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Duesberg’s math incorrect, say bloggers


Are HIV dissenters refusing to admit imperfection?

What is correct formulation, then?

Interesting comment sparked today by our humungous Comment thread after the Larry Altman’s Guide to AIDS Conferences post on the Good Math Bad Math blog comment and thread Pathetic Statistics from HIV/AIDS Denialists by Mark Chu-Carroll, which Tara Smith points to in Aetiology in her post today on AIDS denial and creationism–common thread of bad statistics.

Tara C. Smith (she of the beautiful and bounteous physique as displayed prominently on every page of her in consequence always delightful blog) is an epidemiologist who deplores HIV∫AIDS rethinkers as setting a very bad example in their reasoning in many respects:

Regular readers are very familiar with my refrain that many science deniers use the same tactics: bad arguments, quote-mining, appeals to authority, castigation of originators of respective theories, etc. etc. Another common thread is the complete bastardization of statistical analysis.

Not sure what “castigation of originators of respective theories means”, but her decisive rejection of HIV∫AIDS rethinking has been a feature of her blog for some time. Now she is pleased to find that HIV∫AIDS rethinkers may have perpetrated an incorrect mathematical formulation, and that Mark has jumped on it after Chris Noble, in the wake of the discussion here, alerted him.

The basic point is that Duesberg is said to be wrong and statistically naive to have said “Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission.”

The blogger, Mark C. Chu-Carroll, self-described as “a Computer Scientist working as a researcher in a corporate lab. My professional interests run towards how to build programming languages and tools that allow groups of people to work together to build large software systems’, writes:

“While I was on vacation, I got some email from Chris Noble pointing me towards a discussion with some thoroughly innumerate HIV-AIDS denialists. It’s really quite shocking what passes for a reasonable argument among true believers.

“The initial stupid statement is from one of Duesberg’s papers, AIDS Acquired by Drug Consumption and Other Noncontagious Risk Factors, and it’s quite a whopper. During a discussion of the infection rates shown by HIV tests of military recruits,” he says:

(a) “AIDS tests” from applicants to the U.S. Army and the U.S. Job Corps indicate that between 0.03% (Burke et al.,1990) and 0.3% (St Louis et al.,1991) of the 17- to 19-year-old applicants are HIV-infected but healthy. Since there are about 90 million Americans under the age of 20, there must be between 27,000 and 270,000(0.03%-0.3% of 90 million) HIV carriers. In Central Africa there are even more, since 1-2% of healthy children are HIV-positive (Quinn et al.,1986).

Most, if not all, of these adolescents must have acquired HIV from perinatal infection for the following reasons: sexual transmission of HIV depends on an average of 1000 sexual contacts, and only 1 in 250 Americans carries HIV (Table 1). Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission. It follows that probably all of the healthy adolescent HIV carriers were perinatally infected, as for example the 22-year-old Kimberly Bergalis (Section 3.5.16).”

Computer Scientist Mark continues: “Now, I would think that anyone who reads an allegedly scientific paper like this would be capable of seeing the spectacular stupidity in this quotation. But for the sake of pedantry, I’ll explain it using small words.”

Special note: Here (click “show” below) follows a step by step analysis of what Computer Scientist Mark and Blog Commentator Noble argued was incorrect about the phrase highlighted in bold.

(show)

[TS interjects: Thanks, Mark, for the promise to use small words, since we are glad to see spectacularly bad math corrected, but find probability one of the deeper mysteries of life. But let’s remember that even though the math may be wrong, perhaps because the phrasing is incorrect, the basic point, that sexual transmission is too rare to support an epidemic, may still stand. If it does, the error is not particularly important, though it may be imperfect math/stats. Duesberg is not a mathematician. However, it was presumably questioned and checked by his friendly colleagues and by the peer reviewers so you are certainly exposing a lot of people as having missed a “spectacular error”.]

“If the odds of, say, winning the lottery are 1 in 1 million, that does not mean that if I won the lottery, that means I must have played it one million times. Nor does it mean that the average lottery winner played the lottery one million times. It means that out of every one million times anyone plays the lottery, one person will be expected to win.

[TS: Obviously correct, and well phrased. But is it a match for what Duesberg said?]

“To jump that back to Duesberg, what he’s saying is: if the transmission rate of HIV/AIDS is 1 in 1000, then the average infected person would need to have had sex with an infected partner 1000 times.

[TS: OK, but let’s be clear. He is saying that on average an infected person must have been exposed 1000 times to an infected partner. Is that not true? Apparently you don’t think so, so let’s see.]

“Nope, that’s not how math works. Not even close.

Suppose we have 1000 people who are infected with HIV, and who are having unprotected sex. If we follow Duesberg’s lead, and assume that the transmission rate is a constant 0.1%, then what we would expect is that if each of those 1000 people had sex with one partner one time, we would see one new infected individual – and that individual would have had unprotected sex with the infected partner only one time.

This isn’t rocket science folks. This is damned simple, high-school level statistics. “

[TS: Certainly seems likely to be true. If 1000 people all screwed once with a positive partner, with a 1 in 1000 chance, one should become positive. Now is this meaningfully different from the above, or simply a variation on the way of looking at the problem? How long would it take for all the 1000 people to become positive? Presumably for ALL of them to become positive, it would take 1000 screws each, before the last one converted. Obviously if they stopped when they became positive, only the last one would need 1000 screws. But if they didn’t know and just kept on screwing, wouldn’t it take 1000 screws for all? And if the chances of their partner being positive was 1 in 250, wouldn’t it take 250,000 screws in all?

Isn’t that what Duesberg is saying? That for any number in the population to become positive, taken as a whole every one of them would have to screw 1000 times until the very last one was infected by a positive partner. And if there are Y positives in the population Z to start with, then it would need 1000 (Z/Y) screws – in this case, 250,000?]

Mark continues with an evisceration of TS’s evidently moronic try at refuting his friend Chris Noble:

“Where things get even sadder is looking at the discussion that followed when Chris posted something similar to the above explanation. Some of the ridiculous contortions that people go through in order to avoid admitting that the great Peter Duesberg said something stupid is just astounding. For example, consider this from a poster calling himself “Truthseeker”:

If Duesberg had said that, he would indeed be foolish. The foolishness, however, is yours, since you misintepret his reasoning. He said, as you note

Most, if not all, of these adolescents must have acquired HIV from perinatal infection for the following reasons: sexual transmission of HIV depends on an average of 1000 sexual contacts, and only 1 in 250 Americans carries HIV (Table 1). Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission.”

[TS: This states the average transmission requires 1000 contacts, not every transmission. With such a low transmission rate and with so few Americans positive – you have to engage with 250 partners on average to get an average certainty of 100% for transmission, if the transmission rate was 1. Since it is 1 in 1000, the number you have to get through on average is 250,000. Some might do it immediately, some might fail entirely even at 250,000. But the average indicates that all positive teenagers would have had to get through on average 250,000 partner-bouts.

But Mark evidently thinks this is wrong. Darned if we can see it!]

“Truthseeker is making exactly the same mistake as Duesberg. The difference is that he’s just had it explained to him using a simple metaphor, and he’s trying to spin a way around the fact that Duesberg screwed up.

[TS: This is disappointing, since we had hoped Mark was going to explain where we went wrong. Does it imply that we were right? Surely not. But he doesn’t actually SAY we were wrong. Phew! We got off lightly, with not even a “moron” in the dismissal.

But were we right? He implies we are not. But what is wrong with what we said? That is what we need to know.

Perhaps Duesberg’s “all” is wrong too, as in” Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission.” Perhaps “all” should be “typical”.

What would the correct statement have been, then? Mark doesn’t say. The trouble is any way we look at it, it looks OK to us. We vaguely remember looking at this striking statement in the draft of Duesberg’s article, and double checking to see if it was true, and deciding it was. Apparently this was an error, but we still cannot see why.

Surely it is true to say, “Thus, since there is a 1 in 1000 chance of transmission, any positive teenager would have had to achieve an absurd average 1000 contacts with a positive partner to acquire HIV by sexual transmission.”

Isn’t it then true to say, if there are only 1 in 250 in the population at large who are positive, “Or an even more absurd average 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission.

Whatever, we cannot fathom the error, and nor can a consultant who is not a mathematician but pronounced the statement in his opinion “flawless”.]

Mark continues: “But it gets even worse. A poster named Claus responded with this indignant response to Chris’s use of a metaphor about plane crashes:

CN,

You would fare so much better if you could just stay with the science points and refrain from your ad Duesbergs for more than 2 sentences at a time. You know there’s a proverb where I come from that says ‘thief thinks every man steals’. I’ve never seen anybody persisting the way you do in calling other people ‘liars’, ‘dishonest’ and the likes in spite of the fact that the only one shown to be repeatedly and wilfully dishonest here is you.

Unlike yourself Duesberg doesn’t deal with matters on a case-by-case only basis in order to illustrate his statistical points. precisely as TS says, this shows that you’re the one who’s not doing the statistics, only the misleading.

In statistics, for an illustration to have any meaning, one must assume that it’s representative of an in the context significant statistical average no? Or perphaps in CN’s esteemed opinion statistics is all about that once in a while when somebody does win in the lottery?

Mark says “Gotta interject here… Yeah, statistics is about that once in a while when someone wins the lottery, or when someone catches HIV, or when someone dies in a plane crash. It’s about measuring things by looking at aggregate numbers for a population. Any unlikely event follows the same pattern, whether it’s catching HIV, winning the lottery, or dying in a plane crash, and that’s one of the things that statistics is specifically designed to talk about: that fundamental probabilistic pattern.”

But never mind we’ll let CN have the point; the case in question was that odd one out, and Duesberg was guilty of the gambler’s fallacy. ok? You scored one on Duesberg, happy now? Good. So here’s the real statistical point abstracted, if you will, from the whole that’s made up by all single cases, then applied to the single case in question:

Thus, all positive teenagers would have had to achieve an absurd 1000 contacts with a positive partner, or an even more absurd 250,000 sexual contacts with random Americans to acquire HIV by sexual transmission.

This is the statistical truth, which is what everybody but CN is interested in.

Mark rejects this out of hand:

“Nope, this is not statistical truth. This is an elementary statistical error which even a moron should be able to recognize.”

Reminder: Whenever somebody shows a pattern of pedantically reverting to single cases and/or persons, insisting on interpreting them out of all context, it’s because they want to divert your attention from real issues and blind you to the overall picture.

Mark: “Reminder: whenever someone shows a pattern of pedantically reverting to a single statistic, insisting on interpreting it in an entirely invalid context, it’s because they want to divert your attention from real issues and blind you to the overall picture.

“The 250,000 average sexual contacts is a classic big-numbers thing: it’s so valuable to be able to come up with an absurd number that people will immediately reject, and assign it to your opponents argument. They can’t let this go, no matter how stupid it is, no matter how obviously wrong. Because it’s so important to them to be able to say “According to their own statistics, the HIV believers are saying that the average teenage army recruit has had sex 250,000 times!”. As long as they can keep up the pretense of a debate around the validity of that statistic, they can keep on using it. So no matter how stupid, they’ll keep defending the line.”

[TS: OK, Mark, but what is the correct statement and why?

The Comments don’t seem to reveal the answer so far:

Comments

see probability tree for putative rate of infection given rate assumptions.

caution! unrealistic!

Posted by: ekzept | September 4, 2006 02:31 PM

Well… Okay, then what would a valid analysis of the numbers indicate?

Assuming the articles sources weren’t afflicted by similar bad logic, we have that between 0.03% and 0.3% of the (presumably all healthy, as I doubt anyone with full-blown AIDS is applying to the USMC) applicants to the USMC present as HIV positive. Meanwhile, a stat. that is used (without background source) is that 0.4% of the population as a whole is HIV-positive. (the vast, vast majority of those without any symptoms)

So where does this lead us? Frankly, I don’t know. If we assume that prior to being tested, each teenager’s number of partners and number of unprotected intercourse occasions/partner followed a poisson distribution, then in theory one could come up with estimates for both the number of partners and number of encounters/partner. (Though the two estimates might depend on each other)

However, I don’t think I could. At this point I’d reach for the discrete computer simulation and just let it crunch.

Posted by: Daniel Martin | September 4, 2006 04:10 PM

the point of my tree is that with the assumptions Duesberg makes, it’s not likely anyone could get HIV, let alone AIDS. thus, his assumption of independence is not correct.

for example, assuming that indeed the risk of HIV given random unprotected couplings in a U.S.-like population is 1 in 250000, the inverse cumulative probability of a binomial model seeking the number of couplings needed to have a 0.9 chance of acquiring HIV suggests 100000.

unbridled assumptions of independence will necessarily make the risk estimates smaller.

Posted by: ekzept | September 4, 2006 04:50 PM

At this point I’d reach for the discrete computer simulation and just let it crunch.

that won’t work unless the prevalence of HIV among preferred sexual partners is modelled. it’s just not correct that everyone in the population has as much likelihood of coupling with a particular person as any other, even correcting for gender preferences. is there an epidemiologist in the house? 😉

Posted by: ekzept | September 4, 2006 04:56 PM

BTW, the emphasis has been on Duesberg’s misuse of statistics, which is bad enough, but it’s important to understand why he’s doing that. he’s trying to do an argument that not only isn’t HIV not related to AIDS, it isn’t even a coherent disease. that’s his motive. in short, he’s trying to do a “climate change denier” kind of thing on HIV and AIDS.

Posted by: ekzept | September 4, 2006 04:59 PM

One poster does say what everyone knowledgeable, such as Bialy or Brown, on our thread seemed to say, that a correct statement isn’t possible.

Well… Okay, then what would a valid analysis of the numbers indicate?

Assuming the articles sources weren’t afflicted by similar bad logic, we have that between 0.03% and 0.3% of the (presumably all healthy, as I doubt anyone with full-blown AIDS is applying to the USMC) applicants to the USMC present as HIV positive. Meanwhile, a stat. that is used (without background source) is that 0.4% of the population as a whole is HIV-positive. (the vast, vast majority of those without any symptoms)

So where does this lead us? Frankly, I don’t know. If we assume that prior to being tested, each teenager’s number of partners and number of unprotected intercourse occasions/partner followed a poisson distribution, then in theory one could come up with estimates for both the number of partners and number of encounters/partner. (Though the two estimates might depend on each other)

However, I don’t think I could. At this point I’d reach for the discrete computer simulation and just let it crunch.

Posted by: Daniel Martin

We conclude for the moment that Duesberg may have been wrong in his formulation of the low odds that any one person would achieve a positive status with heterosexual sex, but that the mathematically inclined don’t have a simple corrected formulation, and that the force of his important point remains the same: the chances of heterosexual transmission are too low to support an epidemic, let alone a pandemic.

If this is true, it seems silly not to have a simple correct formulation of the risk. This post will be updated if this puzzle is properly solved.

UPDATE 1 Sep 5 3.11 pm: A couple of interesting points stand out from Aetiology in the Comments following Tara Smith post:

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None of the “rethinkers” have really admitted to the mathematical mistake inherent in the Duesberg Fallacy. Most of them still insist that in some way Duesberg is still correct. The few that have sufficient mathematical training choose not to comment on this issue. They neither admit to the error nor attempt to refute anything that I stated. -Chris Noble

Also

But I was making an entirely different point – that 1 in 15 or 1 in 1000 makes a huge difference in whether the virus could account for a pandemic. Huge.”

———-

Really? Here’s some assumptions: 1 in 250 americans has HIV. 1 million people. If 1 in 10 of them has unprotected sex on a given day, that is 100,000 people. So, 100 people would get HIV every day, based on a 1/1000 infection rate. In 1000 days, you have 100,000 new cases, which is a lot. Is this end of the world stuff? No. A serious health problem? A good sized city getting a mortal disease every 3 years? Yeah. – Seth Manapio

But a “pandemic”? No. Even with those assumptions, giving you the complete benefit of the doubt…

35 million African AIDS cases… hmmmmmm. I’ll leave the facts about HIV causing AIDS to those who know the science. Just don’t try to sell me on the fact that what’s happening is primarily due to sexual transmission. Duesberg was COMPLETELY WRONG in his use of the statistics as Tara says. But the statistics STILL show that there is no AIDS pandemic caused primarily through sexual transmission. – End Times

The line of reasoning followed by Seth Manapio is interesting. There is apparently more potential for an epidemic that one might suppose. Using the same logic, in the US, supposing every one of the million positives engaged in one sex act with a negative. If as the mathematicians say, a chance of 1 in 1000 means that for every 1000 bouts, one transfer of HIV will take place, this means that a million would result in 1,000 more positives. Ignoring the fact that some of the million are in high risk groups, this might mean that at the rate of sex twice a week, you could get 2,000 a week, or 100,000 a year.

This offers the outside chance of an epidemic, it seems, although the assumptions are rather optimistic. For rethinkers to deny the possibility outright, it may be necessary to emphasize that Padian in fact found no transmission at all in more than a score of couples who took no methodical precautions over six years. The 1 in 1000 rate was purely a tipping of Nancy Padian’s hat to the paradigm, in the form of retrospective calculation of supposed HIV transfer earlier in couples included in the trials. The actual data showed no HIV transmission whatsoever.

Some other points worth noting:

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None of the “rethinkers” have really admitted to the mathematical mistake inherent in the Duesberg Fallacy. Most of them still insist that in some way Duesberg is still correct. The few that have sufficient mathematical training choose not to comment on this issue. They neither admit to the error nor attempt to refute anything that I stated. -Chris Noble

But if you accept that it would take 1 in 1,000 sexual encounters with an HIV+ person in order to pass on HIV, while any ONE CASE would indeed only need come from ONE single sexual encounter, it would be mathematically improbable to have a wide-spread epidemic.

This isn’t rocket science either. You would need a thousand million incidents of HIV- persons having unprotected sex with HIV+ partners in order to have just a million new cases of HIV. Now think of the “35 million African AIDS cases” and see if the math works for sexual transmission at the root of the plague. – End Times

Additionally, the 1 in 1000 stat hasn’t been found in all studies. Others have found it to be much higher in Africa, as much as 1 in 80 encounters. Additionally, I’ve mentioned before that it can increase due to other factors as well, such as co-infection with herpes virus, which increases the odds by as much as a factor of 5.- Tara C. Smith

If you want to start claiming at the actual math in Africa is actually about 1 in 15 when you factor in herpes, then we have a whole different argument that would probably start with some pretty strong challeges to those numbers, but nonetheless is, again, a wholey different subject.

A world-wide epidemic based on 1 in 1000 is astronomically improbable.- End Times

I’m not arguing the actual numbers at all. It doesn’t matter what the actual figure is, whether it’s 1 in 15 or 1 in 1000. What matters is the way Duesberg applies that: that you’d have to actually go *through* 15 parters, or 1000 partners, in order to become infected. That is the problem with it. -Tara Smith

You are absolutely right if the only point you want to make is that Duesberg’s math was wrong.

But I was making an entirely different point – that 1 in 15 or 1 in 1000 makes a huge difference in whether the virus could account for a pandemic. Huge.

Steve’s well-taken insights about stats and evolution don’t apply to this. If it was 1 in thousand 20 years ago and is 1 in 1000 today, it has little chance of creating a pandemic. I can say this with confidence, even while fully accepting that anyone could have unprotected sex one time and contract HIV.

Posted by: End Times |

Duesberg also makes completely false assumptions. He assumes that all of the HIV+ 17-19 year old military recruits acquired HIV through heterosexual contacts. This is unlikely to be true. Other acts have much higher risks and would be likely to account for a large proportion of seroconversions. Duesberg also assumes that HIV prevalence is randomly distributed through the entire population. It isn’t. It is largely confined to specific risk groups such as men who have sex with men and injecting drug users. Teenagers that also belong to these risk groups are a) going to experience higher risks per contact and b) see a much higher prevalence of HIV than the ~1/250 national average.

Of course “rethinkers” will debate these issues but the totally damning thing in this case is that the maths in itself is totally and utterly wrong. There is no weasel room for “rethinkers”.

Posted by: Chris Noble

As Chris Noble points out, in the real world, people do not have sex with random samples of the general population. Truck drivers in Africa with untreated STDs who regularly have unprotected sex with truck-stop prostitutes, and a men who very frequently have unprotected receptive anal sex with numerous men in bath-houses, are at very high risk of infection. HIV infection does not spread randomly through the general population but is correlated with a number of other factors, such as those in my examples. Furthermore, as more people become infected the probability of transmission increases exponentially, and as more people receive treatment and live longer the more chance they have of spreading infection.

Posted by: DeanOr

But I was making an entirely different point – that 1 in 15 or 1 in 1000 makes a huge difference in whether the virus could account for a pandemic. Huge.”

———-

Really? Here’s some assumptions: 1 in 250 americans has HIV. 1 million people. If 1 in 10 of them has unprotected sex on a given day, that is 100,000 people. So, 100 people would get HIV every day, based on a 1/1000 infection rate. In 1000 days, you have 100,000 new cases, which is a lot. Is this end of the world stuff? No. A serious health problem? A good sized city getting a mortal disease every 3 years? Yeah. – Seth Manapio

But a “pandemic”? No. Even with those assumptions, giving you the complete benefit of the doubt…

35 million African AIDS cases… hmmmmmm. I’ll leave the facts about HIV causing AIDS to those who know the science. Just don’t try to sell me on the fact that what’s happening is primarily due to sexual transmission. Duesberg was COMPLETELY WRONG in his use of the statistics as Tara says. But the statistics STILL show that there is no AIDS pandemic caused primarily through sexual transmission. – End Times

I just had an amusing thought.

Perinatal transmission is 25-50% efficient. If as Duesberg claims the 17-19 year old military recruits all acquired HIV perinatally then they must have on average been born 2 to 4 times according to his “logic”. – Chris Noble

Just don’t try to sell me on the fact that what’s happening is primarily due to sexual transmission.

Well, that’s a rather separate topic. In fact, we know it’s not primarily sexually transmitted in some areas of the world. The maps here, for instance, emphasize that the epidemic in China and Russia is due largely to IV drug use, while in India and Africa it’s largely sexually transmitted. It’s difficult to make any generalizations about the epidemiology from one place to another.

Posted by: Tara C. Smith

Isn’t a “pandemic” just an outbreak of a disease that is new, infectious and capable of spreading sustainably throughout the population? If so, HIV/AIDS seems to qualify, even at 1/1000 transmission rates with infected people having one sexual encounter every 10 days… an absurdly low number, considering that 1/3 of americans have sex twice a week or more and we would expect a disproportianately high number of HIV positive people to fall within this group.

But yes, I would agree that if you see transmission rates far higher than expected from sexual transmission, it is probable that either there are other vectors at work or else there is a novel variant of the pathogen that is more easily transmitted. Is this a controversial point? – Seth Manapio

IF HIV is passed, genome to genome, then the relatively stable number of nationwide cases of HIV infection would be explainable based on a 25-50% rate with an average of about 3 births per mother (a little higher than the national average. About what you might expect in poorer families).

Just a thought for discussion. – End Times |

No, you need somewhere on average of around 3 daughters per mother all of whom live long enough to have children.

Men don’t give birth.

At 3 daughters per mother the population would triple every generation! – Chris Noble |

t is also rather ironic that the link that Bialy gives for this claim:

Retroviruses (of which HIV is a classic example) are normally transmitted in the wild through perinatal routes (that is from mother to child), making them endemic rather than epidemic microbes

contains this sentence:

Since the virus is not endemic in the U.S., it is transmitted more often by parenteral exposures associated with risk behavior (see below) than perinatally. – Chris Noble |

SOLUTION to the Problem Found (Sept 7 Thu 10.08 AM)

After extended discussion in the Comments to this post, Robert Houston contributed the definitive correction to Duesberg, which revealed that the objections of Chris Noble and Mark Chu-Carroll while correct were trivial and had no effect on the argument advanced by Duesberg. The implication of the stats for heterosexual transmission were as absurd as ever.

Here is the conclusion from in Comments:

Final conclusion: No great error, and the significance stays the same.

Robert Houston has demonstrated that it is indeed not a very great statistical error, and not one which changes the thrust of Duesberg’s point, which is that whichever way you look at it, Duesberg, Noble or Houston, the amount of sex necessary to make sexual transmission a primary route of transmission is absurd.

This is his correction to Duesberg’s paragraph:

“Sexual transmission of HIV depends on an average of 1000 sexual contacts and only 1 in 250 Americans carries HIV… Thus all positive teenagers represent the achievement (by the teenager or his group) of an absurd average of 1000 contacts with a positive partner or an even more absurd 250,000 contacts with random Americans to acquire HIV by sexual transmission.”

In Comments, Noble’s ineffective response indicated he was unable to quarrel with this, Houston’s correct reformulation of Duesberg’s point.

Houston’s reasoning:

The chances of one person contracting HIV from random sex is still 1 in 250,000. In fact, if you take into account Nancy Padian’s study five years later (1997) the chances for negative males to catch HIV in a contact with a positive female are properly 1 in 9000, not 1 in 1000, so the number of random contacts would have to be 2,250,000, which is indeed “even more absurd”, in Duesberg’s phrase.

Noble correctly noticed that the 1 in 3000 positive recruit was part of a group of 3000 that included 2999 negatives, and the chance of contracting the Virus from random contacts had to be spread over the whole group, so the average number of random contacts needed per recruit would not be 250,000 but 250,000/3000 = 83.

The restatement is the outcome of the simple four assertions Houston made:

1) Given Duesberg’s assumptions, the chances for a particular individual to contract HIV heterosexually remain 1:250,000.

2) The chance for such transmission to occur to anyone in a group at the proportion found in teenage recruits (0.00034 or 1/3000) would be one in 250,000/3000 or 1 in 83.

3) Each HIV positive case would still represent an average of 250,000 contacts occurring in the group.

4) But the group average of 83 contacts per member would yield one positive case (83 x 3000 = 250,000).

Does not change absurdity Duesberg referred to

The only significant issue is whether this is still an absurd level of sexual contacts. Is it unexceptional that recruits into the Army aged under 20, by definition, – ie 17.5-19.9 years – could get through an average 83 encounters before being inducted?

If it is not absurd but a reasonable assumption, then heterosexual transmission of HIV might be a significant factor in the spread of the Virus, and perinatal transmission wouldn’t be the only conventional (not high risk ie not IV drug use with dirty needles or gay sex) route indicated.

Well, fairly obviously the absurdity is still there, analysis will show. With the 1997 Nancy Padian correction of 2,250,000 contacts the whole group needs to yield one new positive, that means 750 encounters per male, average. Absurd on the face of it for any 17-19 year old.

Using the original assumption of 1 in 1000 risk for female to male, the 250,000 total contacts needed for one positive and the 2999 that accompany him, or 83 contacts per male, all 3000 of them, might seem more or less possible at a huge stretch as average experience at 18. However, the US Job Corps study quoted by Duesberg in the same paragraph showed a ten times higher rate among their recruits, who were disadvantaged youths, ie mostly blacks and Hispanics. Among them the rate of HIV positivity was 1/300 (actually 1/270), ten times as much as the 1/3000 of the Army recruits, which would require an average 830 total sex encounters per male.

Since there is also information that one third of youths at 18 are or were virgins, or to be more precise 35%, you have to add 50% to the total, which would make it 1277 sex encounters. This is equivalent to saying that the average 18 year old recruit had 13 years of happy marriage under his belt (that would be twice a week or 100 per year).

Not very likely, in fact, quite impossible. In fact highly absurd. Especially when you look at Padian and find the 1/1000 risk applies to women, and the risk for men infected by women is 1/9000. So Padian would add nine times more sex bouts for men, as opposed to women, which comes out as 11,492 each – 115 years of happy marriage for each active adolescent!

At the age of 18, that is to say, they would need 115 years of sexual experiences at the outstanding happy level of twice a week.

Supporters of the paradigm attempt to argue that the 2005 Uganda study by Wawer et al changes this picture for Africa at least by showing a higher risk of transmission of 1/833, but the male use of condoms in the study was negligible, and there is no information as to whether the 1/833 risk estimate is for male or female.

So the level of sexual experience demanded to account for the positives at this young age is still absurdly high and it is clear that perinatal transmission has to be the overwhelmingly important vector for HIV transmission, with added contributions from IV drug use and gay sex. This was Duesberg’s point, precisely, still supported by the figures he used, and even more glaringly by the updated figures from later studies (Padian 1997 etc).

In a nutshell, the figures for black and Hispanic recruits to the Job Corps are ten times higher than for whites, and one third are virgins. So the rate of sexual activity required to account for the 1/300 black recruits found to be positive at 18 would be 12 times a week – from birth.

AS Duesberg worked out, the idea that sexual transmission accounted for most of these positives, rather than perinatal transmission (with a few from IV drug use and gay sex, of course) is indeed absurd.

An unwitting tribute to Duesberg’s quality

So what can the insulting Web mathematicians really claim as an error in Duesberg’s mistaken phrasing? Not much, beyond a misstatement of the probabilities which overreached in making his point more striking than it deserved. But it remains irrefutable, and there is no change relevant to the great debate.

So if anything the strenuous efforts over years by small players who have limited understanding of the entire debate to shoot holes in Duesberg’s massively constructed critique are exposed by themselves as especially ineffective by their behavior in this case. For apparently his errors are so rare that they must crow, insult and wax ecstatic over a trivial correction which doesn’t change Duesberg’s point one iota.

Even mathematicians can be caught

Indeed, even the probability correction that has to be made – and a comment poster reveals that the point was granted by Duesberg six months ago – doesn’t provide anything to crow about. This may be elementary statistics and probability, but it isn’t obvious, and there is no reason to be childishly scathing and triumphant, as Mark the Computer Scientist is, and some of the posters in Comments below. Puzzles like this have caught droves of otherwise smart people. The correct apprehension of risk and probability is famously one of the least intuitive perceptions for most people.

Fo example, the notorious problem of the Monty Hall game show, where two closed doors hide a worthless prize, such as an apple, and the third closed door hides a Lamborghini. The contestant chooses a door and the game show host Monty flings open one of the other doors to reveal an apple.

Monty then asks the contestant if he/she wants to change the door they picked for the other closed door, as if that might change their chances. Would you change?

The reasoning on the right answer is simple and obvious once you think about the problem enough, but droves of people got it wrong when the New York Times featured the puzzle on the front page a decade ago, after the woman with the highest IQ in the world, Marilyn vos Savant put it in her Parade column, and tons of people got it wrong there too.

Among the university professors scolding her for innumeracy were mathematicians, so we suggest that readers here don’t automatically credit Duesberg’s Web critics, especially the ones who are snotty, which quite often goes with a mistake, amusingly enough.

210 Responses to “Duesberg’s math incorrect, say bloggers”

  1. Chris Noble Says:

    Duesberg assumes in his “statistical” analysis that the transmission risk is a constant 1/1000.

    It isn’t constant. In acute infection it is much higher.

    Any model that uses a constant transmission risk is seriously flawed.

    The estimates of HIV transmission risk such as the Padian study have monogamous couples where the infected partner is not in the acute infection period.

  2. john Says:

    The estimates of HIV transmission risk such as the Padian study have monogamous couples where the infected partner is not in the acute infection period.

    But, Chris, where are the studies, which show what happens in the acute period?

    If you look at the paper from CDC (January 2005), you have the references for their data :

    Donegan E, Stuart M, Niland JC, et al. Infection with human immunodeficiency virus type 1 (HIV-1) among recipients of antibody—positive blood donations. Ann Intern Med 1990;113:733—9.

    Kaplan EH, Heimer R. HIV incidence among New Haven needle exchange participants: updated estimates from syringe tracking and testing data. J Acquir Immune Defic Syndr 1995;10:175—6.

    European Study Group on Heterosexual Transmission of HIV. Comparison of female to male and male to female transmission of HIV in 563 stable couples. BMJ 1992;304:809—13.

    Varghese B, Maher JE, Peterman TA, Branson BM, Steketee RW. Reducing the risk of sexual HIV transmission: quantifying the per-act risk for HIV on the basis of choice of partner, sex act, and condom use. Sex Transm Dis 2002;29:38—43.

    Bell DM. Occupational risk of human immunodeficiency virus infection in healthcare workers: an overview. Am J Med 1997;102:9—15.

    Leynaert B, Downs AM, De Vincenzi I; European Study Group on Heterosexual Transmission of HIV. Heterosexual transmission of HIV: variability of infectivity throughout the course of infection. Am J Epidemiol 1998;148:88—96.

  3. Chris Noble Says:

    But, Chris, where are the studies, which show what happens in the acute period?

    Trrll has already mentioned this paper

    The Journal of Infectious Diseases 2005;191:1403-1409

    http://www.newaidsreview.org/posts/1157412418.shtml#1917

    The paper I cited is probably a better indication of infectivity during acute infection

    http://tinyurl.com/mm7lv

  4. john Says:

    But your URL doesn’t work, Chris

  5. john-2 Says:

    When Claus wrote above to Dr. Noble as follows:

    Your latest outrageousness is definitely incontrovertible evidence that you and Dr. Knobless posting at Hank’s blog are one and the same.
    9.11.2006 2:36am

    and the learned AIDS prof. doggie who is so quick to dump on his betters, replied in all seriousness, How so? , he gave every evidence of having read the words of Dr. Knobless as carefully he those of Dr. Bialy at the AIDS Wiki page.

    Since i am john-2 , I will provide a pointer to the relevant material, and a choice quote to introduce the whole affair.

    “As a further example of invertebrate, modern-day HIV/AIDS scientific thinking, I have just now (in my turn-by-turn, systematic and parsimonious tour of the blogs) seen that there is a post-middle aged, assistant professor of education and statistics at a tiny university in the middle of nowhere Australia, who thinks that human beings follow bacterial population dynamics and that maintaining a quasi-genetic marker (like a retrovirus) requires a 100% efficient perinatal route. My my.

    Posted by: George | September 05, 2006 at 08:11 AM

    If perhaps it is I to whom George makes reference, all I can say is there you go again with your ad hominems. I am not an invertebrate, nitwit, as the vast majority of people are either human or murine as I explained at great length somewhere else.

    And further, not content with spewing your denialist rot wherever you can thanks to the open-source software that has *infected* the once, at least partially, controllable internet, you now must cast your vile aspersions at an entire geographical location, namely the placement of my university, which is *not* in the middle of nowhere Australia, (never mind where exactly), although it is close (as we measure things down here, never mind where) to where the famous Murchison meteorite landed some decades ago, containing the almost as famous dextro as well as levorotary amino acid, from which HIV – and all other totally alien organisms, like the bird flu virus – are quite plausibly evolved.

    Posted by: Knobless Oblige | September 05, 2006 at 10:15 AM

    These and other very educational comments can be found HERE, Christopher.

    Care to comment less obliquely now? Maybe you have something to say to George or Hank or Knobless even?

    You seem not to be able to shut up, and to always have nonsense to type when you do. So this should be right yup your back alley prof. ass.

  6. Chris Noble Says:

    But your URL doesn’t work, Chris

    Go to pubmed
    http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed

    and type in this number

    PMID: 16549978

    This is the article

    AIDS. 2006 Apr 4;20(6):923-8

    Molecular analysis of HIV strains from a cluster of worker infections in the adult film industry, Los Angeles 2004.

    Brooks JT, Robbins KE, Youngpairoj AS, Rotblatt H, Kerndt PR, Taylor MM, Daar ES, Kalish ML.

    Note that sequences from the index case and the three people infected were 100% identical.

    The timeline of infection is known to an extremely high precision.

  7. Robert Houston Says:

    According to the paper cited by Chris Noble on “infections in the adult film industry” (AIDS 20:923-8, 2006), the male actor tested HIV negative before the 26 day period in which filming occurred. Thus, he performed in the weeks before a neutralizing antibody response was fully established. The paper states that “the sequences of the HIV strains from the male index case and two of the infected women were 100% similar.” Thus, the strain from the third woman evidently was not, and may have come from another source (e.g., another partner or IV drug abuse). The authors point out that HIV transmission risk for this cluster they investigated “was greater for at least three reasons”, one of which was the nature of the film:

    “…notably, in the case of these infections there was a substantially increased risk of trauma to the anorectum (i.e. double-anal penetration).”

    Not to be indelicate, but the film involved backdoor relations with two gentlemen at the same time! This is an extemely unusual type of activity, even for the adult film industry, and thus the results cannot be generalized.

    The other study that Mr. Noble cited regarding “rates of HIV-1 transmission…in Rakai, Uganda” (M. Wawer et al. J In. Dis 191:1403-0, 2005) was a retrospective analysis of discordant couples (one partner HIV+), none of whom used condoms consistently and 80% of them not at all. Yet the text states, “The overall rate of HIV transmission per coital act was 0.0012” – that’s only one in 830. The overall rate was an average that included the short early period of greater infectivity (which was 0.0082/act, or 1/122). After those early few weeks, the rate sank to 0.0007/coital act, or only 1/1400 – even without condoms!

    Although some couples will transmit at such a low rate of 1:1400, on average this would require about 14 years of marriage without condoms. As Gisselquist et al. (Int J STD AIS 13:657-66, 2002) have pointed out regarding such low rates, “with these estimates, the HIV epidemic…does not reproduce, much less expand – through heterosexual transmission.”

  8. Chris Noble Says:

    Thus, the strain from the third woman evidently was not, and may have come from another source (e.g., another partner or IV drug abuse).

    Blood samples from the third woman were not available and were not analysed.

    The sole non-occupational contact of the third woman (contact no. 3, Fig. 1) tested HIV negative 60 days after her last potential sexual exposure to HIV. The epidemiological investigation of this infection cluster concluded that the three women were infected through occupational exposure.

    Not to be indelicate, but the film involved backdoor relations with two gentlemen at the same time! This is an extemely unusual type of activity, even for the adult film industry, and thus the results cannot be generalized.

    I never claimed that this was representative only that transmission risk is not constant. It varies with stage of infection and as Robert highlights also type of activity. Duesberg’s assumption of a fixed constant transmission risk is invalid.

    Finally, the transmissibility of HIV is greatest within the first months after infection during and near the time of seroconversion. Epidemiological studies in Africa have observed a 12-fold higher risk per coital act for heterosexual transmission within the first 5 months after initial infection [23]. Mathematical models using US data estimate that the higher loads of HIV in semen observed during seroconversion increase the risk eight to 10-fold that a man acutely infected with HIV and free of other sexually transmitted diseases (STD) will transmit the virus to his female partner, infecting 7 24% of susceptible female partners during the first 2 months after infection [24].

    23. Wawer MJ, Gray RH, Sewankambo NK, Serwadda D, Li X, Laeyendecker O, et al. Rates of HIV-1 transmission per coital act, by stage of HIV-1 infection, in Rakai. Uganda J Infect Dis 2005; 191:1403 1409.

    24. Pilcher CD, Tien HC, Eron JJ, Vernazza PL, Leu S, Stewart PL, et al. Brief but efficient: acute HIV infection and the sexual transmission of HIV. J Infect Dis 2004; 189:1785 1792.

    From the last study:CONCLUSIONS: Empirical biological data strongly support the hypothesis that sexual transmission by acutely infected individuals has a disproportionate effect on the spread of HIV-1 infection. Acute hyperinfectiousness may, in part, explain the current pandemic in heterosexual individuals.

    Any analysis that does not take into account the high transmission risk during acute infection is not valid.

    I should also point out for Robert’s benefit that Gisselquist argue that mother-to-child transmission of HIV is unable to explain the epidemic particularly in Africa. So I have to wonder why he brings up this article in a thread where Duesberg supporters are desperately trying to defend this assumption.

  9. john-2 Says:

    Noble,

    I do now think that you and Knobless are indeed the same person as your inanities are now equal to or greater than his own.

    Why don’t you ask Undergrad Gal/Boy for some help. You need it.

  10. Claus Says:

    What you have to wonder about Prof. ass Noble is

    1. Why you chose to bring up this particular study to
    point out what everybody has agreed already about statistics, and which is much more damaging to your side of the argument, or did the pieces of keyboard in your forehead prevent you from picking up on the smirk on TS’s face as he happily conceded the point the tenth time just above?

    2. Why you chose to bring up this particular study as ‘a better example’ of early infectivity transmission, when in fact it’s an example of unusual transmission as results of unusual behaviour, involving continuous stress and trauma over a period of 3 weeks – as Robert Houston, as well as the study’s authors pointed out to you.

    3. Why you chose to bring up a study, where you’re obviously so eager to get to the juicy parts, that you didn’t count right how many female subjects were left – math genius.

    4. Why you chose to bring up a study which assumes what you use it to show, namely that sexual transmission of HIV is the only possibility. Or did you get so excited by the whole thing that you didn’t notice the research team, just like your pervy self, were ONLY interested in the subjects’ sexual history up to moment of infection.

    5. Why you’re now so far out, you start censoring people here, if they cite any study where the authors don’t agree 100% with Duesberg. Doesn’t leave us a lot of studies to discus does it Dumbo?

    As has been pointed out in many places, the only hypothesis that adequately answers all these questions is that you are indeed Knobless

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