Finding the mitochondrial Na’ama

I was having a conversation recently about Biblical ancestry and the antediluvian generations, and it got me to thinking about how scientists sometimes like to use biblical references as attention-grabbing devices, without actually bothering to understand what they’re referring to — in this case, the so-called “mitochondrial Eve”. The expression was not used in the 1987 Nature paper that first purported to calculate the genealogical time back to the most recent common ancestor (MRCA) of all present-day humans in the female line, but it was a central to publicity around the paper at the time, including in academic journals such as Science.

The term has come to be fully adopted by the genetics community, even while they lament the misunderstandings that it engenders among laypeople — in particular, the assumption that “Eve” must in some sense have been the first woman, or must have been fundamentally different from all the other humans alive at the time. The implication is that the smart scientists were making a valiant effort to talk to simple people in terms they understand, taking the closest approximation (Eve) to the hard concept (MRCA), and the simple bible-y people need to make an effort on their part to understand what they’re really talking about.

In fact, calling this figure Eve is a blunder, and it reveals a fundamental misunderstanding of the biblical narrative. Eve is genuinely a common ancestor of all humans, according to Genesis, but she is not the most recent in any sense, and suggesting that she is just confusing. The MRCA in the Bible is someone else, namely the wife of Noah. Appropriately, she is not named, but if we want a name for her, the midrashic Genesis Rabbah calls her Na’ama. She has other appropriate characteristics as well, that would lead people toward a more correct understanding. To begin with, she lived many generations after the first humans. She lived amid a large human population, but a catastrophic event led to a genetic bottleneck that only she and her family survived. (That’s not quite the most likely scenario, but it points in the right direction.) And perhaps most important — though this reflects the core sexism of the biblical story — there was nothing special about her. She just happened to be in right place at the right time, namely, partnered with the fanatic boat enthusiast when the great flood happened.

The poisoned roots of German anti-vax sentiment

I’ve long thought it odd that Germany, where the politics is generally fairly rational, and science education in particular is generally quite good, has such broad acceptance of homeopathy and a variety of other forms of quackery, and a special word — Schulmedizin — “academic medicine” — to express a dismissive attitude toward what elsewhere would be called just “medicine”, or perhaps “evidence-based medicine”. I was recently looking into the history of this, and found that attacks on Schulmedizin — or “verjudete Schulmedizin” (jewified academic medicine) — were as much a part of the Nazi state science policy as “German mathematics” and “Arian physics”.

Medicine in the Third Reich remained a weird mixture of modern virology and pseudo-scientific “racial hygiene”. The celebrated physician Erwin Liek wrote

Es ist mein Glaube, dass das deutsche Volk berufen ist, nach und nach eine ganz neue, rein deutsche Heilkunst zu entwickeln.
(It is my belief, that the German people has a calling, gradually to develop a pure German art of healing.)

Liek was appealing for a synthesis of Schulmedizin with traditional German treatment. As with Arian physics*, and the Nazi state was careful not to push the healthy German understanding so far as to undermine important technology and industry. But the appeal to average people’s intuitive discomfort with modern science was a powerful propaganda tool that they couldn’t resist using, as in this 1933 cartoon “The vaccination” from Der Stürmer that shows an innocent blond arian mother uncomfortably watching her baby being vaccinated by a fiendish Jewish doctor. The caption reads “This puts me in a strange mood/Poison and Jews never do good.”

1933 Cartoon from Der Stürmer: Blond German mother looking concerned as a beastly Jewish doctor vaccinates her baby. Caption: "This puts me in a strange mood/Poison and Jews are seldom good."
1933 Der Stürmer cartoon “The vaccination”.

Today’s anti-vaxers fulminating against Schulmedizin and the Giftspritze (poison shot) are not necessarily being consciously anti-Semitic, but the vocabulary and the paranoid conspiracy thinking are surely not unconnected.

* Heisenberg was famously proud of having protected “Jewish physics” from being banned at his university, considering himself a hero for continuing to teach relativity theory, even while not objecting to the expulsion of the Jewish physicists, and agreeing not to attach their names to their work. Once when I was browsing in the science section of a Berlin bookstore in the early 1990s a man started chatting with me, telling me that he had worked for decades as a radio engineer in the GDR, and then going on to a long monologue apropos of nothing about how wonderful Heisenberg was, and how he had courageously defended German science during the Third Reich.

The first principle of statistical inference

When I first started teaching basic statistics, I thought about how to explain the importance of statistical hypothesis testing. I focused on a textbook example (specifically, Freedman, Pisani, Purves Statistics, 3rd ed., sec 28.2) of a data set that seems to show more women being right-handed than men. I pointed out that we could think of many possible explanations: Girls are pressured more to conform, women are more rational — hence left-brain-centred. But before we invest too much time and credibility in abstruse theories to explain the phenomenon, we should first make sure that the phenomenon is real, that it’s not just the kind of fluctuation that could happen by accident. (It turns out that the phenomenon is real. I don’t know if either of my explanations is valid, or if anyone has a more plausible theory.)

I thought if this when I heard about the strange Oxford-AstraZeneca vaccine serendipity that was announced this week. The third vaccine success announced in as many weeks, the researchers announced that they had found about a 70% efficacy, which is good, but not nearly as impressive as the 95% efficacy of the mRNA vaccines announced earlier in the month. But the strange thing was, they found that a subset of the test subjects who received only a half dose at the first injection, and a full dose later, showed a 90% efficacy. Experts have been all over the news media trying to explain how some weird idiosyncrasies of the human immune system and the chimpanzee adenovirus vector could make a smaller dose more effective. Here’s a summary from Science:

Researchers especially want to know why the half-dose prime would lead to a better outcome. The leading hypothesis is that people develop immune responses against adenoviruses, and the higher first dose could have spurred such a strong attack that it compromised the adenovirus’ ability to deliver the spike gene to the body with the booster shot. “I would bet on that being a contributor but not the whole story,” says Adrian Hill, director of Oxford’s Jenner Institute, which designed the vaccine…

Some evidence also suggests that slowly escalating the dose of a vaccine more closely mimics a natural viral infection, leading to a more robust immune response. “It’s not really mechanistically pinned down exactly how it works,” Hill says.

Because the different dosing schemes likely led to different immune responses, Hill says researchers have a chance to suss out the mechanism by comparing vaccinated participants’ antibody and T cell levels. The 62% efficacy, he says, “is a blessing in disguise.”

Others have pointed out that the populations receiving the full dose and the half dose were substantially different: The half dose was given by accident to a couple of thousand subjects at the start of the British arm of the study. These were exclusively younger, healthier individuals, something that could also explain the higher efficacy, in a less benedictory fashion.

But before we start arguing over these very interesting explanations, much less trying to use them to “suss out the mechanisms” the question they should be asking is, is the effect real? The Science article quotes immunologist John Moore asking “Was that a real, statistically robust 90%?” To ask that question is to answer it resoundingly: No.

They haven’t provided much data, but the AstraZeneca press release does give enough clues:

One dosing regimen (n=2,741) showed vaccine efficacy of 90% when AZD1222 was given as a half dose, followed by a full dose at least one month apart, and another dosing regimen (n=8,895) showed 62% efficacy when given as two full doses at least one month apart. The combined analysis from both dosing regimens (n=11,636) resulted in an average efficacy of 70%. All results were statistically significant (p<=0.0001)

Note two tricks they play here. First of all, they give those (n=big number) which makes it seem reassuringly like they have an impressively big study. But these are the numbers of people vaccinated, which is completely irrelevant for judging the uncertainty in the estimate of efficacy. The reason you need such huge numbers of subjects is so that you can get moderately large numbers where it counts: the number of subjects who become infected. Further, while it is surely true that the “results” were highly statistically significant — that is, the efficacy in each individual group was not zero — this tells us nothing about whether we can be confident that the efficacy is actually higher than what has been considered the minimum acceptable level of 50%, or — and this is crucial for the point at issue here — whether the two groups were different from each other.

They report a total of 131 cases. They don’t say how many cases were in each group, but if we assume that there were equal numbers of subjects getting the vaccine and the treatment in all groups then we can back-calculate the rest. We end up with 98 cases in the full-dose group (of which 27 received the vaccine) and 33 cases in the half-dose group, of which 3 received the vaccine. Just 33! Using the Clopper-Pearson exact method, we obtain 90% confidence intervals of (.781,.975) for the efficacy of the half dose and (.641, .798) for the efficacy of the full dose. Clearly some overlap there, and not much to justify drawing substantive conclusions from the difference between the two groups — which may actually be zero, or close to 0.

Extra precision: Currency edition

I have commented before on the phenomenon where changing units turns an obviously approximate number into a weirdly precise one. Here is a new example, from the Guardian’s disturbing report on the mass slaughter of donkeys for the use of their hides in traditional Chinese medicine:

Since the booming skin trade has driven up donkey prices, owners struggle to replace their animals when they are stolen. The cost of a donkey in Kenya increased from £78 to £156 between 2016-19.

£78 seems like an oddly precise figure for what is surely a very diverse market in animals of varying qualities. Even weirder is that that precise figure precisely doubled in the period under consideration. Then it occurred to me, at current exchange rates £78 is about what you get when you convert the round number of US$100. So I’m going to hazard a guess that the reporter was told that the price had risen from around $100 to around $200, and simply converted it to pounds for the UK market without further comment.

Moon over Brussels

Brexit secretary David Davis, June 2017:

Half of my task is running a set of projects that make the NASA moon shot look quite simple.

And now, soon-to-be-prime-minister-select Boris Johnson:

Boris Johnson: ‘can-do spirit’ can solve problem of Irish border

Favourite to be PM compares Brexit to mission to put astronauts on moon in 1969

There is no task so simple that government cannot overcomplicate if it doesn’t want to do it.

Brexit has gone in two years from being as complicated as the first moon landing to being… as easy as the first moon landing. Continue reading “Moon over Brussels”

The nature vs. nurture debate: High Christology edition

At least since the late nineteenth century the social interpretation of biology — and of genetics in particular — has devolved repeatedly upon the nature–nurture dispute: To what extent is a human’s individual characteristics determined by a predetermined essence or nature — qualities they are born with, commonly identified with inheritance; or by nurture, the particulars of the physical and social environment in which they develop after birth. From one of the most interesting books I’ve read recently, Bart Ehrman’s How Jesus Became God, I learned that an analogous debate roiled the early Christian Church.

One of the key disputes among early followers of Jesus concerned the nature and meaning of Jesus’s divinity. At the extremes you had the “low” christology belief that Jesus was a wise man and preacher, of the same nature as any other human; and the “high” christology claim that Jesus was identical with the creator God of the Hebrew Scriptures, and only appeared to be human. (Perhaps even more extreme were the gnostic claims that Jesus was an even higher being than that nasty Yahweh, who obviously fucked up his one major task*, for possibly nefarious purposes. In between were a range of beliefs that Jesus was entirely divine and entirely human. Ehrman points out that in the ancient Mediterranean world there were two “major ways” that it was believed possible for a human to be divine:

  • By adoption or exaltation. A human being… could be made divine by an act of God or a god…
  • By nature or incarnation. A divine being… could become human, either permanently or, more commonly, temporarily.

In other words, God by nurture or God by nature. Nurture is particularly emphasised in the Gospel of Mark, Nature in the Gospel of John. Reflecting the common prejudice in favour of “nature” as the more powerful, one typically thinks of incarnation as representing a more exalted view of Jesus. A Jesus who grew up as a human, and only in adulthood was adopted by God seems less genuinely godlike than one who is, so to speak, fruit of God’s loins — hence the virgin-birth story of Matthew and Luke.

One of the more fascinating novelties of Ehrman’s account is his elucidation of adoption customs in the Roman world, particularly as regards nobles and rulers. Of course, we know that Roman emperors commonly adopted heirs — most famously, Julius Caesar’s adopted son Octavian — but Ehrman explains how prevalent views of adoption were that today would be called progressive: Adoptive families are families by choice, so could be considered superior to the accidental biological families. An heir chosen by a great leader for the qualities he has demonstrated better incorporates and perpetuate’s the leader’s essence than his biological descendant.

Thus, a Christ nurtured by and ultimately adopted into the divine family by God after he had proved himself worthy is a more genuinely divine being than any merely so-to-speak genetically divine progeny, who might ultimately turn out to be a disappointment to his father.

* A classic joke with a gnostic perspective: A man goes to the tailor to order a new coat. The tailor fusses around taking measurements, asking exacting questions about the fabric, the cut, and so on. Having finished he names a price and tells the customer the jacket will be finished in three weeks. “Three weeks! The Lord created the whole world in just one week!”

The tailor shakes his head, picks up another recently completed coat, and beckons the man to come to the window. “One week you want? Look at the work here. The precision cuts. The minute stitching. The harmonious interplay of the parts. And now” gesturing out the window, “look at this world…”

The time lords

The European parliament has voted to stop the practice of switching clocks forward and backward every year, from 2021. I’ve long thought this practice rather odd. Imagine that a government were to pass a law stating that from April 1 every person must wake up one hour earlier than they habitually do, and go to sleep one hour earlier. All shops and businesses are required to open an hour earlier, and to close an hour earlier. The same for schools, universities, and the timing of private lessons and appointments must also be shifted. Obviously ridiculous, even tyrannical. The government has nothing to say about when I go to bed or wake up, when my business is open. But because they enforce it through adjusting the clocks, which seem like an appropriate subject of regulation and standardisation, it is almost universally accepted.

But instead of praising this blow struck for individual freedom and against statist overreach, we have Tories making comments like this:

John Flack, the Conservative MEP for the East of England, said: “We’ve long been aware the EU wants too much control over our lives – now they want to control time itself. You would think they had other things to worry about without wanting to become time lords,” he said, in an apparent reference to the BBC sci-fi drama Doctor Who.

“We agreed when they said the clocks should change across the whole EU on an agreed day. That made sense – but this is a step too far,” Flack added. “I know that farmers in particular, all across the east of England, value the flexibility that the clock changes bring to get the best from available daylight.

So, the small-government Tory thinks it’s a perfectly legitimate exercise of European centralised power to compel shopkeepers in Sicily and schoolchildren in Madrid to adjust their body clocks* in order to spare English farmers the annoyance of having to consciously adjust the clocktime when they get out of bed to tend to their harvest. But to rescind this compulsion, that is insufferably arrogant.

*Nor is this a harmless annoyance. Researchers have found a measurable increase in heart attacks — presumed attributable to reduced sleep — in the days following the spring clock shift. A much smaller decrease may accompany the autumn shift back.

The Brexit formula

A collaborative project with Dr Julia Brettschneider (University of Warwick) has yelded a mathematical formulation of the current range of Brexit proposals coming from the UK, that we hope will help to facilitate a solution:

Numeric calculations seem to confirm the conjecture that the value of the solution tends to zero as t→29/3.

Medical hype and under-hype

New heart treatment is biggest breakthrough since statins, scientists say

I just came across this breathless headline published in the Guardian from last year. On the one hand, this is just one study, the effect was barely statistically significant, and experience suggests a fairly high likelihood that this will ultimately have no effect on general medical practice or on human health and mortality rates. I understand the exigencies of the daily newspaper publishing model, but it’s problematic that the “new research study” has been defined as the event on which to hang a headline. The only people who need that level of up-to-the-minute detail are those professionally involved in winnowing out the new ideas and turning them into clinical practice. We would all be better served if newspapers instead reported on what new treatments have actually had an effect over the last five years. That would be just as novel to the general readership, and far less erratic.

On the other hand, I want to comment on one point of what I see as exaggerated skepticism: The paragraph that summarises the study results says

For patients who received the canakinumab injections the team reported a 15% reduction in the risk of a cardiovascular event, including fatal and non-fatal heart attacks and strokes. Also, the need for expensive interventional procedures, such as bypass surgery and inserting stents, was cut by more than 30%. There was no overall difference in death rates between patients on canakinumab and those given placebo injections, and the drug did not change cholesterol levels.

There is then a quote:

Prof Martin Bennett, a cardiologist from Cambridge who was not involved in the study, said the trial results were an important advance in understanding why heart attacks happen. But, he said, he had concerns about the side effects, the high cost of the drug and the fact that death rates were not better in those given the drug.

In principle, I think this is a good thing. There are far too many studies that show a treatment scraping out a barely significant reduction in mortality due to one cause, which is highlighted, but a countervailing mortality increase due to other causes, netting out to essentially no improvement. Then you have to say, we really should be aiming to reduce mortality, not to reduce a cause of mortality. (I remember many years ago, a few years after the US started raising the age for purchasing alcohol to 21, reading of a study that was heralded as showing the success of this approach, having found that the number of traffic fatalities attributed to alcohol had decreased substantially. Unfortunately, the number of fatalities not attributed to alcohol had increased by a similar amount, suggesting that some amount of recategorisation was going on.) Sometimes researchers will try to distract attention from a null result for mortality by pointing to a secondary endpoint — improved results on a blood test linked to mortality, for instance — which needs to be viewed with some suspicion.

In this case, though, I think the skepticism is unwarranted. There is no doubt that before the study the researchers would have predicted reduction in mortality from cardiovascular causes, no reduction due to any other cause, and likely an increase due to infection. The worry would be that the increase due to infection — or to some unanticipated side effect — would outweigh the benefits.

The results confirmed the best-case predictions. Cardiovascular mortality was reduced — possibly a lot, possibly only slightly. Deaths due to infections increased significantly in percentage terms, but the numbers were small relative to the cardiovascular improvements. The one big surprise was a very substantial reduction in cancer mortality. The researchers are open about not having predicted this, and not having a clear explanation. In such a case, it would be wrong to put much weight on the statistical “significance”, because it is impossible to quantify the class of hypotheses that are implicitly being ignored. The proper thing is to highlight this observation for further research, as they have properly done.

When you deduct these three groups of causes — cardiovascular, infections, cancer — you are left with approximately equal mortality rates in the placebo and treatment groups, as expected. So there is no reason to be “concerned” that overall mortality was not improved in those receiving the drug. First of all, overall mortality was better in the treatment group. It’s just that the improvement in CV mortality — as predicted — while large enough to be clearly not random when compared with the overall number of CV deaths, it was not large compared with the much larger total number of deaths. This is no more “concerning” than it would be, when reviewing a programme for improving airline safety, to discover that it did not appreciably change the total number of transportation-related fatalities.

Social choice Brexit

The discussion over a possible second Brexit referendum has foundered on the shoals of complexity: If the public were only offered May’s deal or no deal, that wouldn’t be any kind of meaningful choice (and it’s absurd to imagine that a Parliament that wouldn’t approve May’s deal on its own would be willing to vote for the fate of Brexit to be decided by the public on those terms. So you’re left with needing an unconventional referendum with at least three options: No deal, May’s deal, No Brexit (plus possible additional alternatives, like, request more time to negotiate the Better Deal™).

A three-choice (or more) referendum strikes many people as crazy. There are reasonable concerns. Some members of the public will inevitably find it confusing, however it is formulated and adjudicated. And the impossibility of aggregating opinions consistent with basic principles of fairness, not even to say in a canonical way, is a foundational theorem of social-choice theory (due to Kenneth Arrow).

Suppose we followed the popular transferable vote procedure: People rank the options, and we look only at the first choices. Whichever option gets the smallest number of first-choice votes is dropped, and we proceed with the remaining options, until one option has a first-choice majority. The classic paradoxical situation is all too likely in this setting. Suppose the population consists of

  1. 25% hardened brexiteers. They prefer a no-deal Brexit, but the last thing they want is to be blamed for May’s deal, which leaves the UK taking orders from Brussels with no say in them. If they can’t have their clean break from Brussels, they’d rather go back to the status quo ante and moan about how their beautiful Brexit was betrayed.
  2. 35% principled democrats. They’re nervous about the consequences of Brexit, so they’d prefer May’s soft deal, whatever it’s problems. But if they can’t have that, they think the original referendum needs to be respected, so their second choice is no deal Brexit.
  3. 40% squishy europhiles. They want no Brexit, barring that they’d prefer the May deal. No-deal Brexit for them is the worst.

The result will be that no deal drops out, and we’re left with 65% favouring no Brexit. But if the PDs anticipated this, they could have ranked no deal first, producing a result that they would have preferred.

So, that seems like a problem with a three-choice referendum. But here’s a proposal that would be even worse: We combine choices 2 and 3 into a single choice, which we simply call “Leave”. Then those who wants to abandon the European project entirely will be voting for the same option as those who are concerned about the EU being dominated by moneyed interests, and they’ll jointly win the referendum and then have to fight among themselves after the fact, leaving them with the outcome — no-deal Brexit — that the smallest minority preferred.

Unfortunately, that’s the referendum we actually had.