Exact method for computing absolute percent change in a dichotomous outcome from meta-analytic effect size: improving...

Meta-analyses typically compute a treatment effect size (Cohen's d), which is readily converted to another common measure, the binomial effect size display (BESD). BESD is the correlation coefficient and represents a percentage difference in outcome attributable to an intervention. Both d and BESD are in arbitrary units; neither measures the absolute change resulting from intervention. The method used to estimate absolute change from BESD assumes both a 50-50 split of the outcome and a balanced design. Consequently, inaccurate assumptions underpin most meta-analytic estimates of the gain resulting from an intervention (and of its cost effectiveness). This article develops an exact formula without these assumptions.

The formula is developed algebraically from 1) the formula for the correlation coefficient represented as a 2-by-2 contingency table constructed from the relative size of the treatment and control groups and the percentage of people who would have the condition absent intervention, and 2) the BESD correlation coefficient formula showing change in success probability with treatment.

Simulation reveals that BESD only approximates the reduction in the outcome an intervention might well achieve when the problem outcome occurs in 35%-65% of cases. For less common outcomes, BESD substantially overestimates the impact of an intervention. Even when BESD accurately estimates the likely percentage change in outcome, it paints a misleading picture of the proportion of cases that will achieve a positive outcome.

It is time to retire BESD. Our equations can also guide effect size estimation from difficult articles.