>you want to check the accident rate relative to the non-accident rate
You are right - that the "risk of dying decreased by 60 percent from 1935 to 2010" in the U.S. [2] while the unintentional accident death rate remained constant so, yes, the fraction of deaths caused by accidents would have increased. My mistake.
>You should check statistics only for under age 30.
Injury deaths for ages 0 to 29 actually average 36 per 100 000 per year, less than the population average of 39. Granted this is a quirk of injury death rates being lowest for 4 to 12 year olds (average 6 per 100 000 per year) - this is the only age group for which injury death rates are below 10 per 100 000 per year. It then climbs to a local maximum of 75 at age 21, a level not seen again until age 74. A second local minimum occurs at ages 30 to 34 (average 56 per 100 000 per year) and a third at 56 to 67 (average 51 per 100 000 per year).
And presumably the non-accident death rate below 30 is even lower (relative to the population average).
Basically if an under 30 dies it's becoming more and more likely that it's a result of accident rather than anything else. And this causes people to become more and more cautious. i.e. it used to be that people had a real chance of death anyway, so taking a (physical) risk is not that big an increase in risk, but now it's a larger relative risk.
You are right - that the "risk of dying decreased by 60 percent from 1935 to 2010" in the U.S. [2] while the unintentional accident death rate remained constant so, yes, the fraction of deaths caused by accidents would have increased. My mistake.
>You should check statistics only for under age 30.
Injury deaths for ages 0 to 29 actually average 36 per 100 000 per year, less than the population average of 39. Granted this is a quirk of injury death rates being lowest for 4 to 12 year olds (average 6 per 100 000 per year) - this is the only age group for which injury death rates are below 10 per 100 000 per year. It then climbs to a local maximum of 75 at age 21, a level not seen again until age 74. A second local minimum occurs at ages 30 to 34 (average 56 per 100 000 per year) and a third at 56 to 67 (average 51 per 100 000 per year).
[1] http://www.cdc.gov/nchs/data/misc/injury2007.pdf page 16
[2] http://www.cdc.gov/nchs/data/databriefs/db88.pdf page 2