Beyond Hazard Ratios: Translating Health Risks into Real Life Expectancy
Life with Hazard Ratios
I explain why hazard ratios often mislead us about health interventions and how to convert them into meaningful life expectancy changes. While simple math fails, a specific curve for modern humans allows us to estimate that a hazard ratio of 0.75 might add nearly four years to your life, offering a clearer picture of what these statistics truly mean for longevity.
If you were to remove one of those two bullets, that would drop the person's risk of death by HR = 0.5, but life expectancy would barely change because even with just one bullet, almost nobody would survive for any significant amount of time.
- levocardia
This is missing the most important thing which is why HRs are so damn useful. It's because (a) survival analysis is very statistically powerful, but (b) many survival curves do not follow a very well-described parametric function. The genius of David Cox was in realizing that, when proportional hazards hold, you can just cancel out the unknown survival function and get the multiplicative hazard ratio immediately, in a statistically powerful and statistically efficient manner. Extremely useful if you are, say, trialing a novel chemotherapy drug and want to end your trial ASAP to get everyone on the intervention arm if the drug actually works.
The places where proportional hazards gets squirrely (very long observation times, crossing curves) are a small fraction of the use cases of survival analysis, and dunking on them for "not being Bayesian" or whatever misses this broader context.
- jdw64
I read it, and it seems like the core formula is ΔL ≈ ln(1 / HR) × 12.93 years (for U.S. males). It also gives you an easy way to approximate and interpret HR values from health studies, like an HR of 0.90 roughly translates to a little over a year of added life expectancy. Makes it easier to read those papers.
Personally, I found it interesting. But what I'm curious about is this: are there any studies where the lower your exposure to risk, the shorter your lifespan gets?
I've been thinking about this because I recently saw a story about an ultra wealthy guy who tried a reverse aging experiment and ended up with an incurable disease. This person probably had the best diet in the world and received top tier care, so how did he end up with something like that? It makes me wonder, maybe the human body just rejects reverse aging itself. Maybe we're wired to die because that's how species diversify. Just curious.
- nickcw
From the article:
> This is essentially the observation Keyfitz made in his 1977 paper, “What Difference Would It Make if Cancer Were Eradicated?” Cancer is responsible for 18 percent of deaths, so does that mean eradicating it would increase lifespan by 18 percent, or around 13.6 years? Nope, Keyfitz says, it’s only 2.3 years.
A very interesting thought!