The Argument Against Informing The Blood Donors of their HIV Positive Status

The assumptions:

You have a population of 1,000,000 people, all of whom donate blood.

0.1% of the population has HIV antibodies.

You are using a test that is 99% accurate. Ie: if 100 people with HIV antibodies are tested, 99 of them will test positive, and one negative. If 100 people without HIV antibodies are tested 99 of them will test negative and one positive.

These numbers are chose for ease of calculation and are not intended to be the actual numbers found in a real population.

The calculations:

Of the 1,000,000 blood samples, 0.1%, or 1,000 people are actually positive, and 999,000 of them are negative.

Of those that actually are HIV positive, the blood test will identify 99% of 1,000 = 990 correct positives and 1% of 1,000 = 10 incorrect positives (ie: they will be assumed to be negative).

Of those that are HIV negative, 1% of the 999,000 = 9990 will be incorrectly identified as being positive.

So, the final score is 990 correct diagnoses and 10,000 wrong ones. In other words, if you tell someone they have HIV you are going to be wrong ten times as often as you are right.

That is on the assumption that everyone gives blood. In reality, many people with HIV are screened out by an interview process and the actual HIV tests is less than 99% accurate... so if you tell someone they tested positive under these circumstances you are going to be wrong much more than ten times as often as you are right - 50 times??

Now; considering the plausible fallout in terms of anxiety etc. etc. suffered by those who are incorrectly told they are positive, SHOULD YOU BE DOING THIS?

Comments invited.