The Perfect Confounds of Estimating Covid Infection Rates

If you want to squelch the epidemic, or even if your ambition extends only as far as flattening the curve, you want to bring the Rt — the virus’s effective reproduction rate — down below 1. That’s when, on average, each person who gets infected in turn infects fewer than one other person. The lower the Rt, and the longer it stays low, the more rapidly and completely the contagion dies out. To know whether you’re succeeding in reducing the Rt, and to know which interventions are most effective, you need accurate repeated measures of the infection rate in the population.

The rate of diagnosis test-positives is the closest analog to a direct measure of infection. Unfortunately, it’s a woefully inaccurate proxy. Three weeks ago the CDC acknowledged that official total covid test-positive cases in the US underestimated tenfold the actual number of infections in this country. My read on the data supported that assessment. Since then an increase in diagnostic testing has narrowed the undercount — but by how much? It’s hard to know, because diagnostic tests are administered almost exclusively to determine whether the tested individual has been infected, not to ascertain the spread of the pathogen through the population.

From the beginning of the outbreak testing has been an integral element of clinical care, administered to individuals ill enough to seek medical attention. But testing is also essential to public health efforts at slowing or eliminating the spread of the virus in the population via early detection, quarantining, and contact tracing. The guidelines for staged rollback of heavy lockdown are predicated on an increase in the number of tests administered through public health interventions, combined with a decrease in tests administered as part of medical care for sick patients.

Having reopened before it’s ready, the country is forced to play catch-up with its population-based efforts to quell the epidemic. Individuals are lining up to be tested; employers are screening their workforces; state and local governments are reaching out into the communities — widespread testing is being ramped up not in order to identify and extinguish limited localized flare-ups of the virus, but to bring persistent widespread contagion under control.

Instead of the dx test-positive rate, I’ve been using death counts to estimate the infection rate. Based on international serology surveys, a plausible estimate of the US’s age-adjusted covid mortality rate is 0.6 percent. So far 139 thousand Americans have died from covid: how many infections would account for that many deaths?

  • 1/.006 = 167 infections per death
  • 139 thousand deaths x 167 infections per death = 23.2 million infections

So far there have been 3.5 million test-positive diagnoses in the US. 23.2 infections divided by 3.5 million dx test-positives = 6.6 infections per test-positive. So, since the epidemic began, there have been seven times as many Americans infected as have been formally diagnosed.

What about at the margin — the most recent 10-day infection rate? Last post I calculated the relevant numbers for July 2-12:

  • 57.5K new test-positives per day
  • 633 deaths per day
  • 633 deaths/day x 167 infections/death = 105.7K infections per day
  • 105.7K infections/57.5K = 1.8 infections per dx-positive

If the US mortality rate is accurate, then the dx-positives have narrowed the undercount considerably since the CDC published its findings. If deaths continue to stay steady or decrease while testing rates continue to increase, then soon the daily test-positives will measure pretty accurately the actual daily infection rate.

However, in late May the CDC announced that the covid mortality rate is somewhere around 0.3 percent. If true, that would double the infections per death to 333 and double the daily infections to 211K. I.e., at the margin there would be four new infections for every newly diagnosed case. However, the lower mortality rate can’t have been the case from the beginning of the epidemic, since in late June the CDC estimated that 20 million Americans had been infected, which corresponds to the 0.6% mortality rate estimate.

Again, what about at the margins — has the mortality rate decreased over time? Probably.

The virus itself doesn’t seem to have mutated into a more benign form; however, the human host community has over time made itself less vulnerable to fatal outcomes of infection. Infection control at nursing homes — the source of at least 40% of covid deaths in this country — has tightened up. According to this article, contagion may be higher at the onset of an epidemic because the virus picks off those individuals who for whatever reasons are the most vulnerable to contagion. Fatality rates vary widely by age: if relatively more younger people get exposed and infected during the reopening while older people remain self-isolated, then the percentage of those infected who eventually die will be decreasing.

Although there’s still neither a cure nor a wonder drug, medical care of covid patients has improved with experience. Hospitals were overwhelmed in the early runaway contagion phase; since then understaffing and undercapacity have been alleviated, improving patients’ chances of surviving. Per this article, medical treatment has improved substantially over time:

Physicians have come a long way in developing a standardized way of caring for covid-19 patients, compared to the pandemic’s outset. They’ve learned — and research has confirmed — that dexamethasone cuts the risk of death for patients on a ventilator by a third and reduces the risk of death for patients on oxygen by a fifth.

This article further documents improvements in ventilator outcomes:

Anytime you go on a ventilator, there’s a risk you won’t improve and will spend your last days or weeks unable to speak, and heavily sedated. Early in the pandemic, it looked like going on a ventilator was a longshot in terms of survival. Studies showed a minority came off the machines alive. But more recent evidence has been somewhat more promising. For example, a study in The Lancet showed that of 203 critically ill COVID-19 patients who were put on ventilators in New York hospitals, less than half (about 41%) had died a month after follow up. A study conducted in several ICUs in Atlanta, Ga., found that of 165 ventilated patients, 35.7% died, with fewer than 5% still on ventilation at the end of the study.

Increased diagnostic testing, improved medical care, relatively less exposure to contagion of those most vulnerable to the virus’s effects — all good trends. But if the infection rate goes up, so do the deaths and so does the Rt, intensifying and prolonging the epidemic. What’s needed is an accurate measure of infection rate. What we’ve got is a cobbled-together algorithm using counts of test-positives or of deaths. But when test-positives must be interpreted relative to testing rate, and when deaths must be interpreted relative to the virus’s mortality rate, then the available methods for estimating infection rate are, as they say, perfectly confounded.

What’s needed is a periodic survey of diagnostic tests administered to a random sample of the population. It wouldn’t be that hard, or that expensive. Around 700 thousand diagnostic tests are administered daily in the US. Setting aside one thousand tests per day for the survey: presidential election polls typically sample around that number of respondents. The confidence interval for that sample size is around +/- 3%, which is far tighter than the cobbled-together estimates of infection rate available at present. And with daily sampling, the margin of error for trends over time diminishes to practical insignificance. Diagnostic survey results would track progress in controlling the epidemic, evaluate the effectiveness of mitigating interventions and the consequences of removing them, measure changes in Rt and mortality rates over time…

No reason it can’t happen; no way it ever will.

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