### 16.5.5 Heterogeneity considerations with multiple-intervention studies

Two possibilities for addressing heterogeneity between studies are to allow for it in a random-effects meta-analysis, and to investigate it through subgroup analyses or meta-regression (Chapter 9, Section 9.6). Some complications arise when including multiple-intervention studies in such analyses. First, it will not be possible to investigate certain intervention-related sources of heterogeneity if intervention groups are combined as in the recommended approach in Section 16.5.4. For example, subgrouping according to ‘sham acupuncture’ or ‘no intervention’ as a control group is not possible if these two groups are combined prior to the meta-analysis. The simplest method for allowing an investigation of this difference, across studies, is to create two or more comparisons from the study (e.g. ‘acupuncture versus sham acupuncture’ and ‘acupuncture versus no intervention’). However, if these contain a common intervention group (here, acupuncture), then they are not independent and a unit-of-analysis error will occur, even if the sample size is reduced for the shared intervention group(s). Nevertheless, splitting up the sample size for the shared intervention group remains a practical means of performing approximate investigations of heterogeneity.

A more subtle problem occurs in random-effects meta-analyses if multiple comparisons are included from the same study. A random-effects meta-analysis allows for variation by assuming that the effects underlying the studies in the meta-analysis follow a distribution across studies. The intention is to allow for study-to-study variation. However, if two or more estimates come from the same study then the same variation is assumed across comparisons within the study and across studies. This is true whether the comparisons are independent or correlated (see Section 16.5.4). One way to overcome this is to perform a fixed-effect meta-analysis across comparisons within a study, and a random-effects meta-analysis across studies. Statistical support is recommended; in practice the difference between different analyses is likely to be trivial.