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.
>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.