A new research paper, and a census surprise, are calling into question some long-held beliefs about a morbid bit of math: how much mortality rates increase with age.
It's no surprise that the older a group of people get, the higher the percentage of them who will die in any given time period. Benjamin Gompertz, a 19th-century British mathematician, charted the increase in mortality rates as very regular. His Gompertz law of mortality says that each additional period brings a constant percentage increase in mortality rates.
I'm not going to get into the mortality rates of the very old (90+)-- that's not where most of the interesting action is, anyway. While it would be freaking out pensions, etc., if the mass of old people were knocking off at age 100+, the bulk of people are dying in their 80s now. And it can make quite a bit of difference if that mass of deaths moves from age 82 to age 85, for example.
What's interesting is what's happening in the longer-lived populations. Instead of the distribution simply moving rightward over time, there's been what's been called a "squaring of the mortality curve". A perfect "squared" mortality curve is one in which a lot of people live to some maximum age, and then they all drop dead. Obviously, that's not been happening in real life, but what happens is instead of a fairly spread out distribution around some mean, the mean gets pushed right, and the probability mass to the right of the mean is extremely bunched up past it. No long tails of mortality here.
This has been seen with the mortality curves for Japanese women, one of the longest-lived populations in the world currently. To be sure, one may be a bit skeptical of the stats, given how it had been discovered that the "oldest people" in Japan had been dead for years already. (Would be interesting to talk about how to deal with developing mortality tables when there's that sort of fraud going on).
In many respects, the trend of the shape of the mortality/morbidity (disease levels) is heartening, because it's saying one can have a fairly healthy old age, until right before the end, at which point everything falls apart. As opposed to lingering for decades.
Anyway, Bialik has more here. I'm not seeing that any of this is that new or interesting. If you want a better idea of mortality trends, the most advanced studies have come out of the UK (for a variety of reasons), and there are some interesting patterns the the specific UK data set due to WWII, or, more specifically, the austerity following the war. It has negatively impacted particular cohorts. Info is here, at the Continuous Mortality Investigation page.