Biotech Values

[TastyTheElf]

Thank you, iwfal, for the restatement, which for everyone's benefit I'm copying in:

1) disease is 100% fatal in one week if not treated

2) the test for the disease has a 30% false pos rate

3) the test for the disease has a 10% false neg rate

4) the true incidence of the disease among those tested is 1%

5) if you test positive for the disease do you:

A) take a drug that always cures disease but kills 20% of patients from it's side effects

OR

B) take a drug that saves only 70 % from disease mort - but with relatively benign side effects (I.e. No one dies from side effects)

Let's try to keep this simple. First, the false negative rate doesn't matter. I tested positive.

The true incidence of the disease doesn't matter either. I tested positive, and know my chances of having the disease....

There is a 70% chance I have the disease, and a 30% chance that I don't.

If I take drug A, regardless of all the parameters, there is a 20% chance I die. None of the other stuff matters.

If I take drug B:

If I have the disease (70%), I'll be cured 70% of the time, but still die 30% of the time -- 21% of the time overall.

If I don't have the disease, nothing happens.

It's still 20% vs 21%. Nothing has changed.

One might try to impose the following perspective, however:

There's only a 1% chance I have this disease, generally. So if I get a positive result, I should presume that the chances of a false positive massively outweigh the actual probability of having the disease (1%). (Of course we have to consider why I'm taking this test at all if it's only 1%.... I must have had some symptoms that actually pushed that percentage way up.... but never mind that.)

If the test were actually randomly administered, where the expected incidence in my case were genuinely 1%, I should always assume that a false positive is more likely. The percentage of positives that are concurrent with actual disease is very small -- 1% x 90% = 0.9% vs 99% x 30% = 29.7%.... so if the whole population got the test, only 3.0303% of the positives would be associated with actual cases of the disease.

Given that, I would take drug B, because I still assume there's only a 3.0303% chance I have the disease.... so I get a 70% insurance policy against the test being accurate without the 20% killer side effects.

But of course the presumption that I'd be getting this test randomly is suspect.