Life with Hazard Ratios
4 days ago
- #mortality analysis
- #health statistics
- #life expectancy
- Explains the concept of hazard ratios (HR) and why they are commonly used in health and longevity studies, such as HR = 0.90 for eating more fiber or HR = 1.30 for occasional smoking.
- Highlights that converting hazard ratios to changes in life expectancy is complex, as it depends on how baseline mortality risk is distributed over time, using analogies like Russian roulette to illustrate this variability.
- Distinguishes hazard ratios from relative risks (RR), noting that hazard ratios account for time-dependent effects and avoid issues like RR approaching 1.0 in long trials.
- Discusses that interventions often have different hazard ratios at different ages (e.g., chemotherapy works better in younger patients, COVID-19 mortality varies by age), which affects life expectancy changes.
- Introduces a mathematical framework to approximate changes in life expectancy: ΔL ≈ avg(ΔHR) × L†, where L† is mean "life expectancy at death" (12.93 years for US males), and avg(ΔHR) is a weighted average of hazard changes.
- Explains that estimated hazard ratios from papers (est(HR)) approximate a geometric average weighted by baseline mortality probability (P(t)), which is close to but not identical to the ideal weights (P(t) × L(t)).
- Uses simulations to show that plugging hazard ratios from papers into the approximation often yields reasonable estimates, with errors typically within 30%, unless hazard ratios vary dramatically with age or switch signs.
- Mentions Keyfitz entropy (around 0.17 for rich countries), which explains why life expectancy changes are smaller than naive estimates and varies across species (e.g., higher in mice).
- Notes caveats: Estimates depend on trial age ranges and individual factors like personal genetics and lifestyle, which can affect personal Keyfitz entropy and life expectancy impacts.
- Concludes that for modern humans in rich countries, hazard ratios can be roughly converted to life expectancy changes using formulas like ΔL ≈ ln(1/HR) × 12.93 years, despite limitations.