Use of odds ratio in calculation of number needed to treat was inappropriate

Editor—Christopher Del Mar and colleagues' meta-analysis of antibiotics in acute otitis media in children raises some questions.1 The authors included only six studies in the analysis, but an earlier meta-analysis by Rosenfeld et al included 33 studies.2 The authors report that 60% of patients given placebo were pain free within 24 hours but that, two to seven days after presentation, only 14% in the control group still had pain. We would have expected 40% (100% minus 60%) still to have pain.

The number needed to treat, based on pain at two to seven days, was 17 in the meta-analysis. In a Cochrane review of the same trials, however, this number was 12.3 It seems that the authors used the odds ratio for the calculation, which is inappropriate, since it is calculated as the inverse of the risk difference. Using the risk difference, according to figure 1 with a fixed effects model, as the authors also used, we arrived at 23. Furthermore, the use of the number needed to treat does not eliminate the importance of confidence intervals; the confidence interval we calculated was 15 to 56, which is more meaningful than a point estimate. Finally, the authors mention that the number needed to treat was of the same order as that in the meta-analysis by Rosenfeld et al.2 This begs the question of why the authors did a new meta-analysis so soon after the first one, especially since the earlier meta-analysis was published in 1994 and Del Mar and colleagues did not search Medline beyond August 1994.

The authors report that there was a trend for antibiotics to confer benefit in terms of deafness at three months. However, there must be an error in figure 1, since the total numbers affected in the two studies shown …