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Area of Science:

  • Statistical modeling
  • Evidence synthesis

Background:

  • Network meta-analysis (NMA) combines evidence from multiple studies to compare multiple treatments.
  • NMA can exhibit inconsistency, where treatment effect estimates disagree across trial designs, even with heterogeneity.
  • Assessing inconsistency is crucial for reliable NMA.

Purpose of the Study:

  • To propose two novel estimation methods for NMA models incorporating random inconsistency effects.
  • To provide tools for assessing and reporting inconsistency in NMA.

Main Methods:

  • A Bayesian framework using importance sampling for models with random heterogeneity and inconsistency effects.
  • A likelihood-based approach implemented in the metafor package for maximum-likelihood estimation.
  • Comparison of new methods with Markov Chain Monte Carlo (MCMC) for validation.

Main Results:

  • Both proposed methods yield results comparable to MCMC.
  • The methods were illustrated using two examples: one with low heterogeneity/inconsistency (all-cause mortality) and one with substantial heterogeneity/inconsistency (ear discharge).

Conclusions:

  • Assessing and reporting heterogeneity and inconsistency are essential in NMA.
  • The two new methods facilitate fitting NMA models with random inconsistency effects.
  • These methods are readily implementable using provided R code.