Background: Meta-analysis has generally been accepted as a fundamental tool for combining effect estimates from several studies within the framework of systematic reviews. In the case of binary data and rare events, the Peto odds ratio (POR) method has become the relative effect estimator of choice. However, as shown in several simulation studies, the POR leads to biased estimates for the odds ratio (OR) when treatment effects are large or the group size ratio is not balanced. This leads to the hypothesis that the POR estimate does not converge towards the true OR even for rare events.
Objectives: To investigate the limit of the POR estimator for increasing sample size and its deviation from the OR.
Methods: We derived the limit of the POR estimator for increasing sample size by application of the delta method. We investigated in which data situations the POR limit is sufficiently close to the true OR.
Results: It was found that the derived limit of the expected POR is not equivalent to the OR, because it depends on the group size ratio. Thus, the POR represents a different effect measure. We investigated in which situations the POR is reasonably close to the OR and derived the maximum effect size of the POR for different group size ratios and tolerated amounts of bias, for which the POR method results in an acceptable estimator of the OR.
Conclusions: The POR can be considered as a new effect measure. The POR method can be used as a valid estimate of the OR only in in the presented situations.