There are several possible approaches to including a study with multiple intervention groups in a particular meta-analysis. One approach that must be avoided is simply to enter several comparisons into the meta-analysis when these have one or more intervention groups in common. This ‘double-counts’ the participants in the ‘shared’ intervention group(s), and creates a unit-of-analysis error due to the unaddressed correlation between the estimated intervention effects from multiple comparisons (see Chapter 9, Section 9.3). An important distinction to make is between situations in which a study can contribute several independent comparisons (i.e. with no intervention group in common) and when several comparisons are correlated because they have intervention groups, and hence participants, in common. For example, consider a study that randomized participants to four groups: ‘nicotine gum’ versus ‘placebo gum’ versus ‘nicotine patch’ versus ‘placebo patch’. A meta-analysis that addresses the broad question of whether nicotine replacement therapy is effective might include the comparison ‘nicotine gum versus placebo gum’ as well as the independent comparison ‘nicotine patch versus placebo patch’. It is usually reasonable to include independent comparisons in a meta-analysis as if they were from different studies, although there are subtle complications with regard to random-effects analyses (see Section 16.5.5).
Approaches to overcoming a unit-of-analysis error for a study that could contribute multiple, correlated, comparisons include the following.
Combine groups to create a single pair-wise comparison (recommended).
Select one pair of interventions and exclude the others.
Split the ‘shared’ group into two or more groups with smaller sample size, and include two or more (reasonably independent) comparisons.
Include two or more correlated comparisons and account for the correlation.
Undertake a multiple-treatments meta-analysis (see Section 16.6).
The recommended method in most situations is to combine all relevant experimental intervention groups of the study into a single group, and to combine all relevant control intervention groups into a single control group. As an example, suppose that a meta-analysis of ‘acupuncture versus no acupuncture’ would consider studies of either ‘acupuncture versus sham acupuncture’ or studies of ‘acupuncture versus no intervention’ to be eligible for inclusion. Then a study comparing ‘acupuncture versus sham acupuncture versus no intervention’ would be included in the meta-analysis by combining the participants in the ‘sham acupuncture’ group with participants in the ‘no intervention’ group. This combined control group would be compared with the ‘acupuncture’ group in the usual way. For dichotomous outcomes, both the sample sizes and the numbers of people with events can be summed across groups. For continuous outcomes, means and standard deviations can be combined using methods described in Chapter 7 (Section 7.7.3.8).
The alternative strategy of selecting a single pair of interventions (e.g. choosing either ‘sham acupuncture’ or ‘no intervention’ as the control) results in a loss of information and is open to results-related choices, so is not generally recommended.
A further possibility is to include each pair-wise comparison separately, but with shared intervention groups divided out approximately evenly among the comparisons. For example, if a trial compares 121 patients receiving acupuncture with 124 patients receiving sham acupuncture and 117 patients receiving no acupuncture, then two comparisons (of, say, 61 ‘acupuncture’ against 124 ‘sham acupuncture’, and of 60 ‘acupuncture’ against 117 ‘no intervention’) might be entered into the meta-analysis. For dichotomous outcomes, both the number of events and the total number of patients would be divided up. For continuous outcomes, only the total number of participants would be divided up and the means and standard deviations left unchanged. This method only partially overcomes the unit-of-analysis error (because the resulting comparisons remain correlated) so is not generally recommended. A potential advantage of this approach, however, would be that approximate investigations of heterogeneity across intervention arms are possible (for example, in the case of the example here, the difference between using sham acupuncture and no intervention as a control group).
Two final options, which would require statistical support, are to account for the correlation between correlated comparisons from the same study in the analysis, and to perform a multiple-treatments meta-analysis. The former involves calculating an average (or weighted average) of the relevant pair-wise comparisons from the study, and calculating a variance (and hence a weight) for the study, taking into account the correlation between the comparisons. It will typically yield a similar result to the recommended method of combining across experimental and control intervention groups. Multiple-treatments meta-analysis is discussed in more detail in Section 16.6.