HIV/AIDS Skepticism

Pointing to evidence that HIV is not the necessary and sufficient cause of AIDS

Posts Tagged ‘R A J Matthews’

Abuses of statistics in HIV/AIDS research

Posted by Henry Bauer on 2009/09/14

There are many ways of lying under the cover of statistics. One that I’ve not previously emphasized is to imply a correlation where none exists; for example, “the declining incidence in the control group in Rakai — which, although not statistically significant, reduces the difference between the groups” [emphasis added; Gray et al., “Male circumcision for HIV prevention in men in Rakai, Uganda: a randomised trial”, Lancet, 369 (2007) 657-66].

The whole point of this type of statistical analysis is to determine whether or not an association plausibly exists. If there is no statistically significant association, then no association has been found.
The proper statement would be significantly different:
“The declining incidence apparently had nothing to do with the difference between groups”.

Here’s another example: “The odds of being HIV-positive were nonsignificantly lower among MSM who were circumcised than uncircumcised (odds ratio, 0.86; 95% confidence interval, 0.65-1.13; number of independent effect sizes [k]=15)” (emphasis added; Millett et al., “Circumcision status and risk of HIV and sexually transmitted infections among men who have sex with men”, JAMA, 300 [2008] 1674-84).
The enumeration of odds ratio, confidence interval, and effect sizes conveys a sense of technical correctness which, whether intended or not, lends rhetorical weight to the assertion of “lower” when, in actual technical fact, no significance has been established at the 95% probability level.
It is unwarranted, irresponsible, pseudo-scientific to say “nonsignificantly lower”, because that suggests that it is actually lower, though perhaps for purely technical statistical reasons not statistically significantly so.

Again: If the statistics delivers a verdict of “not significant”, then nothing has been established, not lower and not higher. Once more the proper statement would be significantly different:
“No association was found between circumcision and ‘HIV’ status”.

The silver lining in these instances, such as it is, is that I have stimulated many belly laughs — though also some very puzzled expressions — by inviting statistically literate friends to explain to me what “nonsignificantly lower” means.

The dark clouds, however, are that these people — who work at the Centers for Disease Control and Prevention, no less — are capable of writing such a phrase. They are either statistically illiterate or seeking deliberately to deceive. I don’t know which of those two would be the more depressing.

It is also worth noting and regretting that these statistical illiteracies passed the editorial- and peer-review processes of the Lancet and the Journal of the American Medical Association. “Peer review” is no better than the reviewers and the editors make it.


Oxymoronic jargon like “nonsignificantly lower” surely comes about because of an unshakeable belief that there is — must be — a lowering, in the face of data that do not support the belief. There exists a persistent unwillingness among HIV/AIDS mainstreamers to accept facts that contradict their belief — they suffer cognitive dissonance, as I’ve had occasion to remark all too often [Cognitive dissonance: a human condition, 26 December 2008; The debilitating distraction of “HIV”, 21 December 2008; State of HIV/AIDS denial: carcinogenic HAART, 21 November 2008; True Believers of HIV/AIDS: Why do they believe despite the evidence?, 30 October 2008; “SMART” Study begets more cognitive dissonance, 11 June 2008; Death, antiretroviral drugs, and cognitive dissonance, 9 May 2008; HIV/AIDS illustrates cognitive dissonance, 29 April 2008].

Of course, one might try to argue that “95%” is just an arbitrary criterion: one could choose 85%, or 70%, or any other value; or one might say that “lower” is simply expressing the raw numbers in words without attempting statistical analysis to attach a particular probability. But that would mean jettisoning any pretence of being scientific by using statistics to guide judgment as to whether an effect is plausibly real or not. If one offers statistical details then one should also abide by what the statistical analysis concludes and not try to fudge it.


Another abuse of statistical analysis that also may not be obvious until made explicit:

Upon finding  no correlation, divide the data into sub-groups in the hopes that one or other might show an apparently significant effect. This is statistically improper, a prelude to lying with statistics, because if you look at enough sub-groups the probability becomes appreciable that there will be found one or a few that appear to have a statistically significant association. Recall that if one uses a criterion as weak as “95% probability”, one apparently but not actually significant association will show up on average at least once in every twenty times — more often if the looked-for association is inherently unlikely [R. A. J. Matthews, “Significance levels for the assessment of anomalous phenomena”, Journal of Scientific Exploration 13 (1999) 1-7].

In the present instance, there was no association in the sub-group of insertive anal sex, nor between circumcision and sexually transmitted infections, two sub-groups where an association would not be implausible. On the other hand, highly implausible apparent associations were noted in studies conducted before the introduction of HAART, and between “HIV”-preventive circumcision and study quality. It is not easy to conceive why an association between circumcision and “HIV” acquisition would have anything at all to do with what treatment is provided people who have AIDS, long after acquiring “HIV”; and “study quality” is a highly subjective variable.

No. The Millett article leads to only one legitimate conclusion: No association found between circumcision and “HIV” status among MSM.


The problem for HIV/AIDS dogmatists is that they have failed to find any way of preventing people from becoming “HIV-positive”. The mistaken view that it has to do with infection and with sex keeps them searching for data to support that view, rather as rats or guinea pigs are doomed to try eternally to scale the turning wheels in their cages. Study after study gives the same result, no association. At the 4th International AIDS Society Conference, Sydney 2007:
Guanira et al., “How willing are gay men to ‘cut off’ the epidemic? Circumcision among MSM in the Andean region”)
— “No association between circumcision and HIV infection when all the sample is included. A trend to a significant protective effect is seen when only ‘insertive’ are analyzed.”
Note again the unwarranted, illegitimate attempt to assert something despite the lack of evidence: a “trend” toward a significant effect, when the statistical analysis simply says “nothing”, no correlation.
Then there was Templeton et al., “Circumcision status and risk of HIV seroconversion in the HIM cohort of homosexual men in Sydney”)
— “Circumcision status was not associated with HIV seroconversion . . . . However, further research in populations where there is more separation into exclusively receptive or insertive sexual roles by homosexually active men is warranted” [emphasis added].
More research is always warranted, of course, that’s what pays the researchers’ bills [Inventing more epidemics; the Research Trough; and “peer review”, 2 August 2009; The Research Trough — where lack of progress brings more grants, 10 September 2008].

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Statistics can lie, but Jack Good never did — a personal essay in tribute to I J Good, 1916-2009

Posted by Henry Bauer on 2009/04/12

A few years ago, as I was looking into HIV/AIDS data, I came across a claim that certain sets of “HIV” and “AIDS” numbers were correlated. The claim was presented by an image with shadings for the respective numbers, and the shadings do look similar. However, using the actual numbers that were also in the image, I calculated each ratio of “HIV” to “AIDS” and found that the ratios looked more like a random set than like a constant. So I stuck the numbers into an EXCEL worksheet and used the inbuilt CORREL function to derive the correlation coefficient. Lo and behold, it came out as 0.88, which represents — or should represent — a very respectable degree of correlation. Despite that, the set of ratios doesn’t look like “HIV” is correlated with “AIDS”.

For some three decades, I had the privilege and pleasure of regular visits with Jack Good. The next time I saw him after this conundrum about correlation, I told him about it. Drawing on his prodigious memory, he pointed to something he had written, which the index to his publications revealed as #792 (out of more than 2000): “Correlation for power functions”, Biometrics, 28 (Dec. 1972) 1127-1129. This remarks that it’s rather well known that the usual (product-moment) correlation coefficient is an inappropriate measure when the relation between two variables is not linear; and that the presumption is common, that “inappropriate” means that if the calculation is nevertheless done, the result will be a small value for the correlation coefficient. indicating lack of correlation. To the contrary, Good showed that the (usual, product-moment) correlation coefficient between x and x2 (x squared), or x3 (x cubed), etc., is close to 1 (typically >0.95).

In common parlance, by two things being “correlated” we mean that when one changes, the other changes in the same direction and in the same proportion; in other words, that the correlation is linear and the ratio of the two variables is a constant. But “the” correlation coefficient that is most commonly used, and included in such packages as EXCEL as the primary correlation coefficient, measures only whether two variables change in the same direction.

Consequently, statements about “correlation” are very likely to be misunderstood, misinterpreted, by the media, by the public — and by an unfortunately large proportion of doctors and scientists who “do their own statistics” using software packages and standard formulas.

This example is merely one isolated case of the abiding, deep, highly important problem of interpreting what “statistics” is supposed to tell us. Many years of informal education by Jack Good have taught me about some basic pitfalls that seem unsuspected by far too many people who quote and use “statistical data” like the ubiquitous “p” values.

The HIV/AIDS literature — like so many others — is full of articles in which particular relationships are said to be so at “p > 0.05”, or “p > 0.01”, or even  “p > 0.001” or less. The unwary reader sees  “p > 0.001” and accepts that there’s only one chance in 1000 that the claimed relationship is spurious. That’s an incorrect and misleading interpretation.

In the social sciences, the typical cut-off for “statistically significant” is “p > 0.05”, which is commonly given the interpretation that there’s less than 5 chances in 100, less than 1 in 20, that the claimed relationship is spurious, wrong, doesn’t exist. An apparently better interpretation is to emphasize that 1 in every 20 of such claimed relationships doesn’t really exist; of every 20 such claims made, 1 is wrong. But in truth, the chance is far greater than 1/20 that the claimed relationship at “p > 0.05” is wrong, simply doesn’t exist.

Those “p” values stem from an approach credited to, created by, the great early statistician R A Fisher, and it’s sometimes called “Fisherian”, though more often “frequentist”. That “p” stands for “probability”, and one of the things I learned from Jack Good is that the seemingly obvious meaning of “probability” is anything but clear, or obvious, or unambiguous. The frequentist meaning: toss a coin umpteen times, the probability that it comes up “heads” can be measured by counting the number of “heads” or “tails”. But that approach doesn’t cover such questions as, “What is the probability that God exists?”, which is a perfectly possible question with a perfectly intuitive meaning of “probability”.

Jack Good was one of the foremost pioneers in bringing into modern statistical applications the approach credited to the 18th-century Reverend Thomas Bayes. At any given moment, available evidence allows a judgment to be made about how probable the thing of interest is; that’s the “prior probability”, and it’s unashamedly subjective, different individuals can differ over what its value is, between 0 and 1. However, as experiments are done or observations made, evidence accumulates, and the prior probability is modified by a “Bayes Factor” that expresses the “weight of evidence” regarding the thing of interest. When sufficient evidence can be amassed, it doesn’t matter what was the prior probability with which one began, the calculated values will converge to whatever the “true” probability is.

The Bayesian approach is more technically demanding than the Fisherian, and the latter offers those ready-made software packages and formulas. But it’s not sufficiently recognized just how fallible the Fisherian approach really is and how misleading it can be.

The citing of “p” values is typically done to establish a particular hypothesis as “statistically significant”. But that’s not what the calculation means. It actually measures the probability that the “null hypothesis” is true, the null hypothesis being that the claimed relationship does not exist. If the “p” value is small, the null hypothesis is unlikely to be true, so you claim that your hypothesis is correspondingly likely to be correct.

There are several problems with this. The most obvious, and trivial, is that the choice of cut-off for “statistical significance” is arbitrary. Social science typically uses “p < 0.05”. The harder sciences demand <0.01 or less, depending on the particular situation. What must NEVER be done is to equate “statistically significant” with “true” — but, of course, that’s exactly what is done in just about every public dissemination of  “statistical facts”; and it’s implied as well in all too many research publications. One of Jack Good’s persistent campaigns was against the assignment of “p = 0” or “p = 1” to anything within the ken of human beings.

A worse problem with “p” values is their reliance on the null hypothesis: testing what one isn’t interested in instead of what one is interested in. Why is this done? Because it’s easy. The “normal distribution”, the “bell curve”, the Gaussian distribution, expresses the distribution of some measure around its average value when deviations from the average are owing purely to chance, when they occur randomly. For example, toss a penny 100 times, and most often you will NOT get 50 heads and 50 tails; but you can calculate exactly how likely you are “by chance” to get 49 H and 51 T, or 100 H, or whatever (provided, of course, the coin is perfectly balanced and not biased).

So an unspoken assumption is that the quantitative measure of the thing being investigated has a distribution like the normal curve. Some other distributions have also been studied, in particular the asymmetrical Poisson distribution, but this doesn’t help with the basic problem: If you want to use a frequentist or Fisherian approach, you need to know beforehand how the possible values of the variable you want to measure are distributed; and you can’t know that. Thereby there’s an inherent uncertainty, an unreliability, built in but that’s not commonly recognized, let alone openly acknowledged.

Nor is that all. When the null hypothesis is taken  to be disproved to some (subjective!) level of significance, the commonly drawn conclusion is that the hypothesis “being tested” is confirmed. But that presumes this hypothesis to be the only alternative to the null hypothesis; and there’s absolutely no warrant to assume that you thought of the only possible hypothesis capable of explaining the phenomenon you’re interested in, or the best one, the one most likely to be true.

So the Fisherian approach is beset by uncertainties, of which the most troubling are occult, hidden, not revealed when “p” values are cited. By contrast, the Bayesian approach places its subjective aspects in the open and up front, in the choice of a prior probability. Moreover, in calculating the Bayes Factor one is gauging probabilities relative to one’s hypothesis, and thereby one may be continually reminded that there might be other hypotheses equally or even better able to accommodate the data.


There are nowadays many expositions of Bayesian statistics and its superiority over the Fisherian because of the latter’s weaknesses. One exposition I found particularly readable is by R A J Matthews — “Facts versus Factions: The use and abuse of subjectivity in scientific research”, European Science and Environment Forum Working Paper (1998), reprinted (pp. 247–282) in J. Morris (ed.), Rethinking Risk and the Precautionary Principle, Butterworth, 2000. Matthews has also provided a concise overview of how misleading “p” values can be, increasingly so as the inherent (prior) probability of the thing you’re interested in differs from 50:50:

For example, if your initial belief is that there’s only 1 chance in 100 that something is true (moderate skepticism: an observation of it is a fluke 99 times out of 100), to establish it as real you need not a “p” value of 0.01 but of 0.000013  (1.3 x 10-5); in other words, p-values are a vastly insufficient criterion for estimating “statistical significance”.


I began this essay because Jack Good had just died, and I’m going to miss him enormously. I learned so much from him, not only about matters of probability and statistics. But I’ll mention one more example of the latter. “The birthday problem” is a commonly used demonstration of how wrong are our untrained estimates of probability: how many people do you need to gather in order to have a 50:50 chance that two of them will have the same birthday (day and month, of course, not year)? The answer, which surprises most people, is 23. A usefully simple explanation is that the number of pairs of people, which is what matters, increases much more rapidly than the number of people. Jack once extended that to the perhaps even more surprising numbers needed to have a 50:50 chance of 3 people with the same birthday (83), or 4 (170), or more — he gave a formula for calculating the result for any given situation (Good’s publication #2323, “Individual and global coincidences and a generalized birthday problem”, J. Statist. Comp. & Simul., 72 [2002] 18-21).

A concise but accurate, though understated, bio-obituary of Jack Good is at the Virginia Tech website . What you won’t find there is that this genius, utterly devoted to the life of the mind, was the best possible company, interested in and fascinating about everything under the sun, endlessly witty, able to find humor everywhere and to express everything humorously; a most cultured, erudite person, and also as gentle and civilized and courteous and without malice as one could ever find. It is an extraordinary blessing and gift to have known him.

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