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Ten Seconds to Inject

Macneil of Barra (Letters, 29 July) manifests the very misunderstanding about probability that my example was meant to illustrate. The example involves a disease that affects 1 in 10,000 people in the population being studied. The test for the disease is 99 per cent reliable in the sense that it gives correct (negative) results for 99 per cent of healthy people and false positive results for the other 1 per cent – in the standard medical terminology, the test’s ‘specificity’ is 99 per cent. I explained why it is that if a randomly selected person tests positive, the chance that she actually has the disease is, contrary to what most people expect, less than 1 per cent. Macneil raises the stakes by positing that the disease is always quickly fatal, and that the antidote always works, but will kill the patient if she is not ill. He claims that if my reasoning were applied to a group of 100 patients with positive test results, 99 would die and 1 would be saved. In his view, a doctor should give the antidote to everyone who tests positive. Macneil’s reasoning is fatally flawed: on the facts of his own example, his counsel would result in the deaths of nearly ten thousand people.

His mistake is to ignore the prevalence of the disease in the population being studied. He supposes that there are 99 correct results, i.e. 99 sick people. But since only 1 person in 10,000 has the disease, in order to find 99 sick people by random testing, we would have to test about 990,000. We would expect 989,901 of them to be healthy, and of these, 9899 (1 per cent) would falsely test positive. In other words, for every 99 sick people who test positive, 9899 healthy people also do so. Macneil would give the antidote to everyone who tests positive, thus saving 99 people and killing 9899 healthy ones. (A false negative rate would make Macneil’s success rate even worse. If there were a false negative rate of 10 per cent, for example, only about 90 of the 99 sick people would test positive and be saved, and there would be an additional 9 deaths.)

His premise is that a 99 per cent reliable test is one whose results are correct 99 per cent of the time. But it was precisely the point of my example that this apparently common-sense understanding of reliability is badly confused. (Fortunately, the accuracy of medical tests is not specified in a way such as Macneil’s that ignores the prevalence of the disease.) Macneil has made the error of trying to determine the probability of a hypothesis in the light of a specific piece of evidence without taking into account the prior probability of the hypothesis.

Macneil is right to emphasise that what is at stake ‘is not just a hypothetical question’. His letter neatly, if inadvertently, demonstrates the potential real world consequences of common but mistaken ways of reasoning about probabilities.

Mark Greenberg
Jesus College, Oxford

Macneil of Barra (Letters, 29 July) manifests the very misunderstanding about probability that my example was meant to illustrate. The example involves a disease that affects 1 in 10,000 people in the population being studied. The test for the disease is 99 per cent reliable in the sense that it gives correct (negative) results for 99 per cent of healthy people and false positive results for the other 1 per cent – in the standard medical terminology, the test’s ‘specificity’ is 99 per cent. I explained why it is that if a randomly selected person tests positive, the chance that she actually has the disease is, contrary to what most people expect, less than 1 per cent. Macneil raises the stakes by positing that the disease is always quickly fatal, and that the antidote always works, but will kill the patient if she is not ill. He claims that if my reasoning were applied to a group of 100 patients with positive test results, 99 would die and 1 would be saved. In his view, a doctor should give the antidote to everyone who tests positive. Macneil’s reasoning is fatally flawed: on the facts of his own example, his counsel would result in the deaths of nearly ten thousand people.

His mistake is to ignore the prevalence of the disease in the population being studied. He supposes that there are 99 correct results, i.e. 99 sick people. But since only 1 person in 10,000 has the disease, in order to find 99 sick people by random testing, we would have to test about 990,000. We would expect 989,901 of them to be healthy, and of these, 9899 (1 per cent) would falsely test positive. In other words, for every 99 sick people who test positive, 9899 healthy people also do so. Macneil would give the antidote to everyone who tests positive, thus saving 99 people and killing 9899 healthy ones. (A false negative rate would make Macneil’s success rate even worse. If there were a false negative rate of 10 per cent, for example, only about 90 of the 99 sick people would test positive and be saved, and there would be an additional 9 deaths.)

His premise is that a 99 per cent reliable test is one whose results are correct 99 per cent of the time. But it was precisely the point of my example that this apparently common-sense understanding of reliability is badly confused. (Fortunately, the accuracy of medical tests is not specified in a way such as Macneil’s that ignores the prevalence of the disease.) Macneil has made the error of trying to determine the probability of a hypothesis in the light of a specific piece of evidence without taking into account the prior probability of the hypothesis.

Macneil is right to emphasise that what is at stake ‘is not just a hypothetical question’. His letter neatly, if inadvertently, demonstrates the potential real world consequences of common but mistaken ways of reasoning about probabilities.

Mark Greenberg
Jesus College, Oxford

Thomas Laqueur writes (LRB, 29 July) that a medical textbook becomes obsolete within five years. In fact the information in a textbook may be out of date long before the book is published. The routine use of streptokinase in myocardial infarction, for example, began to be advised in textbooks in 1987, 13 years after an analysis of the published clinical trials would have revealed clear and compelling evidence to support its use. No one expects their GP to stay abreast of a literature in which a new paper is published, on average, every 15 seconds. On the other hand, any patient with Internet access can quickly obtain the results of all the latest research pertinent to their condition. The consequences of this for the doctor-patient relationship may be one of the things that future generations examine when they study medicine at the end of the 20th century.

Statistical textbooks age less rapidly. According to those on my shelf, pace Mark Greenberg and Macneil of Barra, the reliability of a medical test is not a measure of its capacity to differentiate between sick and healthy patients but of the extent to which that capacity is vulnerable to error. Greenberg makes it clear that he is actually talking about the sensitivity and specificity of medical tests. Macneil appears to use the term to refer to predictive value. The key difference between sensitivity and predictive value is exactly the thing that interests Greenberg: the impact of the prior probability of having the disease. In clinical terms, its prevalence. The point is that you can only calculate the predictive value of a test for a given prevalence, and the prevalence of exposure to nerve gas, to use Macneil's example, will vary widely between different groups of patients. I'd be happier with Dr Greenberg.

Paul Taylor
University College London


Belgitude

Like Mary-Kay Wilmers (LRB, 29 July), who was obliged to move to Brussels, I, too, had to move to ‘a dark, rainy, unfriendly, unseductive, unappealing, charmless city’. The city was Antwerp, and the city my family left was Brussels. Brussels had been for me – this was the late Fifties – a childhood paradise. There were no Hershey bars or Hamburger Heaven, but – much better – the mimosa sold on the city streets in winter mixed with the perfume of roasted chestnuts; and there were streets in my neighbourhood where one could play all day long. In Antwerp (as Wilmers said of Brussels), ‘I don’t remember knowing the neighbours or playing with the children next door or downstairs.’

Brussels seems to be the city Anglo-Americans love to hate. I have lived in Paris, Frankfurt, Zurich, Amsterdam and now live in Nijmegen (where no one would have wanted to grow up in the Fifties). On returning recently to Antwerp, I realised that my feelings of hatred towards it had to do with pre-adolescent gloom. At that time any city, apart from Brussels, would have been unbearable. Would Wilmers have been happier in Paris? I doubt it. There were no Hershey bars in Paris either, no Hamburger Heaven. And even more attention would have been paid to food than in Brussels. Not loving Brussels is a cliché, as easy as saying that we ‘are in love with Paris’.

Wilmers writes that none of the ‘three Belgian writers known outside Belgium’ was concerned with his own country. Well, let’s see. Simenon wrote a lot about Belgium – much of his memoirs concern his childhood in Liège – though it’s true he didn’t write about Brussels; Maeterlinck’s symbolism cannot be understood without his Flemish background; Tintin is rightly considered the essence of ‘Belgitude’. And it’s not true that ‘only one’ English novelist wrote about Brussels. Thackeray’s sketches of the city in Vanity Fair – he calls it ‘one of the gayest and most brilliant little capitals in Europe’ – have a joie de vivre. Wilmers quotes Byron on the Duchess of Richmond’s ball: ‘who could guess … upon night so sweet such awful morn could rise.’ Perhaps it would have been more apt to quote from Vanity Fair, where the snobbish Mrs O’Dowd declares ‘that the Hôtel de Ville was not near so large or handsome as her father’s mansion of Glenmalony.’

Eric de Kuyper
Nijmegen

Mary-Kay Wilmers overlooks one literary reminiscence of Brussels which adds a visionary quality to the ‘dreariness’ she associates with the city. W.H. Auden spent most of December 1938 there, writing a handful of poems that encapsulate his disabused state of mind at the fag-end of a low dishonest decade. In ‘Brussels in Winter’, ‘Wandering the cold streets tangled like an old string,/Coming on fountains silent in the frost’, Auden evokes a city which eludes the stranger, where only ‘the homeless and the really humbled/Seem to be sure exactly where they are.’ In the poem’s desolate conclusion, ‘fifty francs will earn the stranger right/To warm the heartless city in his arms.’ The city’s greatest cultural asset, the Breughel collection in the Musée des Beaux Arts, in Auden’s poem of that name merely confirms his disenchantment with a world insensible to suffering and morality. Another poem from his stay, ‘Rimbaud’, entertains for the first time the idea of running away permanently from Europe’s clever hopes and empty promises. The indifference of the city towards human unsuccess led Auden to fantasise, like Rimbaud, Marlow and Lord Jim, some complete break with Europe, only to acknowledge, in ‘Hong Kong’ and ‘Macao’, those sketches of a Conradian Eastern world also written in Brussels, that such faraway places are merely unreal, comic-opera reinstatements of the European illusion.

Stan Smith
Nottingham Trent University

Mary-Kay Wilmers’s Diary is rather unfair. But her remarks do illustrate an observation which Fanny Burney attributed to one of the characters in Cecilia: ‘Travelling is the ruin of all happiness! There’s no looking at a building here after seeing Italy.’ The young Wilmers’s ‘Italy’ was New York. I first went to Brussels on a school visit in 1946 with only the experience of war-weary London. I found a magical city full of neon lights, wonderful restaurants and tins of fruit. The sun in that city was always shining.

Brian Taylor
Walton-on-Thames, Surrey


The Stephen Lawrence Case

John Upton (LRB, 1 July) implies that in arresting the five suspects in the Stephen Lawrence case for the murder, the police were exercising a technical power that it was somehow unfair to use in the absence of conclusive evidence of guilt. In my experience, as someone who has practised criminal law for eight years both as a Crown Prosecutor and a criminal defence solicitor, it is almost unheard of for the police not to arrest anyone they reasonably suspect of having committed a serious offence.

Given the way the police were handling the Lawrence investigation, can anyone be surprised that the Lawrence family's legal representative Imran Khan took it on himself to obtain a statement from Duwayne Brooks? I cannot comment on the strength of the prosecution case, but I can say that it is not unusual for a prosecution to be mounted on the strength of the uncorroborated evidence of one witness alone – in this instance, that of Duwayne Brooks. There have been a number of successful prosecutions of paedophiles on the uncorroborated evidence of their victims, even though the crimes involved took place a decade or more ago. The same is true of rape cases. Nor is it unusual for the defence, the prosecution and the court to take different views of the same evidence.

To suggest that this was a weak case which should not have been taken any further simply because the CPS was of that opinion is to assume that the CPS always gets it right. It doesn't. Between 30 and 50 per cent of prosecutions mounted by the CPS in the Crown Court which result in contested trials end in the acquittal of the person(s) charged. This is not to suggest that the CPS is sloppy or incompetent. Deciding whether there is sufficient evidence in any particular case for a prosecution to succeed is not an exact science. That the judge took the decision to exclude Brooks's identification evidence does not mean that every judge would have made the same decision or that to admit such evidence would have been wrong. Upton accuses Michael Mansfield of attempting to manipulate the rules of evidence in order to admit evidence which should not have been admitted and thus of trying to deny the defendants their rights. But this is the essence of advocacy and takes place every day in the courts.

The McPherson Inquiry was set up as a direct result of the failure of the police to do their job properly. Whether we care for its recommendations or not, it is wrong to characterise it as a kangaroo court.

Norman Cho
London E2

John Upton’s attempt to deflate the ‘cultural balloon with Stephen Lawrence’s image on it’ was a myopic exercise in not seeing the political wood for the legalistic trees. Of course there is almost certainly no clear evidence for the prosecution of the five main suspects. Why not? Because the investigation was never carried out in a way likely to get evidence. Why not? Because the Met is institutionally racist – getting that clearly and publicly established is the great service performed by the McPherson Inquiry. Those of us active in campaigns for other black people who have been failed by the police – Michael Menson, Ricky Reel, Christopher Alder – are still waiting for real change.

Richard MacSween
Justice for Christopher Alder Campaign Colne, Lancashire


Out of Sight, out of Mind

George Barnard (Letters, 29 July) seems to have misunderstood Frank Kermode, who, in his review of Ben Rogers’s A.J. Ayer: A Life, said not that ‘Ayer never met Wittgenstein’ but that ‘at Ryle’s suggestion he gave up the idea of sitting at Wittgenstein’s feet in Cambridge and instead went to Vienna to work with Moritz Schlick.’ The two men did meet, on at least two occasions, both of which are described by Rogers, as they were earlier, and more fully, described by Ayer himself, in Part of My Life. Rogers and Ayer give divergent accounts of Ryle’s reasons for recommending that Ayer should study with Schlick rather than Wittgenstein. According to Rogers, Ayer’s ‘first thought had been to work under Wittgenstein at Cambridge. Ryle, however, argued that the veneration Wittgenstein expected from his students was bad for both teacher and pupil’ and Ryle ‘must have realised that Ayer was particularly ill-suited to sit at anyone’s feet’. But Ayer’s account is as follows:

My first inclination was to spend this time in Cambridge, learning all that I could from Wittgenstein, but Gilbert Ryle had what he thought was a better idea. He had met Moritz Schlick … and been very impressed by him. He therefore suggested that I should go to Vienna, enrol myself at the University, and learn as much as I could of the work that the Vienna Circle was doing. As almost nothing was known about them in England, he represented to me that by coming back with a report of their activities I should not only be benefiting myself but performing a public service.

Philip Hoy
London N4


Tennis Lessons

Edward Said (LRB, 1 July) is entirely justified in complaining about the unbridgeable gulf that now exists between even a decent amateur player and a professional, a gulf which, although it certainly existed back in faux-amateur days, could at least be stared across and once in a while, for a couple of hours, jumped over. In some inexact year of the early Twenties, before my time though not much before, the British Davis Cup team was barnstorming in Ontario and stopped for a match in Woodstock, where one of its players fell ill and a call went out for any local who might replace him in one of the two singles matches. My father, a fine athlete and pretty good tennis player, not long back from the war, was nominated. He knew he was outgunned and decided – what the heck – to hit every ball as hard as he could and to go for every line. He won the match. Of course the two teams were not the world's best; of course it was not a famous stage, but still: nobody in the same position would today ever come close to Henman, to Rusedski, or to tour players a thousand places below those two.

Don Coles
Toronto


Anyone for tip-cat?

Richard Taylor (Letters, 29 July) does not even consider the possibility that, far from having been carried to India from England, tip-cat might have come to Gloucestershire from India. Polo, of course, is the most clear-cut case of such a phenomenon; and I have seen it stated that in Canada the natives played a game not dissimilar to lacrosse, which European invaders took up. They changed the name, changed the rules and began teaching it back to the natives. This has not exactly happened with chess, another game said to have been invented in India; but it could be argued that Indian numerals, of which the Arabic are merely a modification, have been used in the same way as lacrosse, rewritten and taught back so that the originals have been superseded. One must, however, draw the line somewhere; and I would not go so far as to claim that snooker, proficiency at which is the proverbial sign of a misspent youth, was also an Indian invention. Now I come to think of it, though, it was invented in India, but by an Englishman, at Jubbulpore. If the Indians did not invent the game, they at least provided Sir Neville Chamberlain, an officer in the Devonshire Regiment in the 1870s, with the leisure to do so.

George Chowdharay-Best
London SW3


Chef de Codage

Brian Rotman (LRB, 15 July) is wrong when he writes that because of the SOE’s disastrous mistake in what the Germans (and the Dutch) called the ‘Englandspiel’, ‘there was no Dutch resistance at work when Northern Europe was liberated.’ There certainly was and it was the better for having no contact with the Dutch agencies in England. The cost of SOE’s ‘mistake’ was, however, quite high. Of 44 men dropped into Holland, 42 were immediately arrested and then sent to camps. All of them were murdered before the war was over, though the Germans had promised them their lives. Two men escaped to Switzerland. The Germans succeeded in leaking the rumour that they were German agents and they had a tough and lengthy struggle to get themselves believed and sent back to England, where they put the record straight.

Hans Koning
Southport, Connecticut


Three Degrees

A friend who writes from Germany evidently likes my poem ‘The Bells of Saint Babel’s’ (LRB, 10 June) but points out the navigational impossibility of ‘West/Longitude one-/eighty-three’. I wouldn’t excuse myself to her, or to any other reader similarly troubled, by arguing that a poem which submerges Mt Everest in the Pacific may be allowed a small liberty in fixing the Kermadec Trench: the truth being that in consulting my excellent, detailed map of the sea floor in this hemisphere, I added three degrees to the 180 instead of subtracting them. Vanity hardly knows whether to hope the variant will be noted, or pass unnoticed, next time I print the poem.

Allen Curnow
Auckland