When vaccination rates are high, most positive cases will be among the vaccinated (and that's okay)

Two recent COVID outbreaks have made headlines because of the high proportion of "breakthrough" cases, where people test positive for COVID despite being fully vaccinated.  San Francisco hospitals in July reported 50 staff members tested positive for COVID, despite 75% of them being vaccinated.  In Provincetown, MA, a July outbreak of the delta variant led to several hundred new cases, the majority of whom were fully vaccinated.

• Physicians, nurses, ancillary staff': How hundreds of SFGH and UCSF staff got infected with COVID

• Most Covid-19 cases in Massachusetts outbreak among vaccinated: CDC, United States News & Top Stories

How can the majority of new cases be among the vaccinated?  Some people wrongly (if understandably) worry this means the vaccines aren't working, particularly against the delta variant. 

The truth is the numbers show that the vaccines ARE very effective, even against the delta variant.

The problem here is the reporting.  News agencies are going for provocative headlines, and in the process are falling for what is known in statistics as the "low base rate fallacy" or base rate bias.  In this case, breakthrough infections have a very low base rate, and all of other numbers are meaningless without keeping that in mind.  

The low base rate of breakthrough infections should be the focus in reporting.  For instance, the headline does not mention that the 50 new cases in July among SF hospital staff is out of 7,500 staff members, a breakthrough base rate of less than 1%.  They don't mention that until later in the article.

How can positive rates be higher among the vaccinated?

What does it mean that, in the delta outbreak in Provincetown, there were a higher proportion of positive cases among vaccinated folks compared to unvaccinated?  Does it mean the vaccine is ineffective agains the delta?  NO.  Because of the low base rate, when vaccination rates are high, more positive cases will be among the vaccinated.  

What it really means is just that most people in MA are vaccinated! To understand this, a picture is worth 1000 words. I came across this diagram that clearly shows what's going on. 

source: https://i.redd.it/cpjwvqv2s0d71.png

The left half of the diagram shows what happens in a highly vaccinated population, based on real-world data from England.  There was a 2% chance of getting symptomatic COVID among the unvaccinated (red dots).  For the vaccinated, it was a much smaller percentage who got COVID (only 20% of 2%, aka 0.4%).  But since so many more people were vaccinated (over 10x as many), that led to a higher number of vaccinated people who tested positive (blue dots).  This explains the counterintuitive result that even though the vaccine is working, more people who test positive are vaccinated.  There's just so many more vaccinated people! (Notice there are still way fewer vaccinated who end up hospitalized.)

The right half of the diagram shows what happens when a lower percentage of the population is vaccinated.  First - and most importantly - there are more overall cases and hospitalizations.  Second, since there are more unvaccinated people, the higher proportion of people who test positive are unvaccinated.  This matches our usual intuitions.

In summary: When most people are vaccinated, it brings down the total # of positive cases drastically (yay!), but can end up with a higher proportion of positive cases among vaccinated folks. This can be confusing, because humans aren't great at doing statistics when there's a low base rate involved.  It really helps to visualize it. 

Remember that breakthrough cases are normal and to be expected, and extremely rare in reality (much less than 1% in MA and nationwide). The vaccines help in multiple ways: they reduce positive cases and also lead to a lower rate of hospitalization among those who test positive (only 1% of vaccinated positives from the recent MA delta outbreak were hospitalized). 

TLDR: Vaccines are working well, even when a higher percentage of positive cases are among the vaccinated!

Epilogue: Simpson's Paradox

The base rate fallacy leads to all sorts of funky, counterintuitive results:  

  

• My favorite comes from baseball - In 1989 Andy Van Slyke had a higher batting average than David Justice (0.237 vs. 0.235).  In 1990 Van Slyke again had a higher average than David Justice (0.284 vs. 0.282).  But when you look at their combined 2-year battering average 1989-1990, David Justice is the one with the higher average (0.278, compared with Van Slyke's 0.261).  How can this be?  David Justice had far fewer at bats in 1989, so his combined average is skewed closer to his 1990 season.  
• Simpson's paradox is what philosophers and statisticians call an association between variables at the population level that reverses when divided into subpopulations.  Understanding Simpson's paradox has important ramifications for epidemiology and for equity.
• At the population level, vaccinated people are less likely to get COVID.  But when comparing vaccinated to unvaccinated, a higher proportion of new cases can be among the vaccinated.  This is Simpson's paradox.  Of course, it's not truly a paradox - it is just so counterintuitive you have to think it through carefully. Every. Time.

What's wrong with the Bill Gates' foray into educational research & reform

#1 Bill Gates is not an education researcher, let alone an educator, or a researcher.
Don't get me wrong.  I love that Bill Gates is identifying education as a key issue to focus on.  I love that he is taking an interest in improving education.  I am not questioning his motives.  Just his methods.

What I hate is that his approach is the same know-it-all attitude that many take towards education and education research.  It's the old "I turned out okay, and I know what worked for me, therefore I am an expert on education" approach.

Good ol' Uncle Bill knows all there is to know about education reform

Which would be bad enough if he were just Uncle Bill, telling-it-how-it-is from his comfy chair at a holiday party.  But instead, he is using his name to garner authority on a subject he knows little about.

#2 His ENTIRE research program is explicitly based upon students' scores on standardized tests
The following is taken from a recent report by Gates' MET project:

THE THREE PREMISES OF THE MET PROJECT
The MET project is based on three simple premises: 

• First, whenever feasible, a teacher’s evaluation should include his or her students’ achievement gains.
• Second, any additional components of the evaluation (e.g., classroom observations, student feedback) should be demonstrably related to student achievement gains 
• Third, the measure should include feedback on specific aspects of a teacher’s practice to support teacher growth and development. 

NB: "Achievement gains" are edu-jargon for increases in standardized test scores.  There are so many problems with this, I don't know where to begin.  For one, there is the obvious: these standardized tests DO NOT MEASURE what students are learning.  But a more important issue to me is that: THESE TESTS DO HARM TO STUDENTS.  And I'm not talking just about "they get stressed when they take tests."  I'm also talking about the WEEKS of instructional time lost to testing throughout the school year, and the MONTHS of instructional time lost to test-preparation throughout the school year.  I'm talking about the science classes, the history classes, the art classes, which ARE NOT TAUGHT so that reading and math test scores can improve.

This is just a little slice of the Test-Mania inflicting the schools where I make my rounds.   I wonder what the kids make of this poster, as they pass it in the hallway every day.  And I wonder how it makes them feel.
I know what I think when I pass it: 58.3% is SOARing?? 

See, the biggest damage done is not from the 5-hour-long sessions of sitting at a desk to take these tests; it is in the life-long damage to the students done by the test-mania they are subjected to in school.  At the heart of the issue is the damage done to students' conceptions of what it means to learn something.

As a science educator, I am most concerned about how the tests distort students' views on what it means to learn and to do science.  The  students take away such distortions from this test-crazed school culture when it is working as it is supposed to.  That means under Gates' ideal conditions, students' conceptions of science (and who knows what else!) will be destroyed, or at least distorted beyond recognition.  I have seen this first hand in my time in the classroom as an instructor, and as a researcher.

The fundamental principle of educational reform should be the same as it has been in medicine: DO NO HARM.  Gates' program, despite its best intentions, is a way of institutionalizing harm to children.  This is what happens when you jump from your own biases to institutionalizing them as recommendations.  Which brings me to my next wag-of-the-finger:

#3 Gates is jumping right from making assumptions to making recommendations
It's one thing to do descriptive statistics.  It's another to make causal claims.  But causal claims must be substantiated BEFORE making recommendations.  And the research that's already been done must be addressed first.

Yet somehow, Gates decided that he can simply dismiss all the research that shows the positive correlation between small class sizes and student learning (one of the most robust findings in educational research).  His recommendation: INCREASE class sizes, so we can force teachers to do more for less, and with less resources to help them do it.

Again, if this were just Uncle Bill ranting at a party it would be one thing.  But this is a person who is determining the future of the educational system with billions of dollars of investment in harmful and misguided policies and their proliferation.

#4 He wants traffic cameras in the classroom...
...except instead of being used to issue speeding tickets, they will be used to punish teachers.  Big brother, anyone?  What a great way to encourage teachers to enter into the profession and stay there (which, by the way, is really the key issue, if you ask Uncle Luke).  And by "great" I mean "idiotic."

TEACHERS:

Gates knows when you've been boring, Gates knows when you've been late...

Gates knows when kids are snoring, so give them tests for testing's sake!

Okay, enough ranting.  Here is something good I think Uncle Bill is bringing to the table, although he is horribly misusing it: using videos of classrooms to improve instruction & learning.  Video of classroom practice can be extremely helpful for teachers, UNDER THE RIGHT CONDITIONS.  Larry Ferlazzo has written a wonderful article on how video can be used productively to improve teaching.  Mr. Ferlazzo *voluntarily* used video of his teaching in order to have an open discussion with an external evaluator *and his students* about his teaching *in that video* (not to summarily characterize his teaching).  That sort of practice has great promise, if you ask Uncle Luke.

What are the lessons to learn from Columbus?

Was Columbus a hero or a villain?  

We all know that Columbus' legacy is a controversial one.  Many history books have painted him as an intrepid explorer and overlooked the facts that would paint him in a negative light.  Some Columbus scholars have admitted that he encited a devastating genocide, but dedicated no more than a sentence to that fact (see, for example, Samuel Eliot Morison).  


So which is it--was Columbus a hero or a villain?  And how do we decide?  One thing that would be important to determine is what Columbus himself thought he was doing.  Perhaps he was trying to do good.  Perhaps he did not mean to exploit and kill all those natives...maybe it was his lower officers that took things into their own hands and got out of control.  


Fortunately, we have Columbus' log, as well as the log of several of his viceroys, and so we can find some answers to this question.  This, for example, is what Columbus wrote about his first encounter with the natives:


They ... brought us parrots and balls of cotton and spears and many other things, which they exchanged for the glass beads and hawks' bells. They willingly traded everything they owned... . They were well-built, with good bodies and handsome features.... They do not bear arms, and do not know them, for I showed them a sword, they took it by the edge and cut themselves out of ignorance. They have no iron. Their spears are made of cane... . They would make fine servants.... With fifty men we could subjugate them all and make them do whatever we want.


Well, he pretty much just comes out and says that he is intentionally subjugating them and making them do whatever they wanted.  And, also according to Columbus' own words, they wanted them for two things: gold and slavery.  So he took many as slaves and set everyone else to the grueling work of looking for gold where there wasn't any to write home about.   The working conditions for finding the gold were miserable, and the penalty for not meeting one's gold quota was chopping off the hands and bleeding them to death.  

The situation was written about extensively by one of Columbus' appointed governors, Bartolome de las Casas, a young priest who initially took part in the conquest and held slaves and such, but became disgusted by the cruelty of the Spaniards.  Here he describes the working conditions for the Arawaks faced under Columbus' rule:


Thus husbands and wives were together only once every eight or ten months and when they met they were so exhausted and depressed on both sides ... they ceased to procreate. As for the newly born, they died early because their mothers, overworked and famished, had no milk to nurse them, and for this reason, while I was in Cuba, 7000 children died in three months. Some mothers even drowned their babies from sheer desperation.... in this way, husbands died in the mines, wives died at work, and children died from lack of milk . .. and in a short time this land which was so great, so powerful and fertile ... was depopulated. ... My eyes have seen these acts so foreign to human nature, and now I tremble as I write. ...


When Las Casas arrived in the Bahamas in 1508 he documented the unbelievable scale of the devastation:


"there were 60,000 people living on this island, including the Indians; so that from 1494 to 1508, over three million people had perished from war, slavery, and the mines. Who in future generations will believe this? I myself writing it as a knowledgeable eyewitness can hardly believe it...."


And so the question of whether Columbus' behavior was villainous seems pretty settled, based on his own writings as well as accounts from his officers.  What is not yet settled, for me at least, is how Columbus justified his behavior to himself.  With his reports to the King and Queen of Spain he could talk of subjugation without needing to explain how that is a good thing.  But what was going through his head when he went to sleep each night?  Was there any recognition of the evil actions let alone remorse?  Did he think he was being a hero?  Did he, as a devout Christian, think he was saving the souls of these natives?  If so, did he somehow twist this reasoning to render his maniacal methods as somehow forgivable, even noble?  Is there a way we can ever find this out?


I don't know the answer to these questions, perhaps nobody does and nobody ever will; but I think it is an extremely important set of questions with which to struggle.  You see, Columbus is not the only instance of such a horrible turbulence between two cultures as they newly meet.  If anything, subjugation and genocide seem to be the norm of two intersecting cultures, especially in the Americas.  The same sort of despicable treatment of human beings, from slavery to torture and genocide, accompanied the missions of Cortes in Mexico, Pizarro in Peru, and English settlers in English Settlers in Virginia and Massachusetts with the Powhatans and Pequots.


The lessons we learn (or do not) from such conquests could make or break the survival of the Earth, if extraterrestrial beings ever pay us a visit.  Is there a way for two cultures to intersect and mutually reinforce each other, or is war and death the only inevitable outcome?  Or maybe we will one day venture out to the stars, and we could end up being Avatars, i.e., Columbus 2.0.  These are big IF's, of course, but I think it is worth thinking about how we might do things better next time, whichever end of the ordeal we end up on.


Columbus apparently went down a slippery slope, thinking it his spiritual duty to convert these natives and save their souls, which let him to thinking, how better to convert people than by the club, and what makes a better club than a sword?  By turning to the sword, Columbus ultimately succumbed to blind and arrogant self-righteousness which nothing--not the absence of gold nor the decemation of an entire people--could snap him out of.  Let's learn to avoid this in the future, what do you say, fellow humans?

Musicians are underrepresented amongst our national holidays

Holidays are our nation's way of ceremonially celebrating it's most influential people and its proudest accomplishments. They are dedicated to the nation's founders, leaders, influential politicians, and pivotal events.

I think it's safe to say that music is one of the finest gifts to the world that the United States has offered. To quote House Resolution 57, passed by the U.S. Congress in 1987:



Whereas, jazz has achieved preeminence throughout the world as an indigenous American music and art form, bringing to this country and the world a uniquely American musical synthesis and culture through the African-American experience and...makes evident to the world an outstanding artistic model of individual expression and democratic cooperation within the creative process, thus fulfilling the highest ideals and aspirations of our republic...it is the sense of the Congress that jazz is hereby designated as a rare and valuable national American treasure to which we should devote our attention, support and resources to make certain it is preserved, understood and promulgated.

I suggest that one great way to devote our attention, support, and resources to our native music idioms such as jazz would be to dedicate national holidays to our greatest musicians.

Perhaps for starters, we could make next Tuesday, September 23rd, "John Coltrane Day". John Coltrane was born September 23rd, 1926 in Hamlet, NC. On stage and on record, he traveled deep inside to bring back out for his audience virtuosic and hearfelt "sheets of sound". His music captured the complexities of the experiences and emotions conjured by life in tumultuous times. His music evolved from cries of despair to soothing cries for peace and ascension. His music has not only stood the test of time, it is timeless. He has influenced generations of musicians to search for diligent virtuosity as well as true expression.

Isn't that enough for one day of recognition?