Screening

I'd like to have a test for breast cancer.

The probability of a positive test and having cancer.

This is a probability of a positive test given cancer.

So if we draw the area where the test is positive, cancer and test positive, then this area over here is 90 of the cancer circle.

So it takes 10 or more years for any screening method to demonstrate a reduction in mortality from breast cancer.

So we organized a screening.

Intuitively, getting a positive test result about cancer gives us information about whether you have cancer or not.

And using this system, we can test the potency of cancer drugs.

Clearly the test has a strong correlation to whether I have cancer.

We did a screening in Germany

Now, the chance of having a positive test and having cancer is 0.009.

So, the test really helped us gaining confidence that we are cancer free.

The test sent out as positive even if the person doesn't have cancer.

The probability that the test triggers positive if you have cancer is 0.8, and the probability that the test comes out positive given that I'm cancer free is only 0.1.

Wouldn't you rather test to see if those cancer drugs you're going to take are going to work on your cancer?

Let's assume there's a test for this cancer, which gives us probabilistically an answer whether we have this cancer or not.

Before the test, we had a 1 chance of having cancer, now, we have about a 0.9 chance of having cancer.

In other words, the probability of the test correctly saying we don't have the cancer if we're cancer free is 0.8.

This thing over here is the same as probability of test 2 to be positive, which I'm going to abbreviate with a 2 over here, conditioned on test 1 being positive and me having cancer times the probability of me having cancer given test 1 was positive plus the probability of test 2 being positive conditioned on test 1 being positive and me not having cancer times the probability of me not having cancer given that test 1 is positive.

Here's an example from that screening study.

In the where there isn't cancer, the possible test outcomes add up to 1.

Well, I might when I receive a positive test have cancer or not cancer, so we will just normalize by these 2 possible causes for the positive test, which is 0.009 0.198.

There's a specific cancer that occurs in 1 of the population, and a test for this cancer and with 90 chance it is positive if they have this cancer, C.

Of course, in reality, we don't know whether a person suffers cancer, but we can run a test like a blood test.

In this example, we again might have our unobservable cancer C, but now we're running 2 tests, test 1 and test 2.

We need to individualize screening based on density.

So, let me write down cancer and test and let me go through different possibilities.

We could have cancer or not, and the test may come up positive or negative.

The probability of a negative test and having cancer, and this is not conditional anymore.

And now finally tell me what is posterior probability of cancer given that we know we had a negative test result and the probability of negative cancer given there is a negative test result.

To make this correct, we also have to compute the posterior for the non cancer option, which there is no cancer given a positive test.

We know that our test gives us a negative result if it's cancer free, 0.9 chance

We know there's a test that if you have cancer, correctly diagnose it with 90 chance.

But, also a main problem with our current diagnostic test for pancreatic cancer it's grossly inaccurate.

We have more trials planned for lung cancer, pancreatic cancer, ovarian cancer and breast cancer.

And therefore, as with all biology, you get selection through screening, whether you're screening for hydrogen production, or chemical production, or just viability.

The same test might also be applied to a situation where the person does not have cancer.

Can you compute for me the probability of cancer given that I just received a positive test.

Mammography isn't perfect, but it's the only test that's been proven to reduce mortality from breast cancer.

Cancer

Cancer?

Cancer.

It's fun if we give it a zero probability prior to have cancer and guess what, no matter what the test is, you still don't have cancer.

I'm obsessed with silk screening and bookbinding and box making.