Peto odds ratios demonstrate no advantage over classic odds ratios in meta-analysis of binary rare outcomes

Abstract In this study, we examined the discrepancy between large studies and small studies in meta-analyses of rare event outcomes and the impact of Peto versus the classic odds ratios (ORs) through empirical data from the Cochrane Database of Systematic Reviews that collected from January 2003 to May 2018. Meta-analyses of binary outcomes with rare events (event rate ≤5%), with at least 5 studies, and with at least one large study (N≥1000) were extracted. The Peto and classic ORs were used as the effect sizes in the meta-analyses, and the magnitude and direction of the ORs of the meta-analyses of large studies versus small studies were compared. The p-values of the meta-analyses of small studies were examined to assess if the Peto and the classic OR methods gave similar results. Totally, 214 meta-analyses were included. Over the total 214 pairs of pooled ORs of large studies versus pooled small studies, 66 (30.84%) had a discordant direction (kappa=0.33) when measured by Peto OR and 69 (32.24%) had a discordant direction (kappa=0.22) when measured by classic OR. The Peto ORs resulted in smaller p-values compared to classic ORs in a substantial (83.18%) number of cases. In conclusion, there is considerable discrepancy between large studies and small studies among the results of meta-analyses of sparse data. The use of Peto odds ratios does not improve this situation and is not recommended as it may result in less conservative error estimation.