An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis

BMC Med Res Methodol. 2019 Apr 24;19(1):86. doi: 10.1186/s12874-019-0731-y.


Background: A number of strategies have been proposed to handle missing binary outcome data (MOD) in systematic reviews. However, none of these have been evaluated empirically in a series of published systematic reviews.

Methods: Using published systematic reviews with network meta-analysis (NMA) from a wide range of health-related fields, we evaluated comparatively the most frequently described Bayesian modelling strategies for MOD in terms of log odds ratio (log OR), between-trial variance, inconsistency factor (i.e. difference between direct and indirect estimates for a comparison), surface under the cumulative ranking (SUCRA) and rankings. We extended the Bayesian random-effects NMA model to incorporate the informative missingness odds ratio (IMOR) parameter, and applied the node-splitting approach to investigate inconsistency locally. We considered both pattern-mixture and selection models, different structures for prior distribution of log IMOR, and different scenarios for MOD. To illustrate level of agreement between different strategies and scenarios, we used Bland-Altman plots.

Results: Addressing MOD using extreme scenarios and ignoring the uncertainty about the scenarios led to systematically different and more precise log ORs compared to modelling MOD under the missing at random (MAR) assumption. Hierarchical structure of log IMORs led to lower between-trial variance, especially in the case of substantial MOD. Assuming common-within-network or trial-specific log IMORs yielded similar posterior results for all NMA estimates, whereas intervention-specific structure systematically inflated uncertainty around log ORs and SUCRAs. Pattern-mixture model agreed with selection model, particularly under the trial-specific structure; however, selection model systematically reduced precision around log IMORs. Overall, different strategies and scenarios mostly had good agreement in the case of low MOD.

Conclusions: Addressing MOD using extreme scenarios and/or ignoring the uncertainty about the scenarios may negatively affect NMA estimates. Modelling MOD via the IMOR parameter can ensure bias-adjusted estimates and offer valuable insights into missingness mechanisms. The researcher should seek an expert opinion in order to decide on the structure of log IMOR that best aligns to the condition and interventions studied and to define a proper prior distribution for log IMOR. Our findings also apply to pairwise meta-analyses.

Keywords: Missing at random; Missing data; Network meta-analysis; Pattern-mixture model; Systematic review.

Publication types

  • Comparative Study
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Bayes Theorem*
  • Humans
  • Models, Theoretical*
  • Network Meta-Analysis*
  • Odds Ratio
  • Outcome Assessment, Health Care / methods
  • Outcome Assessment, Health Care / statistics & numerical data*
  • Reproducibility of Results
  • Research Design
  • Systematic Reviews as Topic*