Zero‐cell corrections in random‐effects meta‐analyses

Abstract

The standard estimator for the log odds ratio (the unconditional maximum likelihood estimator) and the delta-method estimator for its standard error are not defined if the corresponding 2 × 2 table contains at least one "zero cell". This is also an issue when estimating the overall log odds ratio in a meta-analysis. It is well known that correcting for zero cells by adding a small increment should be avoided. Nevertheless, these zero-cell corrections continue to be used. With this Brief Method Note, we want to warn of a particularly bad zero-cell correction. For this, we conduct a simulation study comparing the following two zero-cell corrections under the ordinary random-effects model: (a) adding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn> <mml:mn>2</mml:mn></mml:mfrac> </mml:math> to all cells of all the individual studies' 2 × 2 tables independently of any zero-cell occurrences and (b) adding <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn> <mml:mn>2</mml:mn></mml:mfrac> </mml:math> to all cells of only those 2 × 2 tables containing at least one zero cell. The main finding is that correction (a) performs worse than correction (b). Thus, we strongly discourage the use of correction (a).