What bizzaro math are these?

First of all, 10X is not a factor of age! "X" was meant as an arbitrary monetary unit, and the cost is the same 10X for both the kid and the 90 year old.

Second, "returning the investment" doesn't mean "reaching 100 years old". It just means "getting more years of life for the same cost".

Even if the boy lived only to 30 or 40, he still lived 20 or 30 years, whereas for the 90 year old living up to 100 or 110 would be extremely rare.

It's painfully telling that we (or at least some of us) somehow consider the effort in keeping a person alive an "investment" that must be "earned back".

We a species have finite resources and can't sink all of them into every patient. Every time we treat or don't treat someone (and it's not possible to treat everyone of everything), we're making implicit statement in the form of a mathematical inequality about how we value money against human life and quality of life. The question here is whether these statements about how life balances against resources are self-consistent or not. And if they're not consistent, then that means you can re-arrange your decisions to save more lives at the same cost, or alternatively save the same number of lives at less cost. The route the NIH apparently went was to try to make their decisions consistent by explicitly giving a dollar value to a year of human life.

>We a species have finite resources and can't sink all of them into every patient. Every time we treat or don't treat someone (and it's not possible to treat everyone of everything), we're making implicit statement in the form of a mathematical inequality about how we value money against human life and quality of life.

We spend more on dog food than we do on millions of patients.

So, no, it's not a question of "finite resources".

Or, rather, it would be, if we were anywhere near exhausting our resources.

Treating the cost of saving a life as a cost is a completely different question than treating it as an investment. Human lives have value, in and of themselves, irrespective of whether or not sinking some number of dollars into extending them can — let alone should — be "earned back".

Whatever you call it, the value that patient N derives from cost C needs to be compared to the value that patient N+1 would derive from that same cost C.

When the NIH (or equivalent) turn that into a C/expected number of years, they're doing a scarce resource allocation problem. Unless you have infinite resources to give every patient every available treatment, you have to do allocation somehow.

Giving a 10-year old a treatment that you'd deny a 90-year old seems perfectly sane and rational to me.

I can't tell if you're agreeing with the concept and just disagreeing with the terminology, or if you believe there's a fundamentally better way?

If an additional year of life is valued at "X" and the cost of the treatment is "10X", the 10 year old has to live to 20 and the 90 year old to 100 to "break even" (assuming a discount rate of 0).

I literally cannot figure out where your math went off the rails.

I don't have the slightest idea what you're saying.