OBJECTIVES: In a star-shaped network, comparative evaluations among treatments using only indirect evidences were based on an unidentifiable consistency assumption, limiting the reliability of the results. We suggest a data imputation method as a sensitivity analysis to assess robustness of the results depending on an unknown degree of consistency.

METHODS: We attempted to fill data for missing randomized controlled trials (RCTs) that may potentially be linked into the unclosed loop in a star-shaped network. A number of effect sizes and their standard errors were generated from a potential distribution of the unknown direct effect size. Starting from an assumption that the unknown direct results would be perfectly consistent with the existing indirect results, we compared deviance information criterions (DIC) in fitted consistency and inconsistency models. The imputation was finalized when the DIC from the consistency model is close enough to that from the inconsistency model, suggesting a marginally acceptable level of overall inconsistency. We examined how the network meta-analysis (NMA) results after imputation could differ from that from the unclosed loop. For illustration, we took a closed loop data of streptokinase (SK), alteplase (tPA), and anistreptilase (ASPAC) from an existing network comparing thrombolytic drugs, and then eliminated data between tPA and ASPAC. The intentional missing data were re-imputed using the suggested method and the results were compared.

RESULTS: The best drug to reduce mortality based on the original data where RCTs were present in all contrasts was ASPAC, followed by tPA and SK. When one contrast became disconnected, the ranking has changed to tPA, ASPAC, and SK. After the data imputation for the missing link, the results were coherent with that from the original closed loop where the result of inconsistency test was not significant (p-value≈0.43).

CONCLUSIONS: The data imputation method can be useful to help assessing reliability of results from a star-shaped NMA.