A method for assessing robustness of the results of a star-shaped network meta-analysis under the unidentifiable consistency assumption

BACKGROUND: In a star-shaped network, pairwise comparisons link treatments with a reference treatment (often placebo or standard care), but not with each other. Thus, comparisons between non-reference treatments rely on indirect evidence, and are based on the unidentifiable consistency assumption, limiting the reliability of the results. We suggest a method of performing a sensitivity analysis through data imputation to assess the robustness of results with an unknown degree of inconsistency. METHODS: The method involves imputation of data for randomized controlled trials comparing non-reference treatments, to produce a complete network. The imputed data simulate a situation that would allow mixed treatment comparison, with a statistically acceptable extent of inconsistency. By comparing the agreement between the results obtained from the original star-shaped network meta-analysis and the results after incorporating the imputed data, the robustness of the results of the original star-shaped network meta-analysis can be quantified and assessed. To illustrate this method, we applied it to two real datasets and some simulated datasets. RESULTS: Applying the method to the star-shaped network formed by discarding all comparisons between non-reference treatments from a real complete network, 33% of the results from the analysis incorporating imputed data under acceptable inconsistency indicated that the treatment ranking would be different from the ranking obtained from the star-shaped network. Through a simulation study, we demonstrated the sensitivity of the results after data imputation for a star-shaped network with different levels of within- and between-study variability. An extended usability of the method was also demonstrated by another example where some head-to-head comparisons were incorporated. CONCLUSIONS: Our method will serve as a practical technique to assess the reliability of results from a star-shaped network meta-analysis under the unverifiable consistency assumption. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-021-01290-1.