Working with Relative Numbers (AIDS vaccine, Cancer Drugs)

I finally got a chance to sit down and read a bit more about the AIDS vaccine trial. The major media has proclaimed that the vaccine has a protective effect of 31.2%. What this supposedly means is that 31.2% fewer people will contract AIDS when taking the vaccine relative to those not taking the vaccine.

The problem with these numbers is they really don’t mean much. Let’s look at the real numbers.

The trial had approximately 16,000 participants broken into 2 groups:

  1. People given the cocktail of 2 AIDS vaccines (ALVAC-HIV and AIDSVAX B/E)
  2. People given a placebo

Of the participants in the trial, 51 of the vaccinated group got AIDS/HIV, compared to 74 who got the placebo, which is where we get the 31.2% figure. Since the publishing of the paper, they found that 7 tests subjects already had HIV, so the new number is 26.4%.

But, let’s look at the real numbers, rather than relative numbers. Of the 16,000 people on the study, I assume roughly 8,000 got the vaccine and 8,000 go the placebo. If true, then we have the following stats using the original study numbers:

Group Number in Group Number Infected % of total Group
Vaccine 8,000 51 0.64%
Placebo 8,000 74 0.93%


  • With a Thai heterosexual lifestyle, and a vaccine, I have less than 1% chance of getting HIV
  • With a Thai heterosexual lifestyle, and no vaccine, I have a .29% higher chance of getting HIV than with a vaccine

Statistically, this is not a good absolute number. If you take this to its natural conclusion, it breaks down like this. For every 1000 people, the number getting AIDS is 9, but this is reduced to 6 if you get a cocktail of vaccinations. Statistically speaking, the 3 extra people could be a fluke, as the numbers are too small to be statistically significant when you look at absolute numbers. It is only through relative numbers that the percentages appear significant.

You see the same relative numbers in cancer.

Consider Tamoxifen, which showed a 49% reduction in occurrence amongst high-risk participants. Here are the numbers:

Group Invasive Breast Cancer
Tamoxifen 89
Placebo 175

When you run this against the numbers and run some other calculations, you end up with a 49% less likelihood of getting breast cancer. When you look at real numbers, the incidents of invasive breast cancer is 6.76 per thousand with the Placebo group and 3.43 with the Tamoxifen group (page 6 in study). In real numbers, this means 641 additional women will not get cancer this year if they take Tamoxifen over those who do nothing.

Group Invasive Breast Cancer Endometrial Cancer Stroke Embolism
Tamoxifen 89 36 38 18
Placebo 175 15 24 6

And when you look at the totals, they stack up like this:

Group Cancer Non Breast Cancer Non Cancer Negative Event
Tamoxifen 125 92 56 181
Placebo 190 45 30 220

Net result: Less breast cancer, more endometrial cancer, more strokes and more pulmonary embolisms. While you are less likely to develop invasive breast cancer, you are more likely to get something that could kill you.

Here are some real numbers, based on incident rates:

Tamoxifen Placebo Difference
2009 estimates Rate/1000 Total Rate/1000 Total Rate/1000 Total
Breast Cancer 192,370 3.43 660 6.76 1,300 3.33 641
Hip Fracture 243,200 0.46 112 0.84 204 0.38 92
Endometrial Cancer 42,160 2.3 97 0.91 38 -1.39 -59
Stroke 301,000 1.45 436 0.92 277 -0.53 -160
Pulmonary Embolism 234,000 0.69 161 0.23 54 -0.46 -108
In Situ Breast Cancer 42,250 1.38 58 2.68 113 1.30 55
Deep Vein Thrombosis 720,000 1.34 965 0.84 605 -0.50 -360
Total 1,774,980 102
Percent Diff: 0.0058%


The net result is 102 women less per year get a serious disease using Tamoxifen as a preventative than those who do nothing. One question I have, however, is what were the numbers for other types of cancer (brain, lung, liver, colon, breast) between the two groups, as it may actually put Tamoxifen on the negative side of the equation. Oh, and one more thing, the study was choosing women with a higher risk of breast cancer. If we were to re-run these figures with all women, what would the numbers look like. As a side note, Tamoxifen is horrible on the liver and is known to increase the risk of liver cancer by a large factor, yet that is not included in this study (it was never tested).

End Result: Tamoxifen was approved as a preventative drug in high-risk patients because it reduces the relative (low) risk of breast cancer by 49%, despite the fact that the real benefit, spread across diseases and medical conditions studied is extremely low. Even if we examine it myopic, the benefit, in real numbers, is very, very low.

Another way of using relative numbers is in survival. Examine this study of Sorafenib. The pill increases survival by 44%. What this means, in real numbers, is the median life expectancy without Sorafenib was 8 months. With Sorafenib, the median survival was 10.7 months. Three extra months of life is all you get with this miracle pill, but these are also 3 extra months of pure chemo hell.

If you, or a loved one, has been diagnosed with cancer, make sure you understand what the real numbers are, so you can make an informed decision.

Others in this series:

·         The Caroline Pryce Walker Conquer Childhood Cancer Shill Game

·         Childhood Cancer Statistics (13,712 estimated diagnosed in 2008)

·         Understanding Appropriations – The Carolyn Price Walker Conquer Childhood Cancer Act

Peace and Grace,

Twitter: @gbworld


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