Friday, February 26, 2021

The CDC gets life expectancy wildly wrong

According to a CDC spokesman, U.S. life expectancy has fallen by a year as a result of Covid. A little arithmetic shows that that cannot be close to correct. 

Total deaths so far are about 500,000 out of a population of about 330,000,000. The average death cost 12 years of life. Multiply that out and the average person lost not one year but .018 year of life.That's an error of almost two orders of magnitude. Including deaths indirectly caused and additional deaths over the next few months might increase it a little, but there is no way it can be one year or even close.

Dr. Peter Bach explains the error on his blog. What the CDC apparently did was to calculate what the effect on life expectancy would be if mortality rates stayed at their 2020 level,  how much Covid would reduce life expectancy if the pandemic was repeated every year forever.

After an error of that magnitude, it is difficult to take seriously any factual claim they make. It will be interesting to see if they admit the error.

P.S. To be fair, I have not found the claim on the CDC web site, only in media reports that attribute it to "Robert Anderson, who oversees the numbers for the CDC." 

P.P.S. I have now found it on the CDC web site in the form of an interview with Elizabeth Arias, who apparently produced the number:
I posted a version of this to FaceBook. Some people defended the CDC on the grounds that the usual way of calculating life expectancy is by measuring the current mortality rate as a function of age and projecting it it into the future. The problem is that, as you can see by the interview, Elizabeth Arias makes no attempt to explain that what she is describing is a measure that she knows, in this case, badly misrepresents what it is supposed to be measuring. 

Sunday, February 14, 2021

Have We Reached Herd Immunity?

I have been looking at the number of new cases per day, both for Santa Clara County and for the U.S., and the pattern is striking. Over the past month, number of new cases per day in the U.S. has gone down by a factor of about 2.4, for the county by a factor of about 3.5. Death rates are also down, although by much less, but one would expect death rates to lag case rates by a few weeks. I don't think the explanation can be the weather, since it's still winter.  I don't think it can be vaccination because there has not yet been enough of it to substantially affect the case rate.

The other obvious explanation is that the previous high was created by a lower level of precaution due to XMas and New Years. But that explains only a reduction in the rate of increase, not a reduction in the level, since all those people infected during the holidays were then around to infect other people. The fact that the level is falling means that each infected person is passing the infection on to fewer than one person, which is the definition of herd immunity.

If behavior is held constant, herd immunity ought to first appear as a constant rate of infection, each person passing the disease on to one other, then gradually become a shrinking rate. It looks as though we reached herd immunity under non-holiday behavior something close to two months ago, infection rates kept going up due to the holiday bump, and by the time that ended we were far enough into herd immunity (with non-holiday behavior) so that rates were falling. 

I was still surprised that they were falling so fast until I looked at how many cases had occurred recently. I haven't made an exact calculation, but it looks as though, for both the county and the country as a whole, the surge in cases over the two months of the peak  roughly doubled the cumulative total. It wouldn't be that surprising if that had pushed us well past the start of herd immunity.

There are two qualification to be made to the optimistic conclusion that the pandemic is almost over. One is that the requirement for herd immunity depends, among other things, on how people behave. If everyone concludes the pandemic is over and drops all precautions against passing on Covid, cases might start increasing again. The other is that there are at least two new variants of Covid now spreading through the U.S., and we cannot be sure that people immune to the old variant will be equally immune to the new. If, to take the most pessimistic possibility, the protection provided by having had Covid turns out to have no effect one of the variants, we are back to ground zero and in trouble.

My guess, however, is that neither will happen, and that in another few months the case rate will be back to last spring's lows. And falling.