George Rebane
In these pages it is always a bittersweet experience to encounter the extended comments of one of our progressive readers who so absolutely confirms their signature attributes, recorded here over the years, and at the same time illustrates their gross misunderstanding of the issue at hand. Testing for the presence of the C19 virus – both broadscale and at the individual level - is the current widely misunderstood issue at hand.
The progressive reader, firmly clad in the armor of his ideological (socialist, collectivist) and topical (TDS, election year) narratives, comes with lamestream embedded, evidence-free notions about the function and efficacy of tests in fighting the C19 pandemic. In addition to being burdened with these narratives, such readers are almost always from the nation’s cohort of those whose knowledge of the maths is thin, and whose understanding of the fine arts of probabilistics has yet to form – those multi-generational millions of innumerate Americans turned out by our woefully dysfunctional public schools.
These people, here and across the country, share a common and murky misunderstanding of what information testing under various formats for the presence of C19 infection will provide the individual, healthcare workers, or policy makers. They believe that somehow any and all kinds of test applications will do everything from protecting the tested individual, and provide information that would let our political leaders and healthcare authorities devise stratagems to eradicate C19 sooner than later – most certainly within a much better schedule than the current administration is prosecuting. Yet they ignore, or cannot understand, that there is no evidence yet to support such beliefs. Citing the comparative experience of other countries illustrates the futility of their fanatical grip on such beliefs (more here).
Before we again dive into the impact of testing numbers on our progress in this ‘war on C19’, we review some critical definitions without which any reasonable discussion is not possible. Sensitivity - a highly sensitive test means that there are few false negative results, and thus fewer cases of disease are missed – i.e. probability P(TP|V) is high. The specificity of a test is its ability to reliably designate an individual who does not have a disease as negative. A highly specific test means that there are few false positive results – i.e. probability P(TP|¬V) is low. (more here, here, and here; but unfortunately the trigger warning for those references stands)
Some realities to consider before the numbers –
- “Even if you test negative for COVID-19, assume you have it, experts say” (here)
- “The whole testing field is in flux,” said Bill Miller, a physician and epidemiologist at the Ohio State University. “The thing that is different this time is most of these tests are going through a really rapid validation process. As a result we can’t be completely confident in how they will perform.” (here and here)
Suppose we apply broadscale testing with a C19 test that has mid-range performance from the values stated above. Then P(TP|V) = 0.75 and P(TP|¬V) = 0.265, giving us the test’s likelihood ratio L = 0.75/0.265 = 2.83. For a walk-in (randomly sampled) patient whose condition we don’t know, we have his prior probability P(V) = 0.50 of being infected. Administering and interpreting a positive test result gives the post-test or posterior probability P(V|TP) = 0.74 or about 3 out of 4 chance that he’s infected. This means that 26% of the tested positive people in the cohort would not be infected, for them it was a false positive result.
On the other hand, if the test result was negative, then our likelihood ratio is L = 0.34, and our test yields P(V|¬TP) = 0.25. This means that 25% of the walk-ins who tested negative can actually be infected, and the test missed it. This is the prime reason that today physicians are telling people with negative test results to be re-tested. If the test comes back negative again, then the aggregate probability of actually being infected reduces to 0.10 or about one chance out of 10 that they are infected (Bayes formula applied with the new prior of 0.25), or 0.9 or nine out of 10 that they are not infected. Apparently that is good enough to return them into the public arena.
If we were able to concurrently test and get immediate test results (which we can’t) for, say, a million people randomly sampled from a population that from clinical experience is suspected to contain 15% asymptomatic and pre-symptomatic C19 carriers, our recomputed post-test results would be interpreted as P(V|TP) = 0.33 and P(V|¬TP) = 0.06. This means that we would interpret from the test that P(¬V|TP) = 0.67, of those testing positive, 67% would not be infected; and P(¬V|¬TP) = 0.94, of those testing negative 94% would correctly not be infected. However, following the advice of the medicos, the negative test result folks would be retested. And if their second test came back negative, then 98% would be correctly assessed as not infected and released.
If we apply these numbers to our hypothetical one million tested people of whom 150,000 are expected to be infected, then we would catch 0.75, three fourths, or only 113,000 of them for further medical attention. The remaining 37,000 of the infected would presumably be turned loose into the population (or stay-home quarantine with occasional outings). At the same time, we would release 0.735x0.735 = 0.540, 54%, or about 500,000 of the 850,000 uninfected people, requiring the remaining 450,000 whose second test was positive to go through further observation and testing.
From all this, we see that C19 testing today is really a game of playing craps with not only the individuals tested but also with the attempted assessment of what the test results reveal about the current state of the population given the prior ratio of 15/85 infected/uninfected.
At this point, I would take the reader into the realm of revising a population cohort’s infection stats to see what, if any, updates need to be made from the prior 15/85 ratio. At least that is the fundamental reason for testing a comprehensive sample from a population. This would take us into binomial distributions and statistical significance of the newly test-measured ratio. I will postpone that discussion for a later post.
The astute reader would also ask what is the reliability of even determining such a ratio if the testing of the 1,000,000-person sample takes, say, one week, and analyzing the results would add another couple days. Since the early uninfected tested people would have a week plus to get infected, how would you compute what the real (correlated) error bounds are on such a time-delayed measured ratio? All this requires a pretty piece of estimation probabilistics, providing results that I guarantee would give any policy maker pause. For this reason you can bet the ranch that these kinds of germane analyses are neither done nor communicated. Let sleeping dogs lie and all that.
In any event, all of the above is a complete mystery to most of our neighbors across the land, and most certainly to all the progressives who won’t even exercise a brain cell on the matter. Theirs is only to lambast the president and his team for “reckless incompetence” in an enterprise about which they know nothing. Father forgive them, for they know not … .
Might be on topic, might not.
The models that our Administration is currently using has overstated the C-19 deaths and hospitalization by a factor of four....three in NY . Related deaths and hospitalization are the two metrics that matter most in the here and now, not testing, IMHO. Comprehensive tests of millions of folks must include testing for antibodies for those testing negative, positive, and those exposed to the contagious virus but show no effects or have tested positive as a carrier but seem fine.
Suppose that testing shows 50%, 90% of the population has been exposed to C-19 or 50%-% test positive? Then what? More testing? Taking self-distancing more seriously? Nah, the real issue is hospitalization and deaths.
These models currently being used are not from six months ago or a month ago. They are from a two weeks ago, a week ago, now days ago. They are constantly being revised as new data comes it. The situation is fluid. Good news that this week the modeling has been revised downward. Who knows what next week’s modeling will say?
Andrew McCarthy: ‘Dramatic Reduction in COVID-19 Disaster Projections’
https://www.nationalreview.com/corner/dramatic-reduction-in-covid-19-disaster-projections/?
Posted by: Bill Tozer | 07 April 2020 at 08:31 AM
The Nevada county Covid 19 information page is basically worthless considering that doctors won't test you unless you state you have had contact with others. A woman in Nevada City just posted on Facebook that her husband who has been staying home since March 15th has come down with fever, headaches etc. She is the only one who leaves the house to go shopping once a week wearing mask and gloves and disinfecting when she gets home.
Distant relatives in Truckee were sick with bad flu-like symptoms early on and they believe they were infected with Corona virus but they aren't testing there either so who knows.
With all the social distancing and self quarantining I'm surprised anyone would get sick for any reason, seasonal flu or otherwise.
Additional relatives and their friends in Southern California were saying they came down with bad flu symptoms early on and were prescribed inhalers.
But there are still a lot of people walking around here who aren't masked up.
Posted by: D | 09 April 2020 at 02:52 PM