While looking at the sitemeter referrals to GM/BM, I noticed a link

from “New Aids Review”, a denialist website that that I mentioned in

[my critique of Duesberg.](http://scienceblogs.com/goodmath/2006/09/pathetic_statistics_from_hivai.php)

The folks at NAR are continuing to pull bad math stunts, and I couldn’t resist

returning to the subject to show how stubbornly boneheaded people can be,

and how obviously bad math can just slip by without most people blinking an eye.

To remind you, the original Duesberg quote was:

>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 1in 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).

And the problem with that is simple, as I explained last time around. It’s the

same as saying that if the odds of winning to lottery are 1 in 1,000,000, that the average lottery winner has played the lottery 1 million times.

So… Over at NAR, they quibbled and babbled for a while, [before they came

up with the following:](http://www.newaidsreview.org/posts/1157412418.shtml)

>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.

I can certainly quarrel with it. Strictly speaking, there’s something correct hidden in there, in the first clause of the restatement, but it is quite deliberately phrased in a way that makes it sound as if it’s saying something *quite* different – it tries to make it sound like Duesberg’s original statement was essentially correct, when the fact is that it was stupidly, boneheadedly, ridiculously wrong. And from there, it moves into pure bullshit territory, trying to play the big-numbers game. (And all along the way it uses seriously shoddy statistics

to make its case. The one in one-thousand odds is *not* a valid statistic; the transmission rate is *not* a fixed number – it varies over the course of the infection, and you need to do some actual *math* to determine what the correct transmission probability is in the population under discussion. But we can leave that point aside for the moment.)

Anyway – for illustratory purposes, let me take the statement about probability and numbers of sexual contact, and try to rephrase it in a non-misleading way.

>”The probability of acquiring HIV via a single act of unprotected sexual

>intercourse is approximately 1 in 1000. Therefore, one would expect 1000

>unprotected sexual contacts with HIV positive individuals for each sexual

>transmission of HIV.”

Now… That’s an honest restatement. The next step of their reasoning is shoddy

nonsense. It’s classic faulty Bayesian reasoning: 1/1000 is the probability of

transmission via a single unprotected sexual contact; 1/250 is the probability of an

individual being HIV positive; therefore, the probability of transmission by a single sexual contact with an individual with unknown HIV status is (1/1000)×(1/250). But remember the Bayesian rule: P(X and Y) = P(X)×P(Y) *only if* X and Y are independent.

Is sexual behavior within the population under discussing really independent? Of course not! The numbers don’t combine that way. HIV incidence is *much* higher among certain sub-populations; and, by something that is most definitely *not* coincidence, those are *exactly* the sub-populations that are most promiscuous. We can’t combine that 1/250 number with that 1/1000 number *without showing independence*. Which, of course, the denialists can’t do.

NAR continues:

>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.

So, they take the already faulty 1/250,000 number, and quite deliberately combined it with *yet another* non-indendepent probability to artificially inflate the number further.

>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.

This little bit is not *too* bad. It’s not *good* mind you, but it’s not horrible. First, as I said before, combining the 1/1000 and the 1/250 is simple invalid – we need to know the dependence rate first. So… If the infection rate is 1 in 1000, and we have 3000 recruits, if, on average, each recruit had sex with *one* HIV positive partner *one* time, we would *expect* to see 3 HIV positive recruits.

Oops. That doesn’t look so good for the denialists, now does it?

The fact of the matter is: that 83 average sexual contacts simple *is not* an unreasonable figure. Remember that the transmission probability is *per contact*, not *per partner*. How often does a sexual active young adult have sex? I’ll be honest and say that I don’t know. But the statistics I can find claim that the average sexually active american (averaged over all ages) has sex two times per week. At that rate, 83 contacts is less than one year of sexual activity.

How many readers out there think that it’s unreasonable to guess that, on average, new military recruits are having sex two times per week? And that they’ve been sexually active for at least a year before signing up?

See, the thing is, even if you *accept* the bogus numbers and bad math that the denialists are using, their arguments simply don’t stand up if you actually look at the math, and reason out just what those numbers mean.

StephenYou’re assuming that ‘twice a week’ is with different random partners, though. Monogamous relationships (married or otherwise) might skew the rate of contact without contributing a contracted case.

Mark C. Chu-CarrollStephen:

No, I’m not. The Duesberg paper tried to make it sound like the probabilities involved were per-partner. They aren’t. That “250,000” sexual contacts number that the denialists came up, which is their basis for requiring the average military recruit to have had 80-odd sexual contacts for sexual transmission of HIV to make sense already *does not* require that each sexual contact be between a different pair of people. It’s number of sexual contacts.

These are *very* sloppy probability numbers, so there are tons of factors that aren’t properly calculated in. But that’s my main point: that these numbers are sloppily thrown together in meaningless ways in order to create an impressive sounding but meaningless conclusion; and that even if you accept these sloppy numbers at face value, they simply don’t say what the denialists want themto.

(Also remember that monogamy isn’t a factor that only skews numbers downward. There are people who carry HIV without knowing it, because they acquired it from previous partners, and they are having sex repeatedly with their *current* partners, which can skew things up.)

Blake StaceyIn the coming weeks, I will be writing an introduction to probability and statistics for that mysterious being, the general reader. Thank you very much, MarkCC, for bringing these examples of bad thinking into the light; it always helps to have poignant examples of the times people go wrong.

“Poignant”? Well, yes. These HIV denialists are so fixated on an idea they cannot abandon that everything they say becomes mixed up, distorted or deceptive. Arguments are almost useless; as with debating creationists, the only useful tactic is to aim for the undecided or weakly aligned people in the middle. Also like the creationists, they demonstrate the macabre fact that when defending a falsehood, some amount of misrepresentation and outright lying is only to be expected.

quitterI think the misrepresentation and lying is actually required for denialist rhetoric.

From reading the types of arguments they make I’ve identified 5 things that you see from typical denialist arguments.

Denialist arguments are contructed from 1) Conspiracy theories, 2) selectivity (quote-mining, magnifying doubt or only looking at one paper, or one result in the face of all other data), 3) fake experts, 4)impossible expectations of proof (also known as moving goalposts or magnifying doubt) and 5) logical fallacies (red herrings, argument from analogy etc.).

I’ve been having fun monitoring the denialist art of making debate out of thin air and trying to identify the key components of their arguments to come up with a universal denialist-detector (much like Sagan’s BS-detector).

This most recent argument sounds like the usual selectivity route, using a single statistic or finding and amplifying it to reject all other data from the field without reference to the totality of evidence that shows they are full of shit.

CoinThe thing that really is most interesting to me is the parallel between HIV and Evolution deniers, where both groups seem to just be kind of frozen in time, dedicated to re-fighting old battles against the mainstream viewpoint rather than moving forward (for example, into finding an alternative to the mainstream viewpoint). “Normal” science is out there performing experiments and finding cures; HIV denialists are arguing with people on the internet about

how to use basic statistics.Even if Duesberg’s statistics in this paper weren’t blatantly sloppy, the paper itself is only really relevant with respect to the state of science in 1992 when it was written. The paper is arguing over the kinds of basic data that were used in the

earlystages of science identifying how and why HIV causes AIDS. But science has moved way, way beyond that point. If the deniers wanted to respond to the science of today rather than the science of 1990, wouldn’t they need to explain the dramatic success in combatting AIDS symptoms that the “cocktail” treatments have had? Or explain why AIDS vaccines (which are now being developed andwork, the only problem is they don’t workwell) have any effect at all?Come to think of it, how do they even explain this chart if AIDS ultimately stems from “noncontagious risk factors”?

But I don’t think we get answers to these questions, since like with the evolution denial crowd, the focus of AIDS deniers is on attacking details of the established model, rather than developing any kind of even remotely comprehensive model to replace it…

a little night musingNice analysis. I’m amazed you have the patience to keeping whacking this particular mole.

Small, teeeeeny quibble to which I will devote too many words: you say

This is not Bayesian, really. It’s just a basic rule about how probabilities behave. It’s true that if X and Y are not independent then one of those factors has to be changed into a conditional probability, but that’s all.

Bayesian analysis has to do with using prior (conditional) probabilities to derive posterior (also conditional, but going the other way). The example we (by which I mean me) always like to bring in is medical testing: if I know that there is a 99% probability that a person who has HIV tests positive, and a 99% probability that a person who does not have HIV tests negative, and if the incidence of HIV is 0.02% (where I’ve totally made up all of these numbers, but they are not too outlandish), then if we grab a person at random and he tests positive for HIV, what is the probability that he actually has HIV?

Stephen(Also remember that monogamy isn’t a factor that only skews numbers downward. There are people who carry HIV without knowing it, because they acquired it from previous partners, and they are having sex repeatedly with their *current* partners, which can skew things up.)Gotcha, I hadn’t thought of that.

Greg@ Blake Stacey

A suggestion : if you use this example, and present it with the label “AIDS” or “HIV” attached, those whom you wish to reach will simply dispute or dissociate from its relevance. If you can label it with something less emotionally charged, many will appropriate the math and so be innoculated against the lies.

Coin points out that Duesberg’s analysis has history and can be treated as prediction of the present infected population.

Chris NobleThe main problem is the way that Duesberg and every other “rethinker” phrases the problem.

They always ask about the probability of a particular person becoming infected.

The correct question is what is the probability of someone passing the virus onto a second person.

If on average every person that is infected with the virus passes it onto more than 1 other person then you will probably have an epidemic.

An illustrating example would be to ask what happens if one person with a very contagious virus comes into the US. Let’s say that the probability of transmitting the virus to somebody in the same room is 1/10. In this fictional case the virus will spread very rapidly. All that has to happen is for an infected person to meet more than 10 people and they will on average pass the virus onto more than 1 person.

However if we use Duesberg logic we can save the world. If only one person in 250 million is infected with the virus then the probability of a particular person becoming infected by being in the same room as a random American is (1/10)*(1/250,000,000). In Duesberg’s world this would mean that you would have to meet an absurd 2,500,000,000 random Americans in order to get infected.

It basically boils down to a version of the lottery fallacy.

Duesberg asks what is the possibility that a particular person wins the lottery.

The correct question is to ask what the probability that someone will win the lottery.

trrllI thought that the most amusing attempt to rescue Duesberg’s claim that individuals would have to have an “absurd” amount of sex was the following:

At this point, they’ve conceded that Duesberg’s calculation that each infected individual would have to have had sex 250,000 times is wrong, but are desperately trying to convince themselves that this huge mathematical error somehow does not invalidate Duesberg’s conclusion that each individual would have to have had an “absurd” amount of sex. I was dumbfounded to see this. How could anybody seriously believe that young men in their sexual prime are having sex only 5 times per year? Don’t any of them even remember being that age? To anybody who is not desperate to redeem Duesberg, the mistake is obvious–somebody confused the average number of sex partners per year with the average number of sexual acts (the real number, by the way, is something on the order of 40-60). Ultimately, they conceded even this, but as you see, they were never able to bring themselves to let go of the “absurd” claim.

Torbjörn LarssonIt was humorous and paradoxically somewhat hopeful to see that “Truthseeker” first doesn’t get Mark’s and Noble’s argument on the Duesburg Fallacy at all, but later gets it and recants a little. He is not a truthseeker but he has not become totally cut off from the real world as a hardcore denialist should.

But he got me riled: “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 Mark would probably say, there is a nugget of truth in there. A goodlooking fella will surely get better treated at a hasty interaction due to our nature. But that disappears during a serious discussion. I bet there is more than 1:250 000 chance that comment was made because Tara is female.

Speaking of truths: the banner says “A Gold Medallion site of the Council for Scientific Reform”. You would expect a webactive organisation should have a website, but I can’t find it.

However I found a similarly designed aids-denialist site, very confused and nonactive since july, that has the same ‘mark’ and Whitehead citation: http://www.scienceguardian.com/ . Do we need to play the probability game again, and see how many websites we have to go through before we find one with the same ‘infection’? I didn’t think so.

Torbjörn Larsson“But that disappears during a serious discussion.”

Well, maybe not, come to think of it. But it doesn’t stop a serious interaction. (And now I sound like “Truthseeker”‘s recant. I must be in denial! 🙂

Joshua“We can’t combine that 1/250 number with that 1/1000 number without showing independence.”

Well, that’s the thing, isn’t it? They’re working from the assumption that HIV isn’t sexually transmitted and doesn’t cause AIDs anyway, so

of coursethose two probabilities are independent in their analysis.Science and math is so much easier when you get to make whatever assumptions you want without having to prove them against reality.

BCSo, if an HIV-positive person had sex once every day for 8 years (8*365=2920), and there were no “repeat infections” of the same partner, we would expect new 3 HIV infections? That sounds a low. I’m sure we could find cases where a single very promiscuous person infected dozens or even hundreds of different people. Obviously, the 1 in 1000 number must be wrong. Additionally, before I had even done that math, I thought the “1 in 1000” number sounds a bit suspicious to me. I remember taking a class back in college and we were talking about HIV transmission. I don’t remember what the actual numbers were, but I thought I recalled HIV transmission rates being in the single-digit percentages for a single sexual encounter. Those numbers varied on a few factors (like whether the sex was oral, vaginal, or anal). I remember male-to-female transmission rates were about twice as high as female-to-male transmission rates, presumably because men leave HIV-laced semen inside women.

I think you might’ve been incorrect in accepting the “1 in 1000” number in the first place.

Mark C. Chu-CarrollBC:

I’m not accepting their 1 in 1000 number; I’m just showing that *even if* you accept that number, the math *still* doesn’t work for the HIV denialist crowd.

The actual infection rate is highly variable: it’s not a constant. If I remember correctly, the period of time shortly after an individual is first infected is highly contagious; after that, during most of the time when the person is asymptomatic, they remain contagious, but at a *far* lower rate. After symptoms start, they become highly contagious again.

BCOh, one followup: I looked-up HIV transmission rates. Here’s what some websites said:

3 in 1000:

The rate of HIV transmission with sexual intercourse is … approximately 0.3% per sexual contact with an HIV-infected person.http://medlib.med.utah.edu/WebPath/TUTORIAL/AIDS/HIV.html

6.3 in 1000:

Overall, there was a 1 in 159 risk of female to male HIV transmission (95% confidence interval: 110, 286) per act of vaginal sex. This risk was 2.49 times greater in uncircumcised men.. the authors’ rate of female to male HIV transmission is much higher than previous estimates of below 1 in 1000 from studies of serodiscordant couples in the United States and Europe.http://www.aidsmap.com/en/news/47AE661F-F92B-4073-B47E-45730410F81D.asp

8 in 1000 initially, but dropping to an average of 1.2 in 1000:

The overall HIV transmission rate per act of vaginal sex was 0.0012. The risk of transmission was highest in the first two and a half months of HIV infection at 0.0082, before decreasing to 0.0015 during the next ten months.http://www.aidsmap.com/en/news/DC64824C-3739-44D5-9F25-A823E319C2D0.asp

Anton MatesBut he got me riled: “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”.What does he mean, “displayed prominently?” She’s just got the one picture, in her profile, and she’s wearing a full-coverage sleeveless T-shirt. The picture shows up in the sidebar of every post, sure, but so does Mark’s here, or PZ Myers’ on Pharyngula. That’s just how Scienceblogs is set up.

Not that Tara wouldn’t have a perfect right to fill thread after thread with hundreds of bikini pictures…but she doesn’t. That’s just a really weird thing to say.

Steve VerdonNo shit. That is the definition of independent events, see Robert Ash,

Real Analysis and Probability, page 203 and 204. Calling this Bayesian is like calling all cars Fords.Stephen UittiIf an HIV/AIDS denialist doesn’t think that getting HIV causes AIDS, then couldn’t we convince some of them to participate in human trials of an AIDS vaccine? After all, unless they think that HIV does something else, there’s no possible harm, right? We’ll eventually need volunteers.

coolerIts not suprising that many people doubt that hiv causes aids when 99.9% of animals injected with hiv dont get sick, its only present in a small % of t cells, 1/1000 or so and most viruses cause the most havoc BEFORE antibody protection and once you have antibodies youre safe, thats the entire logic behind vaccines.

Many credible scientists have questioned the hiv hypothesis at some time.

Like kary mullis nobel prize winner

walter gilbert nobel prize winning harvard bio professor

duesberg retroviral expert

shyh ching lo cheif of the infectious unit of the armed forces institute of pathology

etc etc

This film hiv fact or fraud summarizes their views.

http://video.google.com/videoplay?docid=5064591712431946916

There is another microbe called mycoplasma incognitus that sickens/kills every animal (As DR. Lo showed) injected thats found by pcr in CFS/AIDS etc read http://www.projectdaylily.com to find out how it was part of the biowarfare program.