Monday, April 06, 2020

"Logarithmic" Is Dr. Birx's Safe Word

by Jamie Hamilton

During the White House COVID-19 press conferences, the word "logarithmic" has been coming up a lot lately.  The way Dr. Debra Birx and President Trump talk past each other around this word is very revealing about what's going on right now in the U.S.

The most important thing to understand is that if you cut through the jargon, Dr. Birx is clearly saying that current levels of testing are inadequate, and she isn't putting her faith in the official numbers in the way you would if they were actually correct.  This nuance is lost on the politicians, including New York Governor Andrew Cuomo, who is flat-out ignoring the issue that Dr. Birx is raising by the way she presents her data.  If you take seriously what she's saying, then it's clear that cases in about 1/3 of the United States, including New York, are growing at truly alarming rates - rates that the official numbers are mostly not capturing.

Let me do my best to translate into everyday English what I see when I watch the Trump press conferences, especially when Drs. Birx and Fauci are interacting with the President.  It only makes sense if you speak a little bit of math and science jargon.  This is a pretty long explanation, but you have to understand this if you want to understand what's going on with the epidemic in the U.S.

Dr. Birx in particular says the word "logarithmic" a lot.  When she says this, it doesn't (just) mean that the numbers are high or that the growth rate is fast.  She uses the word precisely to mean a very specific thing. 

If you start with one sick person, and add one million per day, that sounds scary.  After a week, it's seven million (and one).  After a month, it's thirty million.  Not good.

But if you start with one person and double every day, after a week it's just 128.  Compared to seven million, 128 looks like you're doing great.  It's easy to go up to the podium and say, "Only 128 cases, everything's fine!"  But after a few weeks it starts to look like a tidal wave.  And after a month, if nothing slows it down, it's one billion.

A billion is a hell of a lot scarier than thirty million.  That thirty million is linear growth.  The billion is exponential growth.  Dr. Birx appears to be using "logarithmic" euphemistically to mean "exponential." Presumably what Dr. Birx has in mind is the fact that exponential growth plotted on a logarithmic scale appears reassuringly linear. For clarity, I’ll refer to "exponential growth" except when quoting or citing Dr. Birx, whose use of "logarithmic" should be understood to mean "exponential."

During the White House press conferences, Trump is constantly focusing on low numbers wherever he can see them.  Birx is constantly focusing on the growth rate.  It's the growth rate that really matters.

The whole concept of "flattening the curve" means converting the growth rate from exponential (one month = one billion) to linear (one month = thirty million).  Linear growth is still growth.  It is still a line going up.  When the curve flattened in Lombardy, Italy, the ICU units were still full, and the number of total cases was still going up.  The next step is to get the slope of that line down to the point that more people are leaving the hospital than entering.  Tragically, during that time, the way many people will leave the hospitals is not the good way.  Most of the total deaths happen after you flatten the curve.

Dr. Birx is constantly trying to point this out.  She's saying there will be a turning point soon in the country, where the curve goes from exponential to linear, but that does not mean the deaths will go down right then.  The totals will keep on going up for quite a while - and the longer it takes to flatten the curve, the worse this period of straight-line growth will be.

Trump hears the idea of a "turning point," and he seems to think it's going to be over then.  He wants to open churches and re-start the economy.  But after the curve is flattened, it's going to be a long, hard painful period during which it would be crazy to open things up and risk turning the curve exponential again.

Another thing to really pay attention to is that Dr. Birx shifted the criterion for exponential growth.  Usually, you can tell simply by looking at the daily growth rate.  If it's a steady absolute number, it's linear (think of adding one million per day).  If it's a steady percentage, it's exponential.  By this definition, for example, Texas is on an exponential curve.  Even though the numbers are small, the daily percentage of increase is steady.

If the total caseload is too big for testing to keep up, the normal linear-exponential distinction goes out the window because you can't trust your own numbers.  The growth looks linear because you aren't doing enough tests to capture an exponential increase.  To capture that, you have to expand the amount of testing at the same rate the epidemic is actually growing (or more).  If you simply perform the same number of tests per day, the growth looks far more steady than it really is.  Then you have to use a rule of thumb to take a guess.  When you are under-testing, the rate of positive results will go up (if tests are restricted to the sickest or most symptomatic), so it makes sense to set a cutoff for the positive test rate.  If the numbers are over that cutoff, then you can assume the growth is exponential.

Dr. Birx said she is using a 13% positive rate as a rule of thumb for "logarithmic" (i.e., exponential) growth.  That is very plausible, based on the similarities of COVID-19 to other coronaviruses and the flu.  By that measure there are currently 18 states in exponential growth, with a total population exceeding 100 million.  Then add another 30 million for Texas, which is exponential by the standard definition.

What this means in plain English is that three weeks after the White House announced stringent measures, one-third of the country is still getting infected at a rate that is out of control.  But if Dr. Birx spoke that plainly, it's not clear she'd be back at the podium tomorrow, or still have a job the day after.  The safe way to say it is "logarithmic."

In addition, when Dr. Birx puts out this 13% "rule of thumb," it is a tacit admission that current testing is inadequate to give the administration a real picture of what's happening.  If you have enough testing, you don't need a rule like this at all.  You just look at the actual numbers.

In New York, tests continue to come in about 40% positive (122,031 of 302,280, as of April 5, 2020; down to 36% as announced on Sunday evening).  This is so far above Dr. Birx's cutoff, there's just no way anyone can have much faith in the numbers leveling off soon.  What's actually leveling off is the number of tests they are able to do per day.  Just to compare: tests have been very severely rationed in Lombardy, and the positive rate has been about 25%.  For Veneto, which was hit hard early on but mounted the best response of any region in Italy, including very widespread testing, the positive rate has been about 7%.  To say that New York might be leveling off, with a positive rate at or over 35%, looks very reckless.

The really vital question for the United States right now is when the curve flattens - when the rate of increase goes from exponential to linear.  The Trump team is saying it's probably going to happen in the next week or two, based on other countries.  Trump likes to say that the U.S. is doing much better than Italy, which has its own "unique problems."

Any way you look at it, the U.S. is doing way, way less than Italy to flatten the curve.  Daily movement tracked by cell phones has been down 70-80% in Italy.  It's only down half that in the U.S.  Travel between regions was shut down in Italy weeks ago.  It's still happening in the U.S.  Churches in Italy closed a month ago; they're still open for Palm Sunday in parts of the U.S., and Trump has talked about opening them for Easter (April 12, 2020).  Letting spring break go forward was a truly dire mistake, which will only start showing up in the numbers in the next week or two.

There is no reason at all to think the U.S. will flatten the curve at the same pace as Italy.  It is not clear to me that the U.S. will flatten the curve at all by its own actions.  It's quite possible that the virus will do this on its own by infecting so many people that the U.S. acquires herd immunity.  That's the "worst case" scenario Trump has cited, with 2 million deaths.

When reporters ask Dr. Birx for hard numbers, she usually says she won't give any, and she often falls back on the term "logarithmic."  It seems to be her safe way to say it's going to be really bad, in a code that her bosses do not really understand (yet).  I have a feeling she's going to be using the word "logarithmic" a lot more in the next few weeks and months.

Jamie Hamilton is CEO of a data analytics firm supporting local newspapers worldwide, with offices in New York City and Milan, Italy.  He is a former data analyst for USAID and the World Bank.  He does not claim to be an epidemiologist of any sort.


Michael A Livingston said...

Doesn’t the incipient downturn in numbers from states like NY and PA tend to disprove this analysis? Or is it too early to say?

Karst said...

There is evidence that the false negative rate is high. See, e.g.,

Frank Willa said...

Thanks for this posting. I view these 'briefings' as T's daily form of his campaign rallies that fed his 'need to control the narrative' and 'to get a fulfillment to his self esteem'. The level of what he calls 'loyalty'- a total subservience in my view- is demanded of those that appear with him in public venues; that they must profess a 'blind support' and 'all but adoration' for him, seems surreal to me. To me he has his political 'finger in the wind' each day and these briefings provide a platform for him to play to his base and say whatever he thinks will best benefit his re-election. Science does not matter, public health does not matter, management of the government does not matter; only putting forth a perception that serves his ratings, his daily poll numbers, and re-election polling matters.
As to those 'forced' to violate 'social distancing' to be his props for his show I have never understood what motivates them.
So, this Dr. Birx and her 'safe' word is not making it 'clear' as to what is going on. You say she 'shifted the criterion for exponential growth'. Further, 'But if Dr. Birx spoke that plainly, it's not clear she'd be back at the podium tomorrow, or still have a job the day after.'; and then go on to say '... when Dr. Birx puts out this 13% "rule of thumb," it is a tacit admission that current testing is inadequate, and ' reporters ask Dr. Birx for hard numbers, she usually says she won't give any...'.
Is her job security the primary focus of her position? Why does not she not explain shifting criterion? Why is not an explicit statement that current testing is inadequate the appropriate response? Why not reveal the 'numbers' as best she knows them that day? Why not '...say it's going to be really bad...'; why is using code- 'logarithmic'- acceptable?
Based on what you have written...If you can not tell T the truth, have to obfuscate to the public, and distort (not be clear when you can) science and math to do it...why are you in the position at all?

Michael A Livingston said...

So if the numbers are going up, that’s bad, but if the numbers are going down, then the numbers must be wrong? Do people really believe andy of this, or do they actually want the crisis to be as bad as possible, for their own purposes? It’s hard to avoid the latter.

Unknown said...

Let's say that NY decided to only test 10 people per day. You'd expect 4 of them to test positive. Has NY flattened the curve because their numbers are suddenly dropping so fast?

I presume you say no to that. What if they test 100 and 40 were positive, is that enough? 1000 and 400?

Eventually, when the testing is more proportional to the actual increase in cases, the positive rate will start dropping. Dr Birx is suggesting that when it gets below 13% positive, then the testing is enough to put faith in the top line numbers. We don't know exactly how they arrived at this percentage, but it's in the ballpark of being reasonable.

That is not wanting the crisis to be as bad as possible. That is wanting the testing to be enough so that we know what is actually happening.

Michael A Livingston said...

But it’s harder to fake the death/serious hospitalization numbers than the “test positive” numbers isn’t it? Assuming that the coding of the deaths is accurate?

Greg said...

I mean no disrespect for Dr. Birx, who I'm sure is an expert in her field, but I literally get annoyed when professionals use the wrong word for something that is fundamental and important. Logarithmic and exponential are practically opposites, and using a word to mean it's opposite in a professional setting is, well, annoying. (Yes, "literally" to mean its opposite bugs me too.)

As for Michael A Livingston's question about at least death rates, I agree, that number's more likely to be correct. But if that's the only number you can rely on then you have to assume that the total number of cases is N times the number of deaths. To do that calculation you have to assume a fatality rate for the disease. What's worse about this method is your numbers are always at least 2 weeks behind, since it's 2 weeks or more from when a person is contagious with COVID-19 to when they die. Testing people who have symptoms is closer to 1 week behind, which is much better.

Unknown said...

Here in Italy, the death rates are known to be highly inaccurate due to test rationing. Also very few people who died outside of the hospital were counted in the official numbers.

The same is likely happening in New York -- no one wants to waste a test on someone who's already dead, when they are needed to diagnose the living. Also doctors who are overwhelmed treating the living appear to be falling behind on paperwork, for the already dead, according to funeral homes.

Using deaths is no more accurate than using cases or hospitalizations. There's no easy way to make the numbers accurate.