Vaccine probabilities

From an article on the vaccine being developed by Robin Shattock’s group at Imperial College:

The success rate of vaccines at this stage of development is 10%, Shattock says, and there are already probably 10 vaccines in clinical trials, “so that means we will definitely have one”

It could be an exercise for a probability course:

  1. Suppose there are exactly 10 vaccines in this stage of development. What is the probability that one will succeed?
  2. Interpret “probably 10 vaccines” to mean that the number of vaccines in clinical trials is Poisson distributed with parameter 10. What is the probability that one will succeed?

Putting Covid-19 mortality into context

[Cross-posted with Statistics and Biodemography Research Group blog.]

The age-specific estimates of fatality rates for Covid-19 produced by Riou et al. in Bern have gotten a lot of attention:

0-910-1920-2930-3940-4950-5960-6970-7980+Total
.094.22.911.84.013469818016
Estimated fatality in deaths per thousand cases (symptomatic and asymptomatic)

These numbers looked somewhat familiar to me, having just lectured a course on life tables and survival analysis. Recent one-year mortality rates in the UK are in the table below:

0-910-1920-2930-3940-4950-5960-6970-7980-89
.012.17.43.801.84.2102885
One-year mortality probabilities in the UK, in deaths per thousand population. Neonatal mortality has been excluded from the 0-9 class, and the over-80 class has been cut off at 89.

Depending on how you look at it, the Covid-19 mortality is shifted by a decade, or about double the usual one-year mortality probability for an average UK resident (corresponding to the fact that mortality rates double about every 9 years). If you accept the estimates that around half of the population in most of the world will eventually be infected, and if these mortality rates remain unchanged, this means that effectively everyone will get a double dose of mortality risk this year. Somewhat lower (as may be seen in the plots below) for the younger folk, whereas the over-50s get more like a triple dose.

Buddhist causal networks

A little-publicised development in statistics over the past two decades has been the admission of causality into respectable statistical discourse, spearheaded by the computer scientist Judea Pearl. Pearl’s definition (joint with Joseph Harpern) of causation (“X having setting x caused effect E”) has been formulated approximately as follows:

  • X=x and E occurs.
  • But for the fact that X=x, E would not have occurred.

Of course, Pearl is not the first person to think carefully about causality. He would certainly recognise the similarity to Koch’s postulates on demonstrating disease causation by a candidate microbe:

  1. No disease without presence of the organism;
  2. The organism must be isolated from a host containing the disease ;
  3. The disease must arise when the organism is introduced into a healthy animal;
  4. The organism isolated from that animal must be identified as the same original organism.

I was reminded of this recently in reading the Buddhist Assutava Sutta, the discourse on “dependent co-arising”, where this formula (that also appears in very similar wording in a wide range of other Buddhist texts) is stated:

When this is, that is;

This arising, that arises;

When this is not, that is not;

This ceasing, that ceases.

Lecturing is obsolete — and always has been

Pretty much since I became a professional academic two decades ago there has been constant agitation against lecturing as a technology for teaching. Either new research has proven it, or new technology has rendered it, obsolete. Thus I was amused to read this comment in Boswell’s Life of Johnson:

We talked of the difference between the mode of education at Oxford, and that in those Colleges where instruction is chiefly conveyed by lectures. JOHNSON: ‘Lectures were once useful; but now, when all can read, and books are so numerous, lectures are unnecessary. If your attention fails, and you miss a part of a lecture, it is lost; you cannot go back as you do upon a book.’ Dr. Scott agreed with him. ‘But yet (said I), Dr. Scott, you yourself gave lectures at Oxford.’ He smiled. ‘You laughed (then said I) at those who came to you.’

Guilt of admission

When I first arrived at Oxford I expressed admiration for the rigorously academic nature of the student admissions procedure. I have since soured somewhat on the whole segregate-the-elite approach, as well as on the implicit fiction that we are selecting students to be future academics, but I still appreciate the clarity of the criteria, which help to avoid the worst corruption of the American model. I have long been astonished at how little resentment there seemed to be in the US at the blatant bias in favour of economic and social elites, with criticism largely focused on discrimination for or against certain racial categories. Despite the enormous interest in the advantages, or perceived advantages, of elite university degrees, very little attention has been focused on the intentionally byzantine admissions procedures, on the bias in favour of children of the wealthy and famous (particularly donors or — wink-wink — future donors), the privileging of students with well-curated CVs and expensive and time-consuming extracurricular activities, the literal grandfather clauses in admissions.

Now some of the wealthy have taken it too far, by defrauding the universities themselves, paying consultants to fake exam results and athletic records. The most unintentionally humorous element of the whole scandal is this comment by Andrew Lelling, U.S. attorney for the District of Massachusetts:

We’re not talking about donating a building so that a school is more likely to take your son or daughter. We’re talking about deception and fraud.

Fraud is defined here as going beyond the ordinary bounds of abusing wealth and privilege. You pay your bribes directly to the university, not to shady middlemen. The applicant needs to actually play a sport only available in elite prep schools, not produce fake testimonials and photoshop their head onto an athlete’s body.

Of course, this is all fraud, because no one is paying millions of dollars because they think their child will receive a better education. The whole point is to lay a cuckoo’s egg in the elite-university nest, where they will be mistaken for the genuinely talented. For a careful (tongue-in-cheek) analysis of the costs and benefits of this approach, see my recent article on optimised faking.

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.

Achieving transparency, or, Momus among the rotifers

1561 v. Heemskerck Momus tadelt die Werke der Goetter

At the recent Evolutionary Demography meeting in Miami there were two talks on the life history of rotifers. One of the speakers praised rotifers as a model organism for their generously choosing to be transparent, facilitating study of their growth and physiological changes. I had never really thought much about transparency as a positive feature of organisms (from the perspective of those wanting to study them) — though I guess the same has also favoured the development of the C. elegans system.

I was reminded of the famous quip (reported by his son Leonard Huxley) of T H Huxley, when he asked a student at the end of a lecture whether he had understood everything:

“All but one part,” replied the student, “during which you stood between me and the blackboard.”

To which Huxley rejoined, “I did my best to make myself clear, but could not render myself transparent.”

Momus would have been pleased.

The inflationary university

The universe, the standard model tells us, began with rapid inflation. The university as well, or at least, the modern exam-centered university.

With UK universities being upbraided by the Office for Students (OfS), the official regulator of the UK higher education sector, for handing out too many first-class degrees, I am reminded of this wonderful passage unearthed by Harry Lewis, former dean of Harvard College, from the report of Harvard’s 1894 Committee on Raising the Standard:

The Committee believes… that by defining anew the Grades A, B, C, D, and E, and by sending the definitions to every instructor, the Faculty may do something to keep up the standard of the higher grades. It believes that in the present practice Grades A and B are sometimes given too readily — Grade A for work of no very high merit, and Grade B for work not far above mediocrity.

Noting that letter grades were first introduced at Harvard in 1886, Lewis summarises the situation thus:

It took only eight years for the first official report that an A was no longer worth what it had been and that the grading system needed reform.

UV radiation and skin cancer — a history

If I had been asked when it first came to be understood that skin cancer is caused by exposure to the sun, I would have said probably the 1970s, maybe 1960s among cognoscenti, before it was well enough established to become part of public health campaigns. But I was just reading this 1953 article by C. O. Nordling on mutations and cancer — proposing, interestingly enough, that cancers are caused by the accumulation of about seven mutations in a cell — which mentions, wholly incidentally, in a discussion of latency periods between the inception of a tumour cell and disease diagnosis

40 years for seaman’s cancer (caused by solar radiation).

So, apparently skin cancer was known to be frequent among sailors, and the link to sun exposure was sufficiently well accepted to be mentioned here parenthetically.

Mission accomplished!

Reading Dava Sobel’s book on the women astronomers of the Harvard Observatory in the early 20th century, The Glass Universe, I was surprised to discover that the first Association to Aid Scientific Research by Women was founded in the 19th century. It awarded grants and an Ellen Richards Research prize, named for the first woman admitted to MIT, who went on to become associate professor of chemistry at MIT, while remaining unpaid. The prize was last awarded in 1932. Why?

[After selecting the winners of the 1932 prize] the twelve members declared themselves satisfied with the progress they had seen, and they drafted a resolution to dissolve the organization. “Whereas,” it said, “the objects for which this association has worked for thirty-five years have been achieved, since women are given opportunities in Scientific Research on an equality with men, and to gain recognition for their achievements, be it Resolved, that this association cease to exist after the adjournment of this meeting.”