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 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).
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.
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.
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.
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.
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.
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.
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.
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 estimed opinion statistics is all about that once in a while when somebody does win in the lottery?
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.
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.
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.
Comments
see probability tree for putative rate of infection given rate assumptions.
caution! unrealistic!
Posted by: ekzept | September 4, 2006 2:31 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 4:10 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 4:50 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 4:56 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 4:59 PM
The statistics weren't the only thing to bring up the HUH??
The dates of the publications were ~1990, which would mean that if there were mother-fetal transmission, it would have had to occur in the early '70's. The first cases of the "gay plague" were several years after that. In addition, if there was maternal-to-fetal transmission, then the surviving mothers of those tested positive would be HIV+. Was that checked?
Posted by: natural cynic | September 4, 2006 6:46 PM
cynic:
The thing you need to remember is that Duesberg claims that HIV is completely unrelated to AIDS - and that in fact, that what we call AIDS is not actually a single disease, but in fact a wide variety of unrelated illnesses. According to Duesberg, HIV is a harmless virus that's carried by a large portion of the population. So what he's trying to argue is that the idea of HIV as a sexually transmitted disease makes no sense; that the number of individuals who carry HIV in the general population is the same as the number of people with AIDS and HIV; and that therefore it makes no sense to say that HIV causes AIDS.
The problem that Duesberg has is, the data does not back up his argument. To come up with any statistical argument for the idea that HIV doesn't cause AIDS requires inserting a variety of bizzare and incorrect assumptions; and then misrepresenting the conclusions. So that's exactly what he did.
Posted by: Mark C. Chu-Carroll | September 4, 2006 7:20 PM
ezkept:
The point of *Duesberg's* argument is basically what your tree demonstrates. He's trying to argue that the idea of AIDS as an infectious disease caused by HIV makes no sense. So he wants to put together an argument that shows that HIV as an infectious agent can't explain the statistics that we see for HIV+ individuals.
Posted by: Mark C. Chu-Carroll | September 4, 2006 7:23 PM
MarkCC,
... basically what your tree demonstrates ...
yup, i agree. i was just trying to point out that the mistake in statistics is his model for the transmission mechanism, not the odds of contracting HIV if one buys his setup. he improperly assumes statistical independence.
i've also addressed this separately and elsewhere with a different goal in mind.
Posted by: ekzept | September 4, 2006 8:25 PM
I can provide a more valid analysis.
If the risk per random sexual encounter is r then average number of sexual of random sexual contacts necessary for a proportion p of the 17-19 year old military recruits to be infected can be approximated by:
n = log(1-p)/log(1-r)
A Taylor expansion of log(1-a) gives -a - a^2/2 - a^3/3 ... which if a
Duesberg gives r to be 1/250000 = 4e-6
Literature provides the value of 0.26/1000 for the prevalence rate of 17-19 year old military recruits.
hence
n = a/p = 0.00026/4e-6 = 65
Duesbergs answer is 1/4e-6 = 250,000
The two differ by 1/0.00026 = 3846.15
Duesberg's "solution" effectively assmues that 0.00026 of the population had all the sexual contacts and 0.99974 of the population had none.
Can anyone see any major flaws in this presentation other than the false assumptions that Duesberg makes about HIV prevalence being randomly distributed etc.?
Posted by: Chris Noble | September 4, 2006 11:47 PM
Actually, Duesberg's argument is that the 744 HIV+ 17-19 year old military recruits (out of 2.8 million) could not possibly have acquired HIV through sexual contacts. Therefore most if not all of them acquired HIV from their mothers. Therefore HIV relies on perinatal transmission for survival. Viruses that rely on perinatal transmission cannot be 100% fatal. Therefore HIV cannot be 100% fatal.
The faulty statistics is just the first in a chain of questionable logic.
Duesberg has to ignore the observation that HIV in the US is largely restricted to specific risk groups and it is therefore highly improabable that a significant proportion of these acquired HIV perinatally.
Duesberg also has to ignore the experimental observations that perinatal transmission of HIV is only about 25-50% efficient.
The basic reproduction number for perinatal transmission would be the efficiency of transmission time the average number of daughters per woman. For HIV to survive through perinatal transmission every HIV+ woman would have to on average have 1 or more HIV infected daughters. Thus on average HIV+ women would have to have between 2 and 4 daughters that survive to child bearing age. Even in the baby-boom after world war two this has not been true in the US.
Actually now that I think of it doesn't Duesberg's logic tell us that each HIV+ army recruit must have been born between 2 to 4 times?
Posted by: Chris Noble | September 5, 2006 12:09 AM
Hey everybody. I'm doing a doctoral thesis at the University of Michigan in modeling HIV epidemiology and I would also like to throw in a couple of things into the mix about HIV transmission that I've observed from simulation studies.
First of all, the average probability of transmission per sex act is just that, an average. Empirical studies have shown that the probability varies widely over the course of an infection with the highest probabilities of transmission being at the very beginning and very end of the infection. This is important (w.r.t. the endemic prevalence rather then the epidemic dynamics in this case) when we relax some of the unrealistic assumptions concerning sexual mixing. Sexual networks are not random, and, random graphs are not even a good approximation of real sexual networks. Certain risk factors such as transient risk taking behavior, concomitant partnerships, and selective mixing can act to bring together newly infected individuals (and hence very infectious) with susceptibles more frequently then would be expected by random chance. Modeling such factors is essential to understanding the spread of HIV.
Duesberg's bad stats are only part of the picture here. There is a broader issue of making claims about the behavior of complex, non-linear systems based on simple statistics and very strong modeling assumptions will almost always (at least in epidemiology) lead to bad science, bad predictions, and bad public health.
Posted by: Ethan Romero | September 5, 2006 1:12 AM
Chris, can you state the model for
conceptually?Posted by: ekzept | September 5, 2006 1:26 AM
Ekzept,
I assumed that the proportion of uninfected people after n sexual contacts per person is given
(1-r)^n where r is the transmission risk
Hence we want to solve for n when (1-r)^n = (1-p) where p is the prevalence of HIV.
Taking the log of both sides and rearranging gives n = log(1-p)/log(1-r) ~= p/r for small p and r.
The above calculations make the same false assumptions used by Duesberg that the transmission risk is constant over time and for different individuals rathe than an average and that HIV prevalence is random and that there is no clustering in sexual networks. It is not intended to be an accurate model of reality only more valid than Duesberg's nonsense.
Any realistic calculation must be by necessity much more complex. Unfortunately simplistic nonsense is more attractive than complex reality to innumerate HIV "rethinkers".
Posted by: Chris Noble | September 5, 2006 2:04 AM
Great post. I'm wondering though at the utility of continuing to address denialist arguments at the scienceblogs. The problem, as I see it, is that denialists can pull things right out of their ass, and the poor scientists at the science blogs have to spend an incredible amount of effor debunking it every single time. I think the ratio is about 10:1, that is, it probably takes about 10x as much work and time for Mark to a thorough destruction of a bad argument than it takes for the denialist to just make something up. While this is valuable from an educational perspective, that is the people reading the response learn something even if the denialist never will, I'm wondering if there might be a better shorthand for dealing with this problem generally like you do when dismissing ad hominem or ad populum arguments.
I posted this response over on Orac's blog already, but I think you might forgive me for doing a lazy cut/paste job for the rest.
Generally speaking, I think the scienceblogs should recognize a commonality between these AIDS denialists and global warming/evolution denialists.
Again and again the discussions end up being the same, it's like a syndrome, and I think we should refer to all these guys as a group. They always use the same tactics, they pull quotes out of context, they fudge math/stats, they outright refuse to acknowledge contradictory data, and they never have any evidence of their ideas in peer-revied journals. They should be called "denialists" and we should treat all their arguments in essentially the same way.
I guess I'm saying I don't understand why when these trolls visit the scienceblogs we don't just clump them into this denialist group, and dismiss them out of hand. We could say that the scienceblogs exist to inform the public by debate and shouldn't be elitist or exclusionary, but do debates with denialists actually accomplish anything? It's not like there is any piece of evidence that will convince them to change their minds, that is part of the damned syndrome. In fact, a great starting point with the denialists is to demand from the outset exactly what data it is that will convince them they are incorrect, because if they truly are arriving at their opinions based on facts, if the facts contradict them they should be willing to change their minds.
I get the feeling that most denialists when posed this question, no matter what they are refusing to believe, will either be unable to answer it, or will suggest an unverifiable experiment or impossible situation. At that point, the argument is already over, and they've lost.
Posted by: quitter | September 5, 2006 3:17 AM
I think the point is that it several orders of magnitude better than continuing to debate "rethinkers" on their own forums where apparently nothing is proven until they admit they are wrong.
It provides a record that future "rethinkers" can be referred to in the future rather than going through the whole rigmarole again and again.
These "rethinker" arguments are like undead zombies roaming the earth long after they have been killed.
Peter Duesberg is in a different category because he has used his membership of the NAS, his reputation and contacts with editors to get his work published in peer-reviewed journals.
His supporters argue that because his papers are published in peer-reviewed journals and have never been refuted (they have) that his arguments must be good. This is completely hypocritical because they have no qualms about rejecting the vast majority of peer-reviewed literature.
Posted by: Chris Noble | September 5, 2006 4:33 AM
What worries me about Duesberg, more so than his criminal abuse of statistics, is the fact that he is on the Presidential Aids Advisory Council in South Africa where he seems to have greatly influenced government policy towards the AIDS pandemic in my country. According to the Actuarial Society of South Africa, there are between 5 and 7 million HIV+ people in SA, with an average of 600 people per day dying due to AIDS related causes. Currently our Minister of Health, Manto Tshabalala-Msimang is promoting a diet of olive oil, beetroot, lemons and garlic as an alternative to anti-retroviral drug therapy. Duesberg's malignant influence has proved to be lethal to thousands of South Africans.
Posted by: Eric | September 5, 2006 5:17 AM
"Actually now that I think of it doesn't Duesberg's logic tell us that each HIV+ army recruit must have been born between 2 to 4 times?"
My first reaction is to model HIV infections according to both the main model and Duesberg, and show that the main is consistent while as you imply Duesbergs trivially isn't. Perhaps even a simplified model is enough to give a reasonable answer to which model describes reality.
Duesberg has put his career on the line. He also makes a point of the absence of a working HIV vaccine - it seems to be a sort of virus-in-the-gaps argument. Since there seems to be at least one working vaccine passing first test, it could be a matter of time only before he is neutralised from doing more harm.
The morals are worrying. That a single man can put money before the very probable risk that he is preventing saving thousands from harm is not surprising, but that people want to follow the lone nut is. I remember the sad clip about the HIV denying mother who didn't save her 3 year old girl by trying the nutrition ideas of Duesberg instead of antivirals.
Posted by: Torbjörn Larsson | September 5, 2006 8:55 AM
I suspect that probably the majority of people who read these blogs are lurkers, readers who'd like to know what the rebuttles to these arguments are. I think its important to reach them too, to let them know exactly the (many!) flaws in the denialist's sheild. Granted, changing the mind of a denialists themselves is well neigh impossible, just as changing the mind of a creationist is. They will contort and distort arguments ad nauseam in order to maintain their firmly held beliefs - for example giving uncritical acceptance to any scientific paper that they think supports their views, but vehemently rejecting any that doesn't under the flimsiest of rationalle. Still, there is a bigger audience out there to reach.
I'm not a mathematician by any means, but think of it this issue this way. How many flips of a fair coin do I need to get heads? On average it happens at a probability of 0.5. So if we had 1000 people, each flipping a coin, then we'd expect 500 heads (plus or minus a few, if this experiment is repeated again and again, most of time you'd get a number close to 500, but not exactly 500). But that doesn't mean I need to flip a coin twice to ensure a heads. It could happen on the first flip (p = 0.50); or even after flipping twice, it might not happen at all (p of not getting any heads after 2 flips = 0.25).
Posted by: Dave S. | September 5, 2006 9:18 AM
This is mostly OT, but IIRC there has been a couple of posts on the Loom that has put a beautiful but tenous spin on this.
1. Simian immunodeficiency viruses (SIVs) are common, but typically not as deadly as HIV. Why? Zimmer cited articles that proposes that it is since some human T-cells are much more aggressive than monkeys. Monkeys typically don't get much autoimmune sicknesses such as MS or arthritis.
The idea is that our T-cells attack the HIV retrovirus early and aggressive, so it becomes incorporated in mainly T-cells. (Which BTW is another of Duesberg's discussion points.) In monkeys, SIVs reach more cell types and eventually becomes transcribed into the germline. And the theory is that the more distributed spread helps the immune system to wager a more appropriate response that doesn't induce AIDS.
2. Why are human T-cells more aggressive? Zimmer finds papers that suggests humans lack a certain sugar derivative expressed on cells surfaces among others. They help define cells as "own" cells. Those T-cell types who would otherwise use it seems to be the aggressive ones.
3. Why doesn't humans express that sugar derivative? It seems simians lack this specifically in the brain. Perhaps it is harmful in brain neurons, so some mechanism prevents its expression there. And along the way humans, with our developing big brain, got a mutation that put another stop for the sugar derivative in the whole body metabolism too. Perhaps good for ensuring brain function and possibly for metabolic economy, but seemingly bad for immune response.
The pieces in above picture are all tentative and tenous so I don't expect the image to survive. And it has little bearing on HIV/AIDS denial. Meanwhile it is fun to think about.
BTW, genomics rocks! Apparently we normally have 1-2 kg fungi, bacterias and viruses in our bodies, mainly in the intestines. Since their genome are typically smaller, it means that about 2-4 % percent of genes in our organism are human. And of those one can see about 90 - 100 000 RNA retrovirus gene insertions, which apparently makes about half our entire human genome virus originated.
That genomic material has been reused of course. For example, there are signs that the genes that mediates the immune system interaction between female and fetus is retrovirus in origin. So viruses helped make the mammal placenta possible.
But is still makes about 1-2 % of our healthy bodies genes original animalian. I find it astounding.
Posted by: Torbjörn Larsson | September 5, 2006 9:45 AM
At these small population proportions any number of other transmission mechanisms for HIV can be significant as well. How many recruits have shot up in the past for example?
Posted by: steve | September 5, 2006 10:45 AM
BTW, Chris, thanks for your explanation. yes, the model is better than anything Duesberg promoted if only because the numbers are more realistic. still, it's hard to see the connection between this "discount rate" model and some kind of physical communicability. i mean, what happens if the relaxation process continues to 65? 66? 100?
of course, i know you were not proposing a serious model, just a counterexample of a model which has just as much sense to it as Duesberg-derived ones and, to boot, fits the data better.
Eric, your comment is greatly disturbing to me. i mean, it's one thing to an academic with credentials to pursue a crazy idea and publish it, even if misguided. it's quite something else and reprehensible to be in a position to act upon it without relying upon scientific consensus to guide policy.
Posted by: ekzept | September 5, 2006 12:41 PM
another thing about scientific models: per the pattern, if we collectively understand a subject it should indeed be possible to construct different models for it and arrive at similar estimates.
Posted by: ekzept | September 5, 2006 12:47 PM
If one out of 250 people are HIV+ and the risk of HIV transmission is 1 out of 1000 (based on the work of Nancy Padian, a mainstream AIDS researcher, not Duesberg) then the risk of an HIV-negative person becoming HIV-positive after having sex with one person of unknown status is 1 out of 250,000. It's easier to work with the opposite, the probability of an HIV-negative person not becoming infected: 249,999 out of 250,000. Based on this factor, what's the chances of 1000 HIV negative people all remaining HIV-negative after each having sex with one person of unknown status?
Well, surely this is (249999/250000)^1000 = 0.996. Again, taking the reverse, the chances of one or more of 1000 HIV-negative people becoming infected after each having sex with one person of unknown status is about 0.4%.
Posted by: David Crowe | September 5, 2006 1:23 PM
If 1 out of 250 people in the total population are HIV positive then 1 out of 250 applicants to the U.S. Army and the U.S. Job Corps out to be HIV positive. All that BS about transmission probabilities and number of partners is meaningless as it is already incorporated into the 1 out of 250 number
Posted by: steve | September 5, 2006 5:45 PM
Nancy Padian has also specifically stated that the transmission risk also depends on the stage of infection. Risk is not constant over time and is not constant for different people.
Likewise HIV prevalence is not uniformly distributed throughout the population. It is largely confined to specific risk groups. This should preclude any idea that HIV is spread predominantly by perinatal transmission.
The implicit assumption that HIV is uniformly distributed leads to another statistical error by Duesberg in the same partner.
Statistically, it can be shown that the incidence of HIV-infections among the dentist's clients reflects, almost to the decimal point, the national incidence of the virus in the U.S. The national incidence of HIV-positives among all Americans is 0.4% (1 out of 250) (Table 1), the incidence of HIV-positives among 1100 patients of the Florida dentist was 0.4% (4 to 5 out of 1100) and the incidence among 15,795 patients from 32 HIV-positive doctors, determined by the CDC for the Bergalis case, was 0.5% (84 out of 15,795). Thus the incidence of HIV in patients from HIV-positive doctors reflects the national incidence of HIV. This suggests noniatrogenic and, most likely, perinatal infection as the source of HIV in these patients, particularly in the case of the virgin Bergalis (Section 3.5.2). In addition, it identifies a rich source of insurance income for 0.4% of American patients of HIV-positive doctors!
You might expect 4-5 of a random sample of Americans to be HIV+ but you would not expect any of them to be a white heterosexual female with little or no sexual risks.
The probability 0f 2,813,185 17-19 year olds all having exactly one sexual contact and none of them becoming infected is 0.0013%.
The expected number of seroconversions after each of them having one contact is 11.25.
The actual number of seropositives was 744 so you would need about 65 sex contacts on average.
This all assumes that out of 2,813,185 military recruits none of them had ever had sex with homosexual men and that none of them were injecting drugs users or members of other risk groups.
Posted by: Chris Noble | September 6, 2006 1:48 AM
Chris, the actual number of sexual contacts necessary is even lower than that, considering that about half of all AIDS cases in the US originate in anal sex, for which the probability of infection is 1 in 200, not 1 in 1,000.
Posted by: Alon Levy | September 6, 2006 6:17 AM
My knowledge of statistics is rudimentary at best, but even I can see that if claims like Duesberg's are taken seriously, many more HIV/AIDS-related deaths will follow. The fact that so many people is South Africa die as a result of similar claims, is in my opinion a major crime against humanity. Eric, I'm so sorry for what you're country is going through. How inhumane! Words fail me...
Posted by: makita | September 6, 2006 1:34 PM
I'm a glutton for punishment: I plowed through the whole thread in question at NAR. My impressions- firstly, to Chris Noble: kudos for your near-saintly patience with the dembskiesque dancing and insults there. Are you sure you're not on the payroll of Big Pharma?
Secondly- not only are these guys like the climate-change deniers, but also like all kinds of "true believers", who start out with some conclusion and twist the world to fit: for instance, the Bible code guys ( http://www.truebiblecode.com/ ), who have predicted the nuking of New York eleven times this year, and are sure they've got the bugs out of their methods for the twelfth date (this weekend).
The true believers in Duesberg have grudgingly admitted that their Founder may have made a weensy mathematical error, but insist that His castle still stands, even though one brick has been removed. What they don't seem to grasp, is not only that (as trrll pointed out there) one might be moved to doubt the word of a biologist whose math is so faulty, but that his entire argument on the transmission of HIV (as far as I understood it) is statistically based, and that if the statistics are wrongheaded, the whole deck of cards collapses.
I had a similar exchange at the Bible Code site: one believer "proved" the divine inspiration of the Bible by a mathematical argument (the "heptadic" structure of the Gospel of Mark, first advanced by Ivan Panin- see http://www.newaidsreview.org/ ). When confronted with the spuriousness of Panin's "structure", the believer basically said: "Well, the Bible is divinely inspired anyway, just because." The same reasoning prevails among Dembskiites, Holocaust deniers, and crop circle believers.
Posted by: zilch | September 8, 2006 8:45 AM
Oops, wrong url for Ivan Panin: I should have had http://cs.anu.edu.au/~bdm/dilugim/panin_mark.html . By the way, the big number he waved around to prove the Bible was 54,116,956,037,952,111,668,959,660,849 to 1, supposedly the odds against the repeating patterns of seven in Mark being the result of chance. Reminds me of the big numbers quoted to disprove the evolution of, say, hemoglobin: 574 amino acids in the right order- how can that be the result of chance?
Of course, the evolution of hemoglobin was not the result of chance, and neither was Panin's "heptaditic" Bible: both were built, a baby step at a time; the one by natural selection, the other by Panin's cherrypicking from numerous different texts, until the structure he had in mind reconstructed the "true" text of Mark. I wonder if Dembski and Duesberg have read Panin...
Posted by: zilch | September 8, 2006 9:02 AM
"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."
I think you really mean the probability of winning, not the odds. Odds = p/(1-p), so in this case (since p is very small) the odds and the probability are essentially the same. But still, better to use the correct terminology. Not a big deal.
Posted by: revere | September 10, 2006 11:01 PM
I don't know a whole lot about this whole "HIV denialist" issue (though it seems a little weird to use this kind of language to discuss a virus), but there are a couple of mathematical oddities in this post, also.
It seems like you're pulling out a quote that Duesberg wrote to illustrate a point and attempting to call it a "mathematical model" when all it is is a numerical illustration of (what appears to be) an absurdity. But this isn't really a big deal.
The following quote does contain a rather glaring error that other commenters seem to have slid right over:
"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.
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."
Maybe it's time for a bit of undergraduate statistics. Your "1000 people having sex with one partner one time" is a binomial experiment. Let's say you flip n coins all at the same time, each of the coins has probability p of turning up "heads". The expected number of heads for all n coins is n*p. In the "1000 couples" experiment, n=1000 and the "expected value" of infections is n*p=1, meaning that p=0.001.
Okay. Associated with every binomial (n,p) random variable is a Bernoulli random variable with parameter p. You can think of the Bernoulli random variable as flipping one coin, having probability p of turning up heads, once. The binomial (n,p) random variable is the sum of n Bernoulli (p) random variables. You can think of this as doing the Bernoulli experiment n (=1000) times in succession, and the math doesn't care if it's 1000 couples at once or one couple 1000 times in a row.
Even if you want to focus on following the one couple, it's correct to say that the average person would *expect* to have unprotected sex 1000 times before getting infected, using this probability of 0.001. Why is this? Well, associated with this Bernoulli (p) random variable is a geometric (p) random variable. Think of the geometric random variable as flipping a coin until you get a "head", and counting the number of flips needed. The expected value (mean) number of flips, or instances of unprotected sex *until* getting infected is 1/p=1000. (the number of times you would expect to have sex *without* getting infected is (1-p)/p = 999.)
This may be a simplistic "model", but you're picking on it not for its oversimplistic assumptions (I'm not talking about anyone else's criticisms, Mark, just *yours*), but rather for its poor mathematics. You picked on Duesberg's interpretation of the model as saying that the average person has to have sex 1000 times with an infected partner before getting infected themselves. But Duesberg's interpretation is entirely correct. If, according to this model, the transmission probability is 0.001, then "how math works" is that you can expect 1000 contacts to be necessary to become infected (on average).
I've spent too much time already today reading your goodmath/badmath site and have seen quite a bit of bad math promulgated by the blogger pretending to be a watchdog of others' mathematical gaffes. I read your comment that you weren't going to respond to me anymore, from which I infer that you prefer to dish it out rather than to take it. That's fine, and as you point out this is just a blog, but for Pete's sake if you're going to be throwing stones, don't put up a glass house.
Posted by: Randy Lahey | September 11, 2006 6:33 PM
OK, I thought this thread had died, and wasn't going to say anything.
But it seems alive. This is part of what I do for a living. I can't resist.
Modeling disease transmission is HARD. The model that is being discussed is preposterously simple, for lots of reasons
1) Infectivity is NOT constant over the course of the infection.
2) The chance of getting AIDS is not the same for all sexual acts. Anal sex is much riskier than vaginal. Vaginal is much riskier than oral.
Sex with a condom is much less risky than without, but not risk-free, largely because a LOT of people don't put on condoms right (some folks are drunk or high when doing it....)
3) The chance of getting AIDS from an infected partner depends on many characteristics, including one's one sex and some other sexually transmitted infections
4) The model takes no account of networking. That is, people do NOT have sex with random individuals. You are much more likely to have sex with someone who is the same race, similar income, and so on. Given that heterosexuality is dominant, you are more likely to have sex with someone of hte opposite sex. If you are a woman, you are more likely to have sex with soemone older. If a man, someone younger.
5) The number of partners people have is oddly distributed. Indeed, none of the standard statistical distributions fit it at all well. About the best is a one-inflated negative binomial.
That's just a start.
I just submitted a grant proposal to NIH to use latent space models to track the spread of infections through a network of people. This is complex stuff.
Posted by: Peter | September 11, 2006 7:11 PM
Duesberg is aware of most if not all of these factors. He himself argues that HIV should be most easily transmitted during the intitial acute infection.
Unfortunately Duesberg's target audience do not want difficult mathematics, they want simplistic hand-waving arguments.
Posted by: Chris Noble | September 11, 2006 8:14 PM
Randy:
I said I wouldn't respond to your annoying criticisms in the topology posts.
My criticism of Duesberg is quite simple, and Duesberg's own words are inexcusable. He *explicitly* says that if the probability of getting AIDS from a single instance of unprotected sex is 0.001, then *the average individual* who caught AIDS from unprotected sex should have had unprotected sex 1000 times. His own words: "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."
That's nonsense. *You* know it's nonsense. *Duesberg* knows it's nonsense.
If the probability of infection is 0.001, then it takes *an average of 1000 sexual contacts to infect one individual*. That is an entirely different statement from *an average infected individual had 1000 sexual contacts*. You know that. And either Duesberg knows that, or he's a raging incompetent.
Posted by: Mark C. Chu-Carroll | September 11, 2006 8:50 PM
Oh my god, Randy, you're incredibly wrong.
Mark shows exactly what's wrong in the last paragraph of his response. It's a fallacy committed all too often by anti-evolutionists as well. You take a probability and assume that exactly one person (or molecule) has to fulfill it, ignoring the fact that you have lots of people working on it at once.
.001 chance of passing the infection means that, if you have 1000 infected individuals, 1 of them will pass it to their partner, on average.
Dude, you even got your math wrong earlier in the post, though you seem to like throwing around big math words. Did it contribute anything to your post to mention "Bernoulli variable"? Nope, but it sure makes it sound fancy!
There is a big difference between how many times someone has to have sex *on average* to get infected, and how many times someone should *expect* to have sex before being infected. The latter, which you attempted to show, is properly calculated with n=log(.5)/log(.999), which is nearly 700 times. 1000 is the average because the outliers (people who go a *long* time without being infected) pull the average up.
Way to drag out the undergrad statistics...
Posted by: Xanthir | September 11, 2006 10:16 PM
Mark,
It seems to me that the point this guy (Duesberg) was trying to make is that the .001 is too low, producing "nonsense". Someone mentioned that just because the probability is 1/1000000 of winning the lottery doesn't mean that the 'average' lottery winner has played one million times, which is quite true, as the number of times one can play the lottery is cut off quite short of that. Then again there aren't a whole lot of lottery winners, are there? You seem to want to play this game to say that his 'model' (if indeed that is what he intended -- it appears from the quote, quite short, that he may just be making an aside comment not constructing and analyzing a model, I honestly don't know) does not work. I said from the beginning I wasn't referring to the validity or lack thereof of his model (though that is what a lot of the responses seem to be about anyway). But you didn't criticize his model, you criticized his math, saying that "math does not work this way". Math does indeed work this way, as the mean of the geometric random variable is 1/p.
Xanthir, way to pull out the median instead of the mean. I'm impressed by your attempt at obfuscation, 'dude'.
It seems that I have stepped into some sort of holy war, which since this is a disease "largely restricted to specific risk groups" (see Chris Noble above) is not that interesting to me. Have fun folks,
Randy
Posted by: Randy Lahey | September 11, 2006 11:24 PM
If, on the other hand, one takes "holy war" to mean what it usually does, then that's some quite nice hyperbolizing you're doing there.
Posted by: Xanthir | September 12, 2006 12:22 AM
People, I just can't get it man.
They have a problem called HIV. It's said to cause disease. People die. They find drugs. They try the drugs but the drugs don't really work and they have to admit: "30,000,000 treated, 0 cured." Patients who go on treatment more often than not feel worse after than before.
Here's a guy. He says: "Hey, I think I can see a way out! HIV is not the right interpretation of the observed phenomena. Listen, I can explain."
And the people, what do they do? Do they say: "Hey, that sounds good! Explain, we'll listen"? No! They say: "Fuck off you dummy! Dissident! Denialist! We won't listen to your crap".
Mad scientists. Wizard's pupils. Bunch of assholes all of you. Endless discussions about statistics when the evidence is crystal clear for the first non-indoctrinated brain.
Forget about HIV. Close your laboratories for a couple of days, stay home and think before you act again.
If you really care as much as you say you do when you talk about your lifesaving drugs, here's some hints you might try to include in your research program:
Hungry people you give em eat.
Thirsty people you give 'em drink.
Lonely people you give 'em warmth.
Chased people you give 'em shelter.
Put some generous love and care in the syringe.
Results will be baffling, guaranteed.
But then again, why care? Why should we give a fuck?
We prefer to drive a Porche to giving money to some starving Niggers. Even more so if they buy our drugs saying "Thank you for everythin' you do for us, Sir".
Posted by: jspreen | September 12, 2006 1:17 PM
jspreen:
*If* things were the way you claim, you *might* be right. But they aren't.
You say you've seen people get worse on the current AIDS drugs. Well, I've seen people get better. Cured? No. Better? Yes. And the overwhelming bulk of evidence - from trials of the drugs, and from documented experience with them - is that *most* people get *much* better on anti-retrovirals.
The fact that we don't have a *cure* for AIDS isn't all that surprising, given that we've never yet discovered a cure for *any* viral disease. The best we can do with viruses is try to alleviate symptoms and boost the body's natural immune response to fight off the virus, using things like vaccines. (I was stuck mostly in bed for two weeks this summer, because I caught coxsackie virus from my kids. Went to the doctor, because I thought it was a sinus infection. What did she do? Send me home and tell me to drink lots of liquids and take tylenol. Because we don't have medications to cure viruses.)
Personally, when I see a sick person, what I want to do is whatever I can to help make them better. The evidence shows that the drugs we have are *much* better than nothing. And the evidence *against* the drugs consists of garbage like the Duesberg analysis that I attacked in this post.
If the *truth* is that HIV can't cause AIDS, then someone like Duesberg ought to be able to make the argument *without* resorting to statistical lies. As it is, when I look at the HIV denialists, what I see isn't pretty. Based on Duesberg's paper, I'm forced to conclude one of two things. Either he's incompetent, or he's deliberately misrepresenting the facts (because *no one* competent in epidemiology could make such an incorrect accident by mistake). Either way, why should I trust him? And when I read work by other denialists, I keep on experiencing the same thing: things that are either dreadful errors (implying incompetence on the part of the writer), or lies (implying dishonesty).
Posted by: Mark C. Chu-Carroll | September 12, 2006 2:31 PM
The fact that we don't have a *cure* for AIDS isn't all that surprising, ...
True. The fact that you don't have a cure for AIDS is not surprising at all. You can't cure something if you look at it the wrong way. HIV=Aids=Death is a lie and as such it is a deadly lie.
The only cure that works is "Hey, I figured it all out! It's a lie! Forget about it and it's gone! All you're left with are the same good ol' diseases we already had before the Gallo gang hit home in 1983."
..., given that we've never yet discovered a cure for *any* viral disease.
Of course. You'll never discover a cure for any viral disease because not one single disease is caused by a virus. One century of research, not one cure. You give the evidence yourself so why do you use your brains and THINK!
That's at least a thing you could try to do now that you've said that : Quote Personally, when I see a sick person, what I want to do is whatever I can to help make them better. Unquote
But you cannot think. You can only see "evidence". Evidence that you want to see because it's the only evidence you've been able to figure out. Nobody is taught to use his own brains. The only thing we're taught is to bark with the pack.
Duesberg maybe wrong every once in a while. As we all are. Nobody knows teh thruth on anything. But at least Duesberg is not a nerd in the herd.
Posted by: jspreen | September 12, 2006 4:41 PM
Or is the fact that he's not a "nerd" make him more trustworthy? Boy, you must really hate the Tri-Lambdas, huh? Wow, living in a society where the smarty-pants are always wrong must be really rewarding! Did Duesburg throw the touchdown pass during the homecoming game, too?
...jspreen, nothing you said has any backing, and much of it is completely irrelevant. I recognize you from Tara's blog, actually - I don't know why it didn't click immediately. Here's a question for you, which has been asked in some form of you and all the other virus deniers: If a child's friend had chickenpox (which is caused, I'm sorry, I mean thought by doctors to be caused by a virus), and your child went to play with him during the contagious phase of the disease, would you expect your child to come down with chickenpox as well?
There's certainly no bacteria linked to chickenpox, but you can find a particular type of virus in every chickenpox sufferer. Heck, if you'd ever had chickpox in your life, you can get a spinal tap and find chickenpox virus. You *won't* find that in people who've never had it.
I don't bring in children for any shock value or anything, chickenpox is just on my mind since my brother was hit with shingles last week. If it matters, substitute adults in; children and chickenpox are just linked.
Posted by: Xanthir, FCD | September 12, 2006 6:15 PM
...jspreen, nothing you said has any backing, and much of it is completely irrelevant.
As long as you keep repeating this kind of hollow prases,there's no way we could ever even hope to have an interesting discussion. What I say has extremely solid backing to me but it simply doesn't count for the herd nerds.
We cannot discuss because of all the nonsense evidence you see everywhere and all I can do is do my best to make you the laughing stock of the century. You, the people who defend deadly viruses against so-called denialists instead of attacking them together with people who think differently.
Posted by: jspreen | September 12, 2006 7:45 PM
jspreen:
It's really interesting to watch the you preaching about "herd-nerds" etc. But you don't both to cite *any* evidence. Not a single shred. You just babble about how all of the evidence for HIV and viruses is "nonsense evidence", but you can't be bothered to say what's wrong with it.
Tell me, jspreen, how does the flu vaccine work? Why did I have the flu *every* year until I got my first flu shot, and haven't had a flu since? Why is it that smallpox, which was an absolutely ubiquitous and horrific plague just a few years ago has *completely* disappeared? and in every place around the world, it stayed endemic *until* the virus-based vaccine arrived, and then it disappeared practically overnight?
Posted by: Mark C. Chu-Carroll | September 12, 2006 8:06 PM
jspreen reminds me of boney, that guy who implied that the fact that I play D&D makes his logical fallacies and misrepresentations disappear.
Truth is not relative or subjective. Something is either backed up, or it isn't. There's no "for me" involved in it. We all share the same reality. If we don't, then you might as well head back into la-la land, since a subjective reality would mean that knowledge is impossible.
So, what backup do you have? Remember: Anecdotes don't count for much: They don't control for other explanations, and they're inherently cherrypicking.
By invoking newage (rhymes with sewage) principles of universal inconsistency?
Magical thinking hasn't proven effective, despite being around for millenia. So, why should we entertain magical thought?
Posted by: Bronze Dog | September 12, 2006 9:13 PM
It's one thing to *say* you have evidence, it's another to produce it. Simply believing something doesn't make it true. As Bronze Dog said, magical thinking sure hasn't done much over the past few millenia. Rational thought, on the other hand, has advanced society to levels undreamed of, in much less time.
Mark: Here's a fun (read: depressing) bit of info. The MMR vaccine was first done in the UK in 1988 (previously it did not guard against mumps). It was given to children approximately 1 year old, and again a few years later. In 2004-2005, there was a major outbreak of mumps in the UK and Ireland, with over 50 thousand cases reported in 2005 alone. In the years leading up to that, the yearly average was 200-300 cases, with a low of 94 in 1996. Guess what age range was the most strongly affected? If you guessed "the people that barely missed the MMR vaccine because they were too old", you would be right! The majority of cases were teens and young adults, aged 19-23.
Cites:
http://www.cdc.gov/MMWR/preview/mmwrhtml/mm5507a1.htm
Posted by: Xanthir, FCD | September 12, 2006 9:48 PM
Tell me, jspreen, how does the flu vaccine work?
It doesn't work.
Why did I have the flu *every* year until I got my first flu shot, and haven't had a flu since?
If you have a flu every year around the same period, you'll find out why if you remember what very unpleasant event happened to you slightly before the first time your flu appeared.Your flu shot has nothing to do with the fact that your flu doesn't occur anymore.
So, what backup do you have?
You don't want to know but maybe others are interested. They can start to do some googling with Dr. Ryke Geerd Hamer and Prof. Antoine Béchamp.
But then again, this all sounds totally stupid. We're just a bunch of cells held together by chemical reactions. Traumatic events have nothing to do with diseases.
Cells and chemistry, that's all there is, man! You see a beautiful woman and you fall in love. Chemistry!!
js
---
http://www.nightsofarmour.com
Posted by: jspreen | September 13, 2006 3:53 AM
""So, what backup do you have?""
""You don't want to know but maybe others are interested. They can start to do some googling with Dr. Ryke Geerd Hamer and Prof. Antoine Béchamp.""
I would really like to meet you jspreen because if you really believe the crap that Hamer spouts then I've got this bridge I would like to sell!
Posted by: Thony C. | September 13, 2006 8:48 AM
I would really like to meet you jspreen
Yeah, good idea. Let's meet. I'll explain Hamer's New Medicine to you and you'll be a newborn man. You'll even forget all about the bridge you'd like to sell.
Posted by: jspreen | September 13, 2006 9:28 AM
jspreen:
Fascinating how you completely ingored my question about the eradication of smallpox. What happened, did people all over the world suddenly stop having psychological traumas of a particular kind at the *exact* same time that the smallpox vaccine became available in their location?
It's also quite funny how I suddenly stopped having psychological traumas every winter, when absolutely nothing about my life had changed, *except* that my doctor recommended I get a flu shot.
It;s also quite funny how polio in America has virtually disappeared since vaccines became available. And how live virus polio vaccines sometimes (rarely, but sometimes) trigger an active case of polio, but dead virus vaccine polio *never* do, even though the oral live vaccine is less traumatic than the the injected dead.
Also quite fascinating is how meningitis in newborns virtually *disappears* if we test the mother for group B step, and give her antibiotics before delivery if she's positive. Does having a bag hanging on the IV rack somehow reduce the trauma of birth for the baby?
Posted by: Mark C. Chu-Carroll | September 13, 2006 10:20 AM
Mark.....you are so patient with this guy (I was gonna use another word). Is THAT a characteristic of geeks? :-) Actually, I think it may be, at least when discussing technical matters.
The fact that some people still take Duesberg seriously calls for explanations from psychology, not math, in my opinion. The math and the epidemiology are abundantly clear: Duesberg is wrong. So, why do some people still believe? Well, some people just have a need to believe that everything is a conspiracy. Some people have a need to believe that the accepted wisdom is always wrong. These people are fond of citing examples where the accepted wisdom WAS wrong, and drawing analogies between their own heroes and such people as Galileo or Einstein, who debunked the accepted wisdom of their times. But, while it's true that 'they laughed at Gailileo', it's also true that they laughed at Bozo the clown.
Posted by: Peter | September 13, 2006 10:42 AM
jspreen: Fascinating how you completely ingored my question about the eradication of smallpox.
Well, if you find it fascinating, you're welcome. I think it has nothing fascinating to it. You ask me a question, not because you're interested in hearing my answer, but because you are sure that with your question I'm in checkmate. Why would I give you an answer you can't listen to? We'd be still on it in 2035.
Have it your way, buddy. I couldn't care less what your believes are. I'm not talking to you but to an eventual passer-by who may hear a bell ring while reading my fascinating messages and then says to himself:
"That guy is really far out. I'm gonna have a look at http://www.nightsofarmour.com"
Posted by: jspreen | September 13, 2006 1:24 PM
jspreen:
Splendid example of responding with bluster in order to avoid the fact that you *can't answer the question*.
What happened to smallpox? Why did it disappear? If it wasn't the vaccine, *why* did it disappear all over the world *exactly* when the vaccine was introduced?
Posted by: Mark C. Chu-Carroll | September 13, 2006 1:52 PM
Smallpox. Polio. Flu. Meningitis. Mumps. All of these have been mentioned in our posts as being virus-caused diseases that can be treated with vaccinations. Can you explain them away? I can make a laundry list of vaccination-treatable diseases, and the associated infection numbers before and after vaccination for them became widespread.
The only 'trauma' that stopped happening was being exposed to a virus without the vaccination. Yeah, when we remove that 'trauma', people stop getting the disease! What a wonder!
Seriously, just give some content. If you don't, we'll assume you don't have any. All we want is some reason why, for example, smallpox is virtually GONE from the world after we started vaccinating for it. Same with polio - you no longer see it in developed nations AT ALL.
If you were right, jspreen, then there would be certain consequences. Either specific types of trauma cau