Inconsistent results for Peto odds ratios in multi-arm studies, network meta-analysis and indirect comparisons.

The Peto odds ratio is a well-known effect measure in meta-analysis of binary outcomes. For pairwise comparisons, the Peto odds ratio estimator can be severely biased in the situation of unbalanced sample sizes in the two treatment groups or large treatment effects. In this publication, we evaluate Peto odds ratio estimators in the setting of multi-arm studies and in network meta-analysis using illustrative examples. We observe that Peto odds ratio estimators in a multi-arm study are inconsistent if the observed event probabilities are different or the sample sizes of treatment groups are unbalanced. The same problem emerges in network meta-analysis including only two-arm studies and translates to indirect comparisons of pairwise meta-analyses. We conclude that the Peto odds ratio should not be used as effect measure in network meta-analysis or indirect comparisons of pairwise meta-analyses.