Cond. Probability and Medicine
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1 Cond. Probability and Medicine Conditional probability has an important application in medicine, particularly in studying the eectiveness of tests that detect a disease or condition. Tests have two results: positive or negative. Ideally, anyone with the disease should test positive, while anyone without the disease should test negative.
2 Sensitivity and Positive Predictive Value A true positive occurs if a person with the disease tests positive. The sensitivity is the number of true positives divided by the total number of people who have the disease. It is the probability that someone tests positive given that they have the disease. The positive predictive value (PPV) is the number of true positives divided by the total number of people who test positive. It is the probability that someone has the disease given that they test positive.
3 Specicity and Negative Predictive Value A true negative occurs if a person without the disease tests negative. The specicity is the number of true negatives divided by the total number of people who do not have the disease. It is the probability that someone tests negative given that they do not have the disease. The negative predictive value (NPV) is the number of true negatives divided by the total number of people who test negative. It is the probability that someone does not have the disease given that they test negative.
4 False Positive Rate A false positive occurs if a person without the disease tests positive. The false positive rate is the number of false positives divided by the total number of people who do not have the disease. It is the probability that someone tests positive given that they do not have the disease.
5 False Negative Rate A false negative occurs if a person with the disease tests negative. The false negative rate is the number of false negatives divided by the total number of people who have the disease. It is the probability that someone tests negative given that they have the disease.
6 T/F Positive and Negative Counts Negative True Negative False Negative Positive False Positive True Positive Total
7 Testing a Test (Sensitivity) A test is invented to detect a disease. An experiment is conducted with 100 people: Let's nd the sensitivity. We need the probability that someone tests positive given that they do indeed have the disease: 6 true positives 15 people have disease = 6 15.
8 Testing a Test (PPV) A test is invented to detect a disease. An experiment is conducted with 100 people: What is the PPV (the probability that someone actually has the disease given that they tested positive)?
9 Testing a Test (PPV) The PPV (the probability that someone actually has the disease given that they tested positive) is: 6 true positives 7 people tested positive = 6 7. Notice this is not the same as the sensitivity.
10 Testing a Test (False P Rate) A test is invented to detect a disease. An experiment is conducted with 100 people: The false positive rate is 1 false positive 85 people do not have disease = 1 85.
11 Testing a Test (False N Rate) A test is invented to detect a disease. An experiment is conducted with 100 people: What is the false negative rate?
12 Testing a Test (False N Rate) The false negative rate is: 9 false negatives 15 people have disease = 9 15.
13 Testing a Test (Wrap Up) The specicity is The NPV is 84 true negatives 85 people without disease = true negatives 93 people tested negative =
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