factorial trials.
The 2×2 factorial design can be displayed as a 2×2 table, with the rows indicating one comparison (e.g. aspirin versus placebo) and the columns the other (e.g. behavioural intervention versus standard care):
|
|
|
Randomization of B |
|
|
|
|
Behavioural intervention (B) |
Standard care |
|
Randomization of A |
Aspirin (A) |
A and B |
A, not B |
|
Placebo (not A) |
B, not A |
Not A, not B |
|
A 2×2 factorial trial can be seen as two trials addressing different questions. It is important that both parts of the trial are reported as if they were just a two-arm parallel group trial. Thus we expect to see the results for aspirin versus placebo, including all participants regardless of whether they had behavioural intervention or standard care, and likewise for the behavioural intervention. These results may be seen as relating to the margins of the 2×2 table. We would also wish to evaluate whether there may have been some interaction between the treatments (i.e. effect of A depends on whether B or ‘not B’ was received), for which we need to see the four cells within the table (McAlister 2003). It follows that the practice of publishing two separate reports, possibly in different journals, does not allow the full results to be seen.
McAlister et al. reviewed 44 published reports of factorial trials (McAlister 2003). They found that only 34% reported results for each cell of the factorial structure. However, it will usually be possible to derive the marginal results from the results for the four cells in the 2×2 structure. In the same review, 59% of the trial reports included the results of a test of interaction. On re-analysis, 2/44 trials (6%) had P<0.05, which is close to expectation by chance (McAlister 2003). Thus, despite concerns about unrecognized interactions, it seems that investigators are appropriately restricting the use of the factorial design to those situations in which two (or more) treatments do not have the potential for substantive interaction. Unfortunately, many review authors do not take advantage of this fact and include only half of the available data in their meta-analysis (e.g. including only A versus not A among those that were not receiving B, and excluding the valid investigation of A among those that were receiving B).
A suggested question for assessing risk of bias in factorial trials is as follows:
Are reports of the study free of suggestion of an important interaction between the effects of the different interventions?