Four-fold table cell frequencies imputation in meta analysis

Abstract

Meta analysis is a collection of quantitative methods devoted to combine summary information from related but independent studies. Because research reports usually present only data reductions and summary statistics rather than detailed data, the reviewer must often resort to rather crude methods for constructing summary effect estimate suitable for meta analysis pooling methods. When the studies involve a binary variable, both number of events and sample sizes are required to compute pooled estimate and its confidence interval. Sometimes, only summary statistics and related confidence intervals are provided in the publication. Although it is possible to estimate the standard error of each study's effect measure using the confidence interval from each study, this lack of detailed data compels the reviewers to use the inverse variance method to perform meta analysis, or to exclude the works with incomplete data. This paper shows three methods to reconstruct four-fold tables when summary measures for binary data and related confidence intervals and sample sizes are provided. The methods are discussed through a wider application example to assess the reconstruction precision, and the impact of using reconstructed data on meta analysis results. These methods seem to yield a correct reconstruction if original measures are reported at least with two decimal places. Meta analysis results do not seem seriously affected by the use of reconstructed data. These methods allow the reviewer to use full meta analysis statistical tools, instead of the simple inverse variance method, and can greatly contribute to the completeness of systematic reviews.