The Peto odds ratio viewed as a new effect measure

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Trials

Background:

• Meta-analysis is crucial for synthesizing evidence from multiple studies.
• The Peto odds ratio (POR) is commonly used for rare events in binary data meta-analysis.
• However, POR can yield biased odds ratio (OR) estimates under certain conditions.

Purpose of the Study:

• To derive the asymptotic limit of the POR estimator.
• To determine if the POR limit equals the true OR.
• To identify conditions where POR is a sufficiently close approximation of the OR.

Main Methods:

• Theoretical derivation of the POR estimator's limit with increasing sample size.
• Investigation of the POR limit's dependence on group size ratio and effect size.
• Analysis of baseline risk influence on POR bias.

Main Results:

• The derived limit of the expected POR is not equivalent to the true OR; it depends on the group size ratio, indicating POR is a different effect measure.
• POR's proximity to the OR is minimally affected by baseline risk (0.001-0.1) but substantially by group size ratio and effect size.
• Maximum effect sizes for POR as an acceptable OR estimator were derived for various group size ratios and bias tolerances.

Conclusions:

• The asymptotic limit of the expected POR represents a distinct effect measure.
• POR can serve as a valid estimate of the true OR in specific, defined situations based on group size ratio and effect size.
• Guidelines are provided for using POR appropriately in meta-analyses with rare events.