Contents
- 1 What is the probability of having the disease given that you test positive?
- 2 How do you calculate the probability of a true positive?
- 3 What is the probability of a screen positive for a disease?
- 4 What is the probability that a person does not have the disease?
- 5 Which is the unconditional probability of a positive test?
What is the probability of having the disease given that you test positive?
If the false negative rate is 10% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease. so about 65% of the people who test positive will have the disease.
How do you calculate the probability of a true positive?
The true positive rate (TPR, also called sensitivity) is calculated as TP/TP+FN. TPR is the probability that an actual positive will test positive. The true negative rate (also called specificity), which is the probability that an actual negative will test negative. It is calculated as TN/TN+FP.
What is the probability that a randomly selected patient is tested with a false positive result?
The false positive rate is 5% (that is, about 5% of people who take the test will test positive, even though they do not have the disease). This is even more straightforward.
What is the probability of a screen positive for a disease?
P (Disease | Screen Positive) = (0.85) (0.002)/ (0.08) = 0.021. If the patient undergoes the test and it comes back positive, there is a 2.1% chance that he has the disease. Also, note, however, that without the test, there is a 0.2% chance that he has the disease (the prevalence in the population).
What is the probability that a person does not have the disease?
Similar reasoning tells us that the probability that a randomly chosen person does not have the disease and tests negative is 0.95 ⋅ 0.99 = 0.9405, so the probability that such a person does not have the disease but tests positive is 0.99 − 0.9405 = 0.0495; I’ve added these in red as well.
What is the probability of Bob having the disease?
There are 980 + 180 = 1160 people who tested positive in the sample population. Of these people, 180 have the disease. In other words, given that Bob is in the “tested positive” population, his chance of having the disease is 180/1160 = 15.5%.
Which is the unconditional probability of a positive test?
P (B) is the unconditional probability of a positive test; here it is 198/10,000 = 0.0198.. What we want to know is P (A | B), i.e., the probability of disease (A), given that the patient has a positive test (B). We know that prevalence of disease (the unconditional probability of disease) is 1% or 0.01; this is represented by P (A).