Simplifying fractional polynomials in Bayesian network meta-analysis via variable powers

Area of Science:

• Biostatistics
• Health Technology Assessment
• Network Meta-Analysis

Background:

• Fractional Polynomial (FP) models are crucial for survival analysis in health technology assessment (HTA) and network meta-analysis (NMA).
• Current FP implementations use fixed powers, limiting flexibility, predictive performance, and increasing computational costs in Bayesian settings.
• A need exists for more adaptable and efficient FP modeling approaches.

Purpose of the Study:

• To introduce and evaluate a novel Bayesian FP modeling approach where transformation powers are estimated as continuous parameters.
• To enhance model flexibility, improve statistical fit, and simplify model selection in survival analysis.
• To reduce computational burden and structural uncertainty in Bayesian FP models.

Main Methods:

• Implemented second-order Bayesian FP models using STAN, estimating time transformation powers (p1, p2) from data.
• Evaluated model performance across three oncology NMA datasets (lung, prostate, breast cancer).
• Assessed performance using visual fit, leave-one-out information criteria (LOOIC), root mean square error (RMSE), survival estimates, and computational efficiency.

Main Results:

• Variable power FP models demonstrated superior statistical fit (lower LOOIC and RMSE) compared to fixed power models across all datasets.
• Incremental survival estimates were more stable and clinically plausible with variable power models, especially with complex hazard dynamics.
• While individual runs were slightly longer, variable power models reduced overall computational burden by minimizing required model configurations.

Conclusions:

• Bayesian FP models with variable powers enhance model fit and streamline selection, reducing structural uncertainty.
• This data-driven estimation of transformation powers improves interpretability and computational efficiency.
• The approach yields robust survival projections, supporting reliable decision-making in HTA and comparative effectiveness research.