POST-HOC VALIDATION OF ROBUST MIXTURE PRIORS FOR BAYESIAN CONTROL ARM AUGMENTATION: A STATISTICAL TEST USING MARGINAL LIKELIHOODS
Author(s)
Daniel J. Sharpe, PhD1, Tuli De, PhD2, Jackie Vanderpuye-Orgle, MSc, PhD2;
1Parexel International Ltd, London, United Kingdom, 2Parexel International Ltd, Durham, NC, USA
1Parexel International Ltd, London, United Kingdom, 2Parexel International Ltd, Durham, NC, USA
OBJECTIVES: In innovative trial designs for rare diseases, Bayesian dynamic borrowing with robust mixture prior distributions is a recommended method for control arm augmentation. We proposed that the prespecified mixture weight can be validated post hoc via the ratios of marginal likelihoods (i.e., the Bayes factors) when comparing to the model with the mixture weight at the tipping point, at which the treatment effect is not statistically significant, and to the naïve model.
METHODS: We illustrated the approach with synthetic trial data for second- vs first-generation tyrosine kinase inhibitors in ROS1-positive advanced non-small cell lung cancer (80 patients, 3:1 randomization ratio, 36 months minimum follow-up). Treatment effect on median progression-free survival (PFS) was estimated using log-logistic distributions in a Bayesian framework, with prior expectation represented by a mixture of normal distributions, of which the informative component was derived from a historical trial of first-generation therapy (70 patients, 36 months minimum follow-up). The prespecified mixture weight was w=0.6. Nested sampling was used to calculate marginal likelihoods for models with mixture weights in increments of 0.1.
RESULTS: Kaplan-Meier estimates for median PFS were 23.6 [95% CI: 17.9-32.0] vs 18.5 [12.0-34.0] months for second- and first-generation therapies, respectively, and 16.0 [12.0-18.0] months for the historical control. The treatment effect estimated from the prespecified model (w=0.6) was 7.6 [95% credible interval: 2.9-12.7] months. Estimation of the marginal likelihoods demonstrated that the prespecified model was favored over the model corresponding to the tipping point (w=0.1, treatment effect 6.8 [-0.1-12.7] months, Bayes factor 4.9 [2.4-5.5]) and strongly preferred over the naïve model (w=0, treatment effect 5.0 [-4.0-12.7] months, Bayes factor 103.0 [67.9-156.2]).
CONCLUSIONS: Estimation of marginal likelihoods provides a rigorous and interpretable method for post-hoc validation of Bayesian borrowing models, and can therefore lend further credibility to results from trials with small control arms augmented with external control data.
METHODS: We illustrated the approach with synthetic trial data for second- vs first-generation tyrosine kinase inhibitors in ROS1-positive advanced non-small cell lung cancer (80 patients, 3:1 randomization ratio, 36 months minimum follow-up). Treatment effect on median progression-free survival (PFS) was estimated using log-logistic distributions in a Bayesian framework, with prior expectation represented by a mixture of normal distributions, of which the informative component was derived from a historical trial of first-generation therapy (70 patients, 36 months minimum follow-up). The prespecified mixture weight was w=0.6. Nested sampling was used to calculate marginal likelihoods for models with mixture weights in increments of 0.1.
RESULTS: Kaplan-Meier estimates for median PFS were 23.6 [95% CI: 17.9-32.0] vs 18.5 [12.0-34.0] months for second- and first-generation therapies, respectively, and 16.0 [12.0-18.0] months for the historical control. The treatment effect estimated from the prespecified model (w=0.6) was 7.6 [95% credible interval: 2.9-12.7] months. Estimation of the marginal likelihoods demonstrated that the prespecified model was favored over the model corresponding to the tipping point (w=0.1, treatment effect 6.8 [-0.1-12.7] months, Bayes factor 4.9 [2.4-5.5]) and strongly preferred over the naïve model (w=0, treatment effect 5.0 [-4.0-12.7] months, Bayes factor 103.0 [67.9-156.2]).
CONCLUSIONS: Estimation of marginal likelihoods provides a rigorous and interpretable method for post-hoc validation of Bayesian borrowing models, and can therefore lend further credibility to results from trials with small control arms augmented with external control data.
Conference/Value in Health Info
2026-05, ISPOR 2026, Philadelphia, PA, USA
Value in Health, Volume 29, Issue S6
Code
MSR166
Topic
Methodological & Statistical Research
Disease
SDC: Oncology