Why add anything to nothing? The arcsine difference as a measure of treatment effect in meta-analysis with zero cells

For clinical trials with binary endpoints there are a variety of effect measures, for example risk difference, risk ratio and odds ratio (OR). The choice of metric is not always straightforward and should reflect the clinical question. Additional issues arise if the event of interest is rare. In systematic reviews, trials with zero events in both arms are encountered and often excluded from the meta-analysis.The arcsine difference (AS) is a measure which is rarely considered in the medical literature. It appears to have considerable promise, because it handles zeros naturally, and its asymptotic variance does not depend on the event probability.This paper investigates the pros and cons of using the AS as a measure of intervention effect. We give a pictorial representation of its meaning and explore its properties in relation to other measures. Based on analytical calculation of the variance of the arcsine transformation, a more conservative variance estimate for the rare event setting is proposed. Motivated by a published meta-analysis in cardiac surgery, we examine the statistical properties of the various metrics in the rare event setting.We find the variance estimate of the AS to be more stable than that of the log-OR, even if events are rare. However, parameter estimation is biased if the groups are markedly unbalanced. Though, from a theoretical viewpoint, the AS is a natural choice, its practical use is likely to continue to be limited by its less direct interpretation.