Estimating a summarized odds ratio whilst eliminating publication bias in meta-analysis

Publication bias is a recognized phenomenon, i.e. studies with statistically significant results are more likely to be published than those finding no difference between the groups studied. Summarized odds ratio calculated from odds ratios of published studies in a meta-analysis may be overestimated because of publication bias. This is a significant problem in research areas involving weak associations between causes and results. The magnitude of publication bias in a given research area cannot be determined directly. The present study enables us to calculate the summarized odds ratio of hypothetical unpublished studies from odds ratios of published studies indirectly, employing a moment method by assuming the natural logarithm value of the odds ratio to be distributed normally. We can then estimate summarized odds ratio in all studies, which include not only those published but also those unpublished. When these studies are homogeneous in quality and their odds ratios homogeneous in quantity, the method can eliminate publication bias.