This is highly elementary for most of you. But I've learned a long time ago that what I consider to be obvious and trivial, is not the case for many members of the public. This is one such case because I've heard this uttered in the media, in print, and among some people.
There is a large increase in the number of positive COVID-19 cases being reported in many states in the US. A lot of people, who shall remain nameless, make the excuse that this is due to the increase in testing, and that it shouldn't be alarming. The more you test, the more you find, they argued.
So I'll illustrate this with simple, basic math.
Let's say you have a population of 1000 people. And let's say that 200 of them has COVID-19. This means that 20% of the population has the virus.
If you randomly test 100 people, you'll get 20 people who is positive.
If you randomly test 200 people, you'll get 40 people who is positive.
If you randomly test 300 people, you'll get 60 people who is positive.
So yes, in terms of absolute numbers, the more people you test, the more number of positive results that you will get. HOWEVER, look at the percentage of positive test. No matter how many people you test, the percentage will still be 20%. The absolute number will increase with increasing number of tests, but the percentage (some people call it positive rate) does not change considerably. This is what a lot of people appear to not fully comprehend.
Of course, in real life, the percentage won't be exact, but if we keep having these tests, it will hover around some value and not change systematically or monotonically over time if there is no change in the number of people infected. So what you need is not the absolute number but also the overall percentage of positive result per day, let's say. That is of more importance if you are trying to see if things are getting better, or worse.
The situation, of course, is more complex than this. But the point in all of this is that you simply can't dismiss the increase in numbers by claiming that it is due to an increase in the number of testing. That is not the whole picture. What if you do the above exercise again and instead, you get 50 out of 200 being positive one week, and 90 out of 300 being positive the week after that? Can you still attribute that to increase in testing only?
Zz.
3 comments:
An important assumption in these statements you have made here is that testing is randomly distributed among the population as the testing ratio is increased. Which isn't true. As testing becomes more standardized and more readily available, more people who do not show the more obvious signs of the sickness that is to be tested for are being tested. In that scenario, not just a fluctuation of the measured test statistics are to be expected, but an increase in the measured case rates, while real case rates could fall into i) increasing less ii) remaining constant iii) decreasing.
One piece of evidence that the increase in the US is due to testing is the continual stagnation of the death count, which, if you assume that the case count isn't simply due to more testing, should be going up in proportion to the case count. This piece of evidence does however fall in line with the model that simply more cases are tested for.
Hospitalization numbers should be an obvious metric, even for people who don't understand testing rates, etc. In some sense, what we care about are the absolute numbers of people who are so seriously ill that they need hospital care. Those numbers are definitely trending badly in Texas, Arizona, Florida, etc. right now.
I find it interesting that the media in different countries handle numbers in different ways. In Canada (where I am from) figures like unemployment are almost always quoted as a percentage by the media, whereas in the UK (where I live) absolute numbers are usually given. So in the UK you hear statements like "unemployment has surged to 2.5 million, the highest its been since 1980" -- never mind that the population of the UK has increased by 10 million (err, 19%) since then. I wonder if this is because Canada sees itself as a growing country and people realize that comparisons with the past must be corrected for growth, whereas the UK has a steady-state mentality? Or it could be that the UK media has decided that the average person can't handle percentages?
Post a Comment