Adaptive spline-based weighting functions for blended survival curve extrapolation

Area of Science:

• Biostatistics
• Health Economics
• Survival Analysis

Background:

• Health technology assessment requires long-term survival predictions beyond trial data.
• Single parametric models can introduce bias with short-term fitting.
• External evidence integration is encouraged but must maintain trial data fidelity.

Purpose of the Study:

• To develop a unified method for survival extrapolation using trial data and external evidence.
• To address limitations of single parametric models in long-term bias.
• To provide a flexible and interpretable framework for survival prediction.

Main Methods:

• An adaptive spline-weighted blended extrapolation on the cumulative-hazard scale was developed.
• The method uses a piecewise-exponential Cox-type model for observation and an anchored Gompertz tail for extrapolation.
• A time-varying weight, learned via P-spline, blends the two components, controlled by a 'temperature' scaling parameter.

Main Results:

• Monte Carlo simulations showed consistently lower absolute survival error and improved stability compared to existing methods.
• A SEER registry study demonstrated accurate tracking of Kaplan-Meier estimates and smooth transitions to the anchored tail.
• The blended curve yielded small long-horizon errors across various cancer sites and age groups.

Conclusions:

• The adaptive spline-weighted blended extrapolation method offers a robust and accurate approach for long-term survival prediction.
• This framework successfully integrates trial data with external evidence, enhancing health technology assessment.
• The method is modular, interpretable, and available as an open-source R package (survblendr).