Bridging the Survival Extrapolation Gap in Health Economic Models: A Case Study on Spline-Based Survival Analysis Using ML-NMR to Address Complex Hazard Function
Author(s)
Mohd Kashif Siddiqui, MBA, MPH, PharmD, Raja Rajeeswari C, MSc Biostats, Jatin Gupta, MPharm.
EBM Health Consultants, Delhi, India.
EBM Health Consultants, Delhi, India.
OBJECTIVES: Estimating long-term survival is critical for health economic evaluations, especially with delayed effects or complex hazard functions (CHFs). Flexible parametric approaches (FPMs) offer a promising alternative. This work addresses a key methodological gap by evaluating the performance of FPMs in a multilevel network meta-regression (ML-NMR) framework using a simulated data set with CHF.
METHODS: We simulated a hypothetical patient-level dataset for Trial-AB (treatment-B vs A), Trial-BD, Trial-BC, and Trial-CD. We employed the exponentiated log-Sinh Cauchy cure rate model, which jointly models location, scale, shape, bimodality, and cure proportion. Data were generated using Monte Carlo simulation with 1,000 iterations, projecting survival up to 10 years. We right-censored the follow-up at two-years and fitted standard parametric models (SPMs) and FPMs using ‘multinma’ package. We introduced treatment effects onto the coefficients to account for non-proportional hazards (NPH) and generated 10-year restricted mean survival time (10-y-RMST), median survival (mOS), and landmark survivals and compared these with observed Kaplan-Meier survival estimates. The predictive performance of each model was assessed using the leave-one-out information criterion (LOOIC). FPM with 10-y-RMST difference of ≤0.1 year and 10-y survival proportion difference of ≤1% were considered better-fitted model.
RESULTS: FPMs generally performed better than SPMs, with NPH FPM with 7 knots showing the best fit (LOOIC: 1857). None of the models were able to capture bimodal hazard function for treatments with less mature data, however performance of FPMs improved with more mature dataset. No major differences were observed in the 10-y-RMST (delta within ± 0.1 year). None of the FPM model was able to predict landmark survival closer to observed data (delta >1% at 10 years).
CONCLUSIONS: FPMs within ML-NMR demonstrated superior performance over traditional SPMs in tracing CHFs and generating more accurate long-term survival projections. These findings support their use in economic evaluations where early data and NPHs challenge standard approaches.
METHODS: We simulated a hypothetical patient-level dataset for Trial-AB (treatment-B vs A), Trial-BD, Trial-BC, and Trial-CD. We employed the exponentiated log-Sinh Cauchy cure rate model, which jointly models location, scale, shape, bimodality, and cure proportion. Data were generated using Monte Carlo simulation with 1,000 iterations, projecting survival up to 10 years. We right-censored the follow-up at two-years and fitted standard parametric models (SPMs) and FPMs using ‘multinma’ package. We introduced treatment effects onto the coefficients to account for non-proportional hazards (NPH) and generated 10-year restricted mean survival time (10-y-RMST), median survival (mOS), and landmark survivals and compared these with observed Kaplan-Meier survival estimates. The predictive performance of each model was assessed using the leave-one-out information criterion (LOOIC). FPM with 10-y-RMST difference of ≤0.1 year and 10-y survival proportion difference of ≤1% were considered better-fitted model.
RESULTS: FPMs generally performed better than SPMs, with NPH FPM with 7 knots showing the best fit (LOOIC: 1857). None of the models were able to capture bimodal hazard function for treatments with less mature data, however performance of FPMs improved with more mature dataset. No major differences were observed in the 10-y-RMST (delta within ± 0.1 year). None of the FPM model was able to predict landmark survival closer to observed data (delta >1% at 10 years).
CONCLUSIONS: FPMs within ML-NMR demonstrated superior performance over traditional SPMs in tracing CHFs and generating more accurate long-term survival projections. These findings support their use in economic evaluations where early data and NPHs challenge standard approaches.
Conference/Value in Health Info
2025-11, ISPOR Europe 2025, Glasgow, Scotland
Value in Health, Volume 28, Issue S2
Code
MSR49
Topic
Economic Evaluation, Health Technology Assessment, Methodological & Statistical Research
Disease
No Additional Disease & Conditions/Specialized Treatment Areas, Oncology