## Thursday, December 29, 2016

### Math Thursday: The math of life and death, part 2 Ticks and trends

Death statistics are very rarely news because they are best viewed over the long haul. In the past few months, major news media have had stories about small yearly upticks in some statistic or another. All these stories have found at least one scientist  to make the case this story is about a serious problem. Personally, I remain skeptical.

Here is the graph of the number of reported cases of tuberculosis, usually shortened to TB. You'll notice that there was a peak in the early 1990s which coincides with the height of the spread of AIDS. Since then the number of reported cases has dropped or stay nearly equal each year until a slight uptick in 2015 compared to 2014. It's hard to see on the graph, but the 2015 numbers were lower than 2013, so the rise is not very serious. Given the size of the U.S. population, the number of TB cases is about 3 per 100,000. If this was the death rate, that would be a number worth noting, but the number of TB deaths is not even 1 in 20 compared to the number of reported cases in a year. A cause of death that is below 1 per 100,000 population is not a significant vital statistic.

Simply put, trends should be news, but a tick upward for a single year should not be a major news story.

The next story is also about a single year tick in a average life expectancy, which is a much more important vital statistic than the TB rate.

In general, the life expectancy rate is a non-decreasing sequence, by which I mean it either improves or stays level for almost all years when measured at the level of one tenth of a year. Yet again, the last down tick we saw was a single year in the early 1990s coinciding with the worst of the AIDS deaths. Having so many people in their 20s and 30s dying at increased rates will have an impact on the overall numbers. The reason for the new small downturn is not as clear cut as was the health crisis of the early 1990s, though there is a prime suspect.

To my mind, the most significant news story about vital statistics in the past two years was the 2015 study by the wife and husband team of Case and Deaton looking at middle aged mortality (people from 45 to 54) from 1999 to 2013 here in the United States. Simply put, black folks in that age range showed a great improvement in mortality, but of the three groups listed, they still have the highest mortality. Somewhat to my surprise, Hispanics were slightly better in terms of mortality in this cohort compared to non-Hispanic whites even at the start of this study in 1999. The part of the study that made big news is that middle aged white Americans actually had a worse death rate in 2013 than they did in 1999, bucking not only the trend of other demographic groups in the United States but also almost all the rest of the industrialized world. The graph on the right shows the trend is being cause by that most precious of voting demographics this year, "the white working class".

Are the findings of Case and Deaton the cause of the down tick in the life expectancy rate? Since we have seen the trend they have discussed is about fifteen years long, why has it taken until now to see this downturn? Is this just a tick in the overall life expectancy rate in the U.S. or the start of a trend?

I haven't studied the numbers well enough to have an educated opinion on all of this, but I would say the answer to the first question is very probably yes, while the answer to the second question takes more serious study than I have put in and the answer to the third is harder still.

Next week: breaking down a significant part of the Case and Deaton numbers, deaths from overdoses of drugs both prescribed and illegal.