# Debunking Denialism

Fighting pseudoscience and quackery with reason and evidence.

## The Evidence That HIV Causes AIDS (NIAID Fact Sheet)

National Institute of Allergy and Infectious Diseases (NIAID) used to host a highly useful document on the evidence that HIV causes AIDS and refutations of common denialist claims. This also had important historical and scientific references that provided a lot of insight into the issue. The document was an important resource for fighting HIV/AIDS denialism on the Internet. Since September of 2016, this document was no longer available at its usual location on the NIAID website, likely due to redesign, restructuring and updating of the website that took place at the time. This was unfortunate, because the document contained a lot of useful material.

It is useful enough to be kept and not fade away in some online archiving service or non-formatted news item. Although HIV/AIDS denialism is no longer that prominent in politics and society, there are still pocket of anti-science activism that remains and, like all forms of pseudoscience, lures in the shadows and take every effort to spread and grow. Thus, Debunking Denialism has decided to reproduce the material in full below. Read more of this post

## How HIV/AIDS Denialists Abuse Bayes’ Theorem

Image by Matt Buck, under Attribution-ShareAlike 2.0 Generic.

Note: Snout (Reckless Endangerment) has made some good arguments in the comment to this post. The gist is that HIV/AIDS denialists overestimate the false positive rate by assuming that the initial test is all there is, when in fact, it is just the beginning of the diagnostic process. Snout also points out that it is probably wrong to say that most people who get tested have been involved in some high-risk behavior, as a lot of screening goes on among e. g. blood donors etc. I have made some changes (indicated by del or ins tags) in this post because I find myself convinced by the arguments Snout made.

There have already been several intuitive introductions to Bayes’ theorem posted online, so there is little point in writing another one. Instead, let us apply elementary medical statistics and Bayes’ theorem to HIV tests and explode some of the flawed myths that HIV/AIDS denialists spread in this area.

The article will be separated into three parts: (1) introductory medical statistics (e. g. specificity, sensitivity, Bayes’ theorem etc.), (2) applying Bayes’ theorem to HIV tests to find the posterior probability of HIV infection given a positive test result in certain scenarios and (3) debunking HIV/AIDS denialist myths about HIV tests by exposing their faulty assumptions about medical statistics. For those that already grasp the basics of medical statistics, jump to the second section.

(1) Introductory medical statistics

A medical test usually return a positive or a negative result (or sometimes inconclusive). Among the positive results, there are true positives and false positives. Among the negative results, there are true negatives and false negatives.

True positive: positive test result and have the disease.
False positive: positive test result and do not have the disease

True negative: negative test result and do not have the disease.
False negative: negative test result and have the disease.

For the purpose of this discussion, $+$ will indicate a positive test, $-$ will indicate a negative test, $HIV$ will indicate having HIV and $\neg HIV$ will indicate not having HIV.

$P(A)$ is the probability of an event A, say, the probability that a fair dice will land on three. Conditional probabilities, such as $P(A \mid B)$, represents the probability of event A, given that event B has occurred. If A and B are statistically independent events, then $P(A \mid B) = P(A)$, if $P(B) \neq 0$ (because the definition of $P(A \mid B)$ has $P(B)$ in the denominator).

Let us define some conditional probabilities that are relevant for HIV tests and Bayes theorem: Read more of this post