Biological drugs for inducing remission in patients with Crohn's disease: determining statistical equivalence according to evidence-based methods

In studying the effectiveness of infliximab, adalimumab and certoli-zumab for inducing remission in Crohn's disease, the article by Kawalec et al. [1] included a comprehensive series of pair-wise meta-analyses that compared individual biologic agents versus placebo (direct comparisons), but did not study the indirect comparisons of biologics with one another, an issue that can be managed by application of network meta-analysis. To better address the clinical relevance of differences between these biologics, equivalence testing is another point that can be worthwhile to investigate based on these data. In fact, differentiating between no proof of difference (an " inconclusive result " [2]) and proof of no difference (equivalence, a " conclusive " result [2]) is increasingly recognised to be a crucial step for a correct interpretation of both meta-analyses and clinical trials [3, 4]. We have reanalyzed the trials examined by Kawalec et al. [1] for the end-point of induction of remission. Firstly, the meta-analysis results were re-expressed using risk difference (RD) rather than relative risk [5]. Then, the pooled RDs for direct comparisons of biologics vs. placebo were subjected to network meta-analysis. In this way, the pooled values of RD were estimated for the three indirect head-to-head comparisons between individual biologics. The results of our network meta-analysis revealed non-significant differences for the three indirect comparisons (Figure 1 A). Then, we extended our analysis by performing an equivalence test [2–4] among these three biologics. Testing equivalence requires that a margin is pre-specified to separate clinically relevant improvements in the outcome from clinically irrelevant ones [2]. Margins can be retrieved from the statistical power sections of original trials. According to this procedure, we adopted the margin of ±15% employed by Sandborn et al. [6] and we finally combined, in a forest plot, this margin with the RD values for indirect comparisons. Equivalence testing frequently relies on these forest plots [2–4]. Based on our equivalence testing, the comparisons of infliximab versus adalimumab or certolizumab showed no proof of difference (Figure 1 B), but failed to demonstrate proof of no difference, i.e. equivalence. So, these two comparisons remained inconclusive. More interestingly, the indirect comparison between the two subcutaneous agents (adalimumab vs. certolizumab) showed proof of no difference, i.e. a conclusive result.