SELECTION OF BAYESIAN PRIOR DISTRIBUTIONS FOR BETWEEN-STUDY HETEROGENEITY IN RANDOM-EFFECTS NETWORK META-ANALYSIS MODELS VIA MARGINAL LIKELIHOODS
Author(s)
Daniel J. Sharpe, PhD1, Vikalp Maheshwari, MBA2, Jackie Vanderpuye-Orgle, MSc, PhD3.
1Parexel International Ltd, London, United Kingdom, 2Parexel International Ltd, Hyderabad, India, 3Parexel International Ltd, La Verne, CA, USA.
1Parexel International Ltd, London, United Kingdom, 2Parexel International Ltd, Hyderabad, India, 3Parexel International Ltd, La Verne, CA, USA.
OBJECTIVES: The prior distribution for the between-study heterogeneity parameter in Bayesian random-effects network meta-analyses (NMAs) can have a substantial impact on relative effect estimates and uncertainty thereof, especially when using weakly informative priors to provide regularization when there are few studies. We proposed that marginal likelihoods can in principle be useful to select a preferred hierarchical prior distribution in such models.
METHODS: Hazard ratios (HRs) for progression-free survival outcomes from 11 randomized studies of first-line first- or second-generation EGFR-tyrosine kinase inhibitor therapies in EGFR mutation-positive advanced non-small cell lung cancer (Yin 2025) were synthesized using Bayesian random-effects NMA models employing weakly informative prior information for the between-study heterogeneity, namely half-normal distributions with standard deviation of 0.2 (primary analysis) or 0.5 (sensitivity analysis). Odds ratios quantifying preference for the primary (vs sensitivity) model were calculated based on marginal likelihoods (i.e., Bayes factor, BF) and the deviance information criterion (DIC). Marginal likelihoods were estimated using nested sampling with 400 live points.
RESULTS: The BF expressed a stronger preference for the more informative hierarchical prior distribution than was suggested by the DIC (odds ratios: 7.2 [95% CI: 1.1-45.3] BF vs 1.66 with DIC). The BF therefore more clearly supported the model with lower uncertainty in treatment effect estimates (e.g., HR for dacomitinib vs icotinib: 0.44 [95% CrI: 0.14-1.04] primary analysis vs 0.53 [95% CrI: 0.10-1.70] sensitivity analysis). Both metrics disfavored hierarchical priors with lower variance, thereby avoiding bias from underestimating the magnitude of random effects.
CONCLUSIONS: BFs provide an objective, albeit highly computationally intensive, approach to identify preferred prior distributions for between-study heterogeneity that more strongly penalizes excessive variance than the DIC heuristic. Gauged against BFs, the DIC performed adequately in selecting appropriate weakly informative hierarchical priors for stabilizing estimates from random-effects NMA models, but the magnitude of the corresponding odds ratio had a limited interpretation.
METHODS: Hazard ratios (HRs) for progression-free survival outcomes from 11 randomized studies of first-line first- or second-generation EGFR-tyrosine kinase inhibitor therapies in EGFR mutation-positive advanced non-small cell lung cancer (Yin 2025) were synthesized using Bayesian random-effects NMA models employing weakly informative prior information for the between-study heterogeneity, namely half-normal distributions with standard deviation of 0.2 (primary analysis) or 0.5 (sensitivity analysis). Odds ratios quantifying preference for the primary (vs sensitivity) model were calculated based on marginal likelihoods (i.e., Bayes factor, BF) and the deviance information criterion (DIC). Marginal likelihoods were estimated using nested sampling with 400 live points.
RESULTS: The BF expressed a stronger preference for the more informative hierarchical prior distribution than was suggested by the DIC (odds ratios: 7.2 [95% CI: 1.1-45.3] BF vs 1.66 with DIC). The BF therefore more clearly supported the model with lower uncertainty in treatment effect estimates (e.g., HR for dacomitinib vs icotinib: 0.44 [95% CrI: 0.14-1.04] primary analysis vs 0.53 [95% CrI: 0.10-1.70] sensitivity analysis). Both metrics disfavored hierarchical priors with lower variance, thereby avoiding bias from underestimating the magnitude of random effects.
CONCLUSIONS: BFs provide an objective, albeit highly computationally intensive, approach to identify preferred prior distributions for between-study heterogeneity that more strongly penalizes excessive variance than the DIC heuristic. Gauged against BFs, the DIC performed adequately in selecting appropriate weakly informative hierarchical priors for stabilizing estimates from random-effects NMA models, but the magnitude of the corresponding odds ratio had a limited interpretation.
Conference/Value in Health Info
2026-11, ISPOR Europe 2026, Vienna, Austria
Value in Health, Volume 29, Issue 12S
Code
MSR196
Topic
Economic Evaluation, Methodological & Statistical Research
Disease
Oncology