 Hello. I'm Josh Grabe and I'm here to talk about probability in a specific application in medical testing and subtitled this. Do I have a disease doc? You go to the doctor, you want to know. You're not feeling so hot. I think there's something wrong with you. You go to the doctor and you say, what's wrong with me? The doctor runs some tests and comes back and says, I think you have a certain disease. Is the doctor right? How do we know? Your doctor has three options. Doctor can come back and say, yes, you have the disease, no, you don't have the disease, or maybe I'm not 100% certain. I don't recall having a doctor say this one to me. Maybe I'm not 100% certain. People don't really want that answer. We want, yes, you have it, no, you don't have it. I can go on about my day and plan accordingly. Which means your doctor really has two options. But with either option, the doctor says you have the disease or the doctor says you don't have the disease. Either way, the doctor could be wrong and we don't always think about that. But it's a real possibility. You might have the disease, or sorry, the doctor says you have the disease, but you actually don't have the disease. I would be angry about that. That's not me, but I would be angry about that. The doctor might say, you don't have the disease, but you know you're not feeling well and it turns out you really do have the disease. I'm not going to be happy about that either. It's going to be a different kind of unhappy than this. And then there's a chance that your doctor's actually correct and hopefully it's a high probability. The doctor says you have the disease, oops, the doctor says you have the disease and you do have the disease. I'm still not thrilled about that. I have a disease, but at least I have accurate information. Or the doctor says I don't have the disease and I really and truly don't have the disease and I'm pretty darn happy about that. There might be something else wrong with me. I wasn't feeling well on to the doctor, but at least I don't have a certain specific disease. We can think about these from a probability standpoint. These four things. Two ways to be correct in the diagnosis and two ways to be incorrect in the diagnosis. We're going to put some names on those. Before I put names on them, I want to write in some things. If you have the disease and the diagnosis agrees with that and says you have the disease, we'd call you a true positive. The test result came back positive and it actually is positive. You do have the disease. If you don't have the disease and the diagnosis agrees with that, that's a true negative and the other ones, these were both true and the other ones are both going to be false. One's a false negative and one's a false positive. Which one's a false positive? The doctor came back with a test result that was positive, but it was wrong. That's a false positive. It's a positive test result from the doctor. The doctor says you have it, but you don't. That is a false positive. The other last blank, we need a false negative. The doctor said you don't have it, but that was false. That's some language that we use to determine the validity of a specific medical test. How likely is a particular test to come back with false negatives or false positives? We would hope it would always have true positives or true negatives. That brings up two new terms that are related to probability, sensitivity and specificity. Sensitivity is the probability, you can see both of these definitions start immediately with probability, probability that the test will give a positive result for a person who does have the disease. Positive result, positive test and positive for disease. That's thinking about the true positives. Let's write that as a probability. We know that probabilities have to be numbers between zero and one. We can think of them as fractions. What are we counting in this probability? Person who does have the disease, say number with disease. And for some of those people, they'll get a positive test result, number, positive test. That's only of the people who have the disease. There will also be some people who don't have the disease who get a positive test, but they're not in here. This denominator is people with disease of those. How many had a positive test? We call that one of the two. Let's pick the right one. Is that sensitivity or specificity? If you're sensitive, you pick up on things from sort of an emotional definition of sensitivity. If you're sensitive, you pick up on things. If somebody has the disease, the test picks up on it. That's a sensitive test. This is sensitivity. Specificity is looking at the opposite. Probability that the test will give a negative result for someone who does not have the disease. That's equally important. I don't want to have a test that's, you could have a test that's perfectly sensitive, picks up every case of the disease, but sometimes says people have a disease when they really don't. You want to test that specific. If I don't have the disease, I want to test that says I don't have the disease. That's specificity here. The denominator, people or persons who do not have the disease, number without disease, of those, how many had a negative test result? That's specificity. We would like to have a test that's perfectly sensitive and perfectly specific, and unfortunately that doesn't happen too often in the real world. Let's give an example of a sensitive, very sensitive test. I'm a doctor and 200 women file into this room and as soon as they walk in, I tell them, you have breast cancer. Some of those women may have breast cancer and some may not. My test is 100% sensitive. If they have breast cancer, I was correct. My test picked it up. You have breast cancer. I didn't do any medical testing. It's a very cheap test. I won't miss any cases of breast cancer that way, but it's not a very good test. I will tell some people who don't have breast cancer that they do. My test is not very specific. I need a test that balances specificity and sensitivity.