Putting a minimum lower bound on the COVID-19 death rate

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First of all, let me be clear that I am an absolute amateur. Be warned, lest I infect the world with misinformation. I’m putting this out there to try and refine a minimum lower bound for the death rate due to COVID-19, based on mortality in New York. This is extremely tentative.

At present, 0.1% of all New Yorkers are recorded as having died from COVID-19. That’s not 0.1% of New Yorkers diagnosed with COVID-19, that’s 0.1% of all New Yorkers, or 1 in a 1000. Presumably, then, the death rate can’t be below this.

Now there are two difficulties with this number:

A) Some of these people may have died of something else.

B) Some COVID-19 deaths probably aren’t being recorded as such.

In other words, there are probably both false negatives and false positives.

Exactly how these balance out is mysterious. We could try looking at excess deaths over what is normal for this time of year. The New York Times did this and found 17,200 excess deaths, over a period during which 13240 had been recorded as having died of COVID-19, suggesting up to 4000 COVID-19 deaths have gone uncounted.

But not so fast! Some of these excess deaths might be people dying of other diseases, having not gone to the hospital for fear of catching COVID-19.

On the other hand, the excess death rate might be an understatement, because deaths usually fall during economic recessions- a somewhat mysterious but well-replicated phenomena.

My guess is that while the official, recorded deaths due to COVID-19 may be off, it is unlikely to be over or under by more than a third. Personally, I suspect it’s more likely to be an underestimate than an overestimate but I’ll leave that to your judgement. We’ll take the officially recorded deaths due to COVID-19 as-is and go from there. Using this death rate, the absolute minimum infection fatality rate of COVID-19 is 0.1%

Full disclosure, we are discounting the possibility that New Yorkers are much more vulnerable than other people, and the possibility that the strain in New York is much more virulent than the strain elsewhere.

So our initial lower bound is a death rate of 0.1%. Let’s use some extremely generous assumptions, conceding as much as possible to those who think the death rate is very low, and see what refined lower bound we come up with.

Two factors need to be considered, viz:

  1. Not everyone in New York has or has had, COVID-19.

  2. Not everyone in New York who has COVID-19, and will die of it, has died of it yet.

Let’s start with point 1 and estimate the portion of New Yorkers who have, or ever had, the virus. Unfortunately, we have to get somewhat speculative, but I think we can arrive at a lower bound that is hard to argue with.

Today, according to Worldometer, there have been 20657 COVID-19 tests in New York, and 5713 new diagnoses. This isn’t a realistic estimate of the portion of people who have COVID-19 or have had it because:

  1. The test does have false positives and negatives

  2. There is a delay between testing and results.

  3. Some people who get tested presumably had it once, but no longer do.

  4. ABOVE ALL, THE PROBABILITY OF BEING TESTED IS NOT INDEPENDENT OF THE PROBABILITY OF HAVING COVID-19. People with COVID-19 are more likely to be tested for COVID-19.

In light of this last biasing factor, which is absolutely massive, I would be beyond shocked if the real population prevalence of those who have ever had it exceeded the prevalence of those who currently have it in this “sample” of those just tested 5713/20657= ~28%. I take this to be a very comfortable upper-bound on the proportion of New Yorkers who have or ever had, the virus. I say with 98% confidence that the real figure is below 28%.

I want to flag that this is a guess. I feel that, at this stage of the infection for a relatively long-lasting disease, with tests mostly being contacted on suspected cases, it is unlikely that the portion who currently have it in the sample exceeds the portion who have it or have ever had it in the population. If you think that factor 3 in the above list is more important than factor 4 you might disagree. If you think false negatives are very common you might disagree. But I do think it is a reasonable guess, especially given that of the time of writing, the testing criteria for COVID-19 are very strict in New York- officially speaking you shouldn’t be tested for it unless you need to be hospitalised.

If 28% of New Yorkers have the virus or have had it, and 0.1% have died of COVID-19, this gives a death rate of 0.35% among those who have had it. But as mentioned above, not everyone who will die of the disease has died yet. According to one study, the mean time from onset of symptoms to death is 18 days. Mean time between infection and death will be much longer still. In light of this, I think we are extremely safe to estimate that the real death rate among those who currently have it, or had it, has got to be at least 0.5%. This adjustment 0.35 to 0.5%, is eminently reasonable as a lower bound, given how long this disease takes to kill.

Extrapolating this 0.5% to all of America, if everyone got it, over a million people would die (closer to 2 million). Again, this is a lower bound estimate made using what I take to be very conservative assumptions. Even using these very conservative assumptions, our lower bound estimate is inconsistent with some of the extreme claims about the virus being more benign than is usually thought. For comparison, a typical flu season kills 12,000 to 61,000 according to the CDC.

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