Imputing 2x2 contingency tables from odds ratios: Difficulties, constraints and impact in meta-analysis results

Article type
Authors
Veroniki A1, Patsopoulos N2, Pavlides M3, Salanti G1
1Department of Hygiene and Epidemiology, School of Medicine, University of Ioannina, Greece
2Brigham and Women’s Hospital, Harvard Medical School, Department of Medicine, Boston, US
3General Department, Frederick University, Cyprus
Abstract
Background: A frequently encountered problem in a systematic review is that studies do not provide enough information to extract the appropriate numerical estimate and include the study in the meta-analysis. For binary data, a method has been suggested for reconstructing the 2×2 table when the Odds Ratio (OR), its Standard Error (SE) and arm sizes are provided. Reconstruction of the table is particularly useful when the Peto or Mantel-Haenszel methods for meta-analysis are employed. The method produces two possible solutions and for selecting the correct one, the Control Group Risk (CGR) is compared to a threshold value. As CGR is typically unknown and only rounded figures of the OR and SE are provided, the accuracy of the reconstruction method varies.

Objectives: To evaluate the accuracy of the reconstruction method and the conditions under which it is successful.

Methods: We evaluated the performance of the method in a simulation study (where CGR is assumed known). Using a database of 546 meta-analyses (4288 studies) we evaluated the implications of estimating CGR from other studies in the systematic review to inform re-construction and the impact of reconstructing studies on the meta-analysis summary effect and heterogeneity.

Results: This method performed satisfactorily for small studies, large ORs and when CGR is not close to 50%. Estimating CGR from other studies is problematic as it exhibits very high heterogeneity in most cases. When reconstructing the most influential study or the least successfully reconstracted table in each meta-analysis the summary estimate and its precision were affected in 57% (with an indication of overestimating the effect size) and 85% of the cases, respectively. Heterogeneity standard deviation was affected in 40% and 50% of the meta-analyses, respectively.

Conclusions: When the assumed CGR is close to the threshold value one should be very skeptical about the accuracy of the reconstructed data.