Hazard Ratio to Life Expectancy: Gompertz-Makeham Validation of Emerging Risk Factors Collaboration Cardiometabolic...

Area of Science:

• Epidemiology
• Biostatistics
• Actuarial Science

Background:

• Emerging Risk Factors Collaboration (ERFC) provides high-risk cardiometabolic life years lost (LYL) tables.
• Existing tables require validation for broader application in insurance and medico-legal contexts.
• Gompertz-Makeham models offer a flexible framework for survival analysis.

Purpose of the Study:

• To validate the ERFC high-risk LYL tables.
• To calibrate a Gompertz-Makeham model using hazard ratios (HR).
• To establish a reproducible framework for actuarial risk assessment and life expectancy projections.

Main Methods:

• Utilized data from 91 cohorts (689,300 participants) with high hazard ratios (HR≥5).
• Benchmarked ERFC LYL tables against Irish Life Tables No. 17.
• Applied Gompertz-Makeham modeling to generate survival curves and calculate LYL based on baseline risk differentials (ages 40-85).
• Assessed model performance using mean absolute error (MAE).

Main Results:

• The Gompertz-Makeham model accurately reproduced ERFC high-risk LYL estimates.
• Achieved low mean absolute error (MAE) for males (1.21 years) and females (1.16 years) across ages 40-85.
• Preserved the empirical survival curve without requiring disease-specific adjustments.
• Life years lost at age 40 were estimated at 20-22 years, and at age 75, 5-6 years.

Conclusions:

• The hazard ratio-calibrated Gompertz-Makeham model provides aetiology-independent LYL estimates with high accuracy (1-2 years MAE).
• This approach extends existing disability models to accommodate multimorbidity.
• Offers a robust and reproducible framework for actuarial risk assessment and forensic life expectancy reports.