Friday, March 19, 2021

Case Rates, Death Rates, and Vaccination: A Puzzle

I have been following Covid figures for the U.S., for Israel, and for Santa Clara County, where I live.  In all three vaccination has been largely of the elderly, which one would expect to bring death rates down much faster than case rates. The only place where that seems to have happened is Israel. Even there, the effect does not seem to be as large as one would expect.

For each of the three I calculated the ratio between the most recent 7 day average of death rates that I could find and the earlier peak 7 day average, then calculated the corresponding ratio for case rates, assuming a 9 day lag between cases and deaths, and compared the two ratios. I chose a nine day lag because it let me match a death rate peak to a case rate peak. A longer lag might be more plausible, but I do not think it would change my results by much.

The U.S. and Israel give the death rate figures up to yesterday, while the county gives them only up to two and a half weeks ago on the theory that the more recent death figures are not reliable, so the interval for the county was shorter than for the countries. Since what I was comparing was not county to country but fall in death rate in the county to fall of case rate in the county and similarly for each country, that should not be a problem.


The results:


In Santa Clara County, case rates fell by a factor of 6.5 while death rates fell by a factor of 3.9.


For the U.S., case rates fell by a factor of 4 while death rates fell by a factor of 2.6


For Israel, case rates fell by a factor of 2.95 while death rates fell by a factor of 4.3


Only in Israel did death rates fall faster than case rates. I do not know if recent death rate figures for Israel are reliable, so redid the calculation using the same dates I used for Santa Clara County. That gave me ratios of 2.3 for cases, 2.6 for deaths. Deaths were still falling faster than cases, but not by very much.


Israel has had the highest vaccination rate of the three, so it makes sense that it would look better on the deaths vs cases comparison. But at this point, 11% of the U.S. population has been fully vaccinated, another 12% have received one dose. Vaccination has been largely, although not entirely, of the elderly. People 65 and over are  about 20% of the population and about 80% of all deaths from Covid, so one would expect vaccination alone to have cut deaths roughly in half. For Israel, 80% of adults over 60 have received two doses of the vaccine, which should have cut deaths relative to cases more than in half, a larger effect than my calculations show.


I  see two possible explanations for the pattern. One is that older people are not only much more likely to die if infected, they are also much more likely to show symptoms if infected; people who are infected but don’t show symptoms are unlikely to be tested and so don’t go into the count of cases. That would explain why deaths don’t fall faster than cases but not why, in two of my three areas, they fell substantially slower. And it requires that older people are not only more likely to show symptoms but as much more likely to show symptoms as to die. That does not seem to be the case, according to a source I found online.


The other possible explanation is that many of what are counted as deaths due to Covid are actually deaths while having Covid, people who die from some other cause but are tested and found to be infected. We would expect the number of those to be proportional to the number of cases.


If the first explanation is correct, figures on the number of cases overstate how fast it is falling, since symptomatic cases are falling faster than asymptomatic ones. Since asymptomatic cases are apparently still contagious, although less contagious than symptomatic cases, that implies that the risk of getting Covid from a random stranger has not fallen as fast as the decline in cases would imply.


If the second explanation is correct we have badly overestimated how deadly Covid is, hence probably over reacted to it.

P.S. (3/22): I now have a third and more plausible explanation of my puzzle. I was using a 9 day lag between case and death because that was the lag in the peaks. But even if, on average, it takes nine days from detecting a case to a death, the actual lag is a range, say sixteen days to two days (actually longer, but that will do for my example). I was starting my calculation with the date when cases were at their peak, and nine days later for deaths. That meant that I was including in deaths ones from cases well before the peak, when the case rate was lower, which pulled down the death rate, making the drop from then until now smaller.
To test this conjecture, I redid my calculation starting two weeks later. Now I got the expected result. For all three cases — Santa Clara County, the U.S., and Israel, death rates fell faster, not slower, than case rates nine days earlier.


Benjamin Cole said...

"The other possible explanation is that many of what are counted as deaths due to Covid are actually deaths while having Covid, people who die from some other cause but are tested and found to be infected. We would expect the number of those to be proportional to the number of cases."--DF

This seems to be a live possibility. There have been some reports that a healthcare provider might have a financial incentive to count an illness or death as COVID-19.

From what I read, multiple co-morbidities is the norm on a COVID-19 death.

At the risk of sounding callous, in many cases one could wonder if COVID-19 merely hurried the Grim Reaper to his task.

I am over 65 years old. I never felt that commerce should grind to a halt as I am at risk.

I would like to know if COVID-19 was a lab creation.

BIll Sommerfeld said...

There appear to be significant lags in death reporting in California.

Compare the plots by death date and by reported date under "Confirmed Deaths in California" here:

By "Death date", the peak 7-day average rate was 1.7/day per 100k in late December, was around 0.4 per 100k on February 1st, and was around 0.1 per 100k at the beginning of March.

By "Reported Date", the peak 7-day average was 1.4/day per 100k in late January, and is only now dropping to 0.4/day per 100k; there was a large "dump" of backlogged death reports on February 25th which was noted as:

"Deaths reported on February 25, 2021, include a backlog of 806 deaths from Los Angeles County that were not initially recorded as COVID-19 deaths. The majority of these deaths occurred between December 3, 2020, and February 3, 2021."

I suggest repeating this analysis in a month or two with date-of-death based stats.

Josh Sacks said...

The Israeli data suggest that time-to-die from covid is on three order of 5 weeks!
They have data by cohort... about 5 weeks after vaccination hits 80% for 65+, death rates are down about 75%. The lag is very long... Much longer than most people think apparently

Dan said...

I agree with Josh that 9 days is an unrealistically low lag.

Also, time to die is a distribution, not a fixed timespan. In particular, it's a distribution with a long tail -- a minority of patients will suffer on for weeks or months before they finally succumb. So some of the current deaths will be of people infected at the peak.

David Friedman said...

My nine day lag isn't vaccination to death, it's recognition as a case to death. After someone shows symptoms, is tested, and found to have Covid, how long is it until he dies?

So far as the vaccination to case or death lag, the most recent data suggests that effectiveness is something over 80% as of two weeks after the first shot, so one or two weeks before the second shot.

Benjamin Cole said...

Add on:

I wonder if the lockdowns actually promoted the new variants of COVID-19. No herd immunity was achieved, so the virus had time to mutate.

David R. Henderson said...

I don't follow your numbers. No number can fall by more than a factor of 1 without becoming negative. So when you write, for example, that "In Santa Clara County, case rates fell by a factor of 6.5," what do you mean. By what % did they fall? I know it's not 650%. So what is it?

Eric said...

The evidence for asymptomatic transmission of covid is very weak at best.

And that financial incentive is no myth. It made the news back around last March when one of the early pieces of national legislation to address COVID was passed - hospitals get to charge Medicare 15% more when an illness or death is COVID-related.

I remember thinking at the time that we would never have accurate figures on actual incidence and morbidity again.

Michael Wolf said...

The third possibility is that the vaccines don't work as well as they're being touted to work. Before the anti-vaxx insults come fast and furious, this is a comment specifically ON THIS PRODUCT, not vaccines in general, so hear me out.

Based on the actual data in the clinical trials (Pfizer), only 162/18325 of the PLACEBO group got symptomatic covid during the trial. This is compared to 8/18192 of the vaccine group. So while the marketing and publicity is that they had a trial of nearly 44,000 participants, of the 36,000+ who completed the trial, only 170 total got symptoms - 162 in placebo vs 8 in vaccine group. This is where the 95% efficacy comes from. So while 162 to 8 is a good ratio, 162 is a VERY small total number to use as a comparative baseline - so the idea that this will necessarily scale and yield similar 95% results in populations of millions is quite a stretch.


I realize some will dismiss this purely on dogmatic "anti vax" grounds, but it's really just looking at Pfizer's published trial data and applying some common sense critical thinking. Remember this isn't actually FDA approved - it's emergency use approved. The full trial data will take ~2 more years to complete.

In a sense, the unofficial phase 4 trial is the numbers we're seeing now. And based on what you're reporting here, it seems like they may not be as efficacious as the 95% being widely touted.

It DOES seem like they're better than nothing, but not as good as the 95% advertised. Which shouldn't even be surprising given the small #s that were actually tested against symptoms, and the emergency use auth, pending full clinical trials.

Casey B. Mulligan said...

I agree with your measurement error theory, which is most dramatically revealed in the nursing home data. But you are incorrect to derive from that theory that COVID death totals have been exaggerated throughout the pandemic.

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