# Prevalence Estimates Revisited

A month ago today I looked at covid testing data from the 50 states plus DC. I wondered whether the rate of testing correlated positively or negatively with the percentage of positive test results. US guidelines for reopening are predicated on the correlation turning negative — states that have lowered their rates of contagion would be able to widen the net, catching infected people who are experiencing few or no symptoms. When I ran the numbers the correlation coefficient (r) between those two variables was +0.65 — a strong positive relationship. States experiencing a more severe outbreak of the epidemic were doing more testing; i.e., increased testing was a poor indicator of readiness to reopen.

Another month has passed. Since then the US has experienced a modest downward trend in confirmed diagnoses, while the testing rate per 100K people has nearly doubled. Consequently the percentage of tests yielding positive results has dropped substantially, from 13% to 5.5%.

Given more widespread testing of a broader swath of the populace, I expected that the relationship between testing frequency and the percentage of tests showing positive would have weakened. Not so: using updated data, the r is still +0.66. Implication: testing isn’t being increased willy-nilly, nor is it reaching people whose symptoms or social contacts imply lower likelihood of infection. Instead, testing is still focused on people who seem clinically likely to have been infected. However, the tests are now being administered to patients whose symptoms are less severe than they were a month ago. That’s sound clinical practice, though still not an indicator of readiness to reopen.

I ran a couple of other correlations:

r (testing frequency by death rate) = 0.57 — this strong positive statistical relationship reinforces the presumption that diagnostic tests are being administered to relatively severe cases.

r (test-positive percentage by death rate) = 0.93 — this correlation is so strong as almost to be an identity function. It doesn’t mean that everybody who tests positive for corona dies from the disease: nationally, 6% of test-positive cases have died. What the strong correlation does mean is that, averaged across individual cases, a state’s test-positive rate serves as a very accurate leading indicator for its death rate.

Now I’m just noodling around with the data… In North Carolina 3.3% of test-positive cases have died. Based on well-designed immunity studies, the covid mortality rate is around 1%; i.e., 1% of those who are infected eventually die. By inference, the NC population has had .033/.01 = 3.3 times as many covid infections as the number of people who’ve tested positive. NC has had 236 test-positive cases per 100K population; 236 x 3.3 = 779 infected people per 100K, or 0.8% of the state population total.

That number seems awfully low on the face of it. Let’s take New York for validation: a well-designed immunity study conducted a month ago estimated that 14% of the NY population had been infected; by now it’s probably around 16%. Using the testing data for NY:  8.1% deaths per test-positives, 1862 test-positives per 100K. .01862 x 8.1 = 15% of the population has been infected — that’s pretty close.

National data show that there have been 523 test-positives per 100K and a deaths per positive test result rate of 5.8%: .00523 x 5.8 = 3% of the US population has been infected — a number that converges on other prevalence estimates.

Take 3% of 330 million = 10 million infected, divide it by 1.7 million test-positives, and you get 6: that’s the national multiplier for transforming US test-positives to population prevalence of covid. The multiplier will continue to shrink as testing rates increase.

## 4 thoughts on “Prevalence Estimates Revisited”

1. An article yesterday about Utah’s readiness to reopen maps well onto the quick-and-dirty formula at the bottom of this post. Utah has 237 test-positives per 100K and a death rate of 1.2% — .00237 x 1.2 = 0.3% covid prevalence in the state population. That’s very low. Though Utah’s trend in new test-positives over the past month is plateaued or slightly rising, it’s been averaging only 2 deaths per day over the past 10 days and has recorded fewer than 100 covid deaths total. Based on officially recognized guidelines, however, Utah is not ready to reopen, because necessary downward trends aren’t established. Only three states are guideline-ready: Alaska, Kentucky, New York.

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2. Here’s a random testing study from Indiana indicating that, in late April, 11 times as many had been infected by corona as had tested positive through usual clinical means. No doubt that multiplier has come down since then. Still, as of that date the state was able to estimate a mortality rate of 0.6% — similar to New York’s. As I noted in a comment on a prior post, mortality rates might be lower in the US than in Europe because the median age here is lower.

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