### 16.9.2 Studies with zero-cell counts

Computational problems can occur when no events are observed in one or both groups in an individual study. Inverse variance meta-analytical methods (both the inverse-variance fixed effect and DerSimonian and Laird random-effects methods) involve computing an intervention effect estimate and its standard error for each study. For studies where no events were observed in one or both arms, these computations often involve dividing by a zero count, which yields a computational error. Most meta-analytical software (including RevMan) automatically check for problematic zero counts, and add a fixed value (typically 0.5) to all cells of study results tables where the problems occur. The Mantel-Haenszel methods only require zero-cell corrections if the same cell is zero in all the included studies, and hence need to use the correction less often. However, in many software applications the same correction rules are applied for Mantel-Haenszel methods as for the inverse-variance methods. Odds ratio and risk ratio methods require zero-cell corrections more often than difference methods, except for the Peto odds ratio method, which only encounters computation problems in the extreme situation of no events occurring in all arms of all studies.

Whilst the fixed correction meets the objective of avoiding computational errors, it usually has the undesirable effect of biasing study estimates towards no difference and overestimating variances of study estimates (consequently down-weighting inappropriately their contribution to the meta-analysis). Where the sizes of the study arms are unequal (which occurs more commonly in non-randomized studies than randomized trials), they will introduce a directional bias in the treatment effect. Alternative non-fixed zero-cell corrections have been explored by Sweeting et al., including a correction proportional to the reciprocal of the size of the contrasting study arm, which they found preferable to the fixed 0.5 correction when arm sizes were not balanced (Sweeting 2004).