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 2x2 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 article, 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: (i) adding 1/2 to all cells of all the individual studies' 2x2 tables independently of any zero-cell occurrences and (ii) adding 1/2 to all cells of only those 2x2 tables containing at least one zero cell. The main finding is that correction (i) performs worse than correction (ii). Thus, we strongly discourage the use of correction (i).

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