Changes in Percent Case-Positives as Proxy for Changes in Infection Rate

Absent ongoing systematic surveillance — which could and should be done — trends in ad-hoc diagnostic case counts and in deaths serve as the main indicators for tracking covid contagion through the population. As proxies these measures leave a lot to be desired: it’s widely acknowledged that the number of diagnostic test-positives greatly underestimates the actual number of infections, while deaths lag two or three weeks behind infections and vary widely from day to day. Still, it seems plausible that trends in case counts and deaths would parallel trends in population infection rates.

In the US, however, case counts and deaths have traced very different trajectories from each other. From the beginning of April until mid-June the daily count of new covid cases tilted very gradually downward from 30K to 20K new cases daily; now, over the past month, the case count has jumped to nearly 70K per day. Deaths have followed a very different course, dropping from a peak of 2,100 per day down to 600, before recently rising back up to 750. While the overall directional trends are similar, the magnitudes of change are very different: case counts are at an all-time high, while even during the current surge only a third as many people are dying from covid as during the April peak. What’s the explanation?

Most likely it’s due to the sevenfold increase in daily testing. The more tests you administer, the more cases you’re liable to find. Increased testing likely underestimated the decrease in infection rates during the lockdown, and it’s likely overestimating the surge in infections during the reopening.

Some models use the percentage of test-positives as a statistical adjuster for estimating trends in infection rate. I’ve harbored doubts about the importance of this particular metric, in large part because it doesn’t take into account changing criteria for selecting people to test. Still, it makes intuitive sense: all else equal, if a higher percentage of all those tested turn out positive, it’s likely that the infection rate is going up. That would seem especially true as the testing net extends beyond hospital admission wards, where symptoms are most severe, into the wider community.

So I started tinkering with an algorithm for quantifying the diminishing return of increasing test rates on test-positives, then correlating the algo with death rates to arrive at a better proxy for infection rate. And it turned out that, conveniently enough, changes in test-positive percentages actually do track pretty closely with changes in death rates. Between the last week of April and the first week of June the test-positive percentage dropped from 12.9 to 4.5. That’s nearly as large a decrease as the death rate over that same two-month interval (factoring in a one-week lag between date of test results and date of death). Since then the test-positive rate has gone up to 8.5. Though that’s nearly double, it’s still a relatively modest climb compared to the daily case count, which is three and a half times what it was in early June.

Test-positive rates started climbing around June 17. Daily body counts started going up a couple of weeks later. If the death trend follows the test-positive rate trend, then daily death totals, which dropped to a low ebb at the beginning of July, could reach around 1,200 per day by the end of this month — still much lower than the peak, but twice as high as the beginning of this month. Test-positive rates have leveled off over the past ten days, which might portend a plateauing of death rates in early August.

What if daily deaths level off before doubling? It could be that the correlation between percent test-positives and deaths is spurious. Alternatively, it could mean that the recent spike in new diagnoses has disproportionately targeted a younger demographic, less likely to die from the viral infection. Younger people going back to work and play without due regard to vectors of contagion, spreading the virus among one another, eventually infecting the older more vulnerable segments of the population: that the media’s current narrative, supported by sporadic data pulled from spiking states in the South and Southwest.

Again, change in percent test-positives is at best only a proxy for changes in the population-wide infection rate, which is what you need to know if you’re going to get a handle on epidemic abatement. Even as a proxy, changes in percent dx+ estimate only the changes in infection rate, not how many people have been infected since the beginning of the epidemic, and not how many people are presently infected and contagious.¬† It’s a public humiliation that the federal government hasn’t conducted, or at least coordinated, the necessary surveillance via diagnostic tests administered at regular intervals to random samples nationwide.


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