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Identifying Conditions Favouring Multiplicative Heterogeneity Models in Network Meta-Analysis

Xinlei Xu, Caitlin H Daly, Audrey Béliveau

TL;DR

This study tackles when to prefer a multiplicative-variance inflation (ME) model over the conventional additive random-effects (RE) approach in network meta-analysis (NMA). Using 31 two-arm NMAs from the open-access nmadb database and a $Δ\text{AIC}$ framework, the authors show that ME often matches or outperforms RE, particularly when heterogeneity is driven by imprecise studies. ME down-weights small, noisy studies through a variance inflation factor $φ$, offering robustness to small-study and publication-bias effects, though it can be sensitive to certain extreme precise outliers in some networks. The findings advocate evaluating ME as a complement to RE in NMA practice, while acknowledging limitations for multi-arm networks and older datasets, and highlighting the need for updated evaluations with newer data and potentially more flexible heterogeneity structures.

Abstract

Explicit modelling of between-study heterogeneity is essential in network meta-analysis (NMA) to ensure valid inference and avoid overstating precision. While the additive random-effects (RE) model is the conventional approach, the multiplicative-effect (ME) model remains underexplored. The ME model inflates within-study variances by a common factor estimated via weighted least squares, yielding identical point estimates to a fixed-effect model while inflating confidence intervals. We empirically compared RE and ME models across NMAs of two-arm studies with significant heterogeneity from the nmadb database, assessing model fit using the Akaike Information Criterion. The ME model often provided comparable or better fit to the RE model. Case studies further revealed that RE models are sensitive to extreme and imprecise observations, whereas ME models assign less weight to such observations and hence exhibit greater robustness to publication bias. Our results suggest that the ME model warrant consideration alongside conventional RE model in NMA practice.

Identifying Conditions Favouring Multiplicative Heterogeneity Models in Network Meta-Analysis

TL;DR

This study tackles when to prefer a multiplicative-variance inflation (ME) model over the conventional additive random-effects (RE) approach in network meta-analysis (NMA). Using 31 two-arm NMAs from the open-access nmadb database and a framework, the authors show that ME often matches or outperforms RE, particularly when heterogeneity is driven by imprecise studies. ME down-weights small, noisy studies through a variance inflation factor , offering robustness to small-study and publication-bias effects, though it can be sensitive to certain extreme precise outliers in some networks. The findings advocate evaluating ME as a complement to RE in NMA practice, while acknowledging limitations for multi-arm networks and older datasets, and highlighting the need for updated evaluations with newer data and potentially more flexible heterogeneity structures.

Abstract

Explicit modelling of between-study heterogeneity is essential in network meta-analysis (NMA) to ensure valid inference and avoid overstating precision. While the additive random-effects (RE) model is the conventional approach, the multiplicative-effect (ME) model remains underexplored. The ME model inflates within-study variances by a common factor estimated via weighted least squares, yielding identical point estimates to a fixed-effect model while inflating confidence intervals. We empirically compared RE and ME models across NMAs of two-arm studies with significant heterogeneity from the nmadb database, assessing model fit using the Akaike Information Criterion. The ME model often provided comparable or better fit to the RE model. Case studies further revealed that RE models are sensitive to extreme and imprecise observations, whereas ME models assign less weight to such observations and hence exhibit greater robustness to publication bias. Our results suggest that the ME model warrant consideration alongside conventional RE model in NMA practice.
Paper Structure (15 sections, 7 equations, 5 figures, 3 tables)

This paper contains 15 sections, 7 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Methods
  4. Results
  5. Case Studies
  6. Rheumatoid Arthritis Treatments Versus Placebo for Pain Improvement
  7. Topical NSAIDs Versus Placebo for Pain Relief
  8. Interventions to Increase Household Possession of a Functioning Smoke Alarm
  9. Biological Therapies Versus Placebo or Standard Care for ACR70 Improvement
  10. Discussion
  11. Conflict of Interest Statement
  12. Data Availability Statement
  13. Appendix
  14. Standard Error Calculation in NMA
  15. Case Study Data and Q Decomposition

Figures (5)

  • Figure 1: Histogram of $\Delta \text{AIC} = \text{AIC}_\text{ME} - \text{AIC}_\text{RE}$ for two-arm NMAs reported OR, RR, and MD in the nmadb database. $\hat{\tau}$ was estimated by DL estimator.
  • Figure 2: Case Study 2: NMA of topical NSAIDs for achieving $\geq$50 % pain relief.
  • Figure 3: Case Study 3: Home-safety interventions for increasing household possession of a functioning smoke alarm.
  • Figure 4: Case Study 4: biological therapies for ACR70 improvement.
  • Figure 5: Histogram of $\Delta \text{AIC} = \text{AIC}_\text{ME} - \text{AIC}_\text{RE}$ for two-arm NMAs reported OR, RR, and MD in the nmadb database. $\hat{\tau}$ estimated by REML.