Final answer:
The positive predictive value (PPV) is a measure that represents the probability that a subject actually has a condition given a positive test result. It is calculated using the formula PPV = P(C AND P) / P(P).
Step-by-step explanation:
The positive predictive value (PPV) is a measure that represents the probability that a subject actually has a condition given a positive test result. It is calculated using the formula:
PPV = P(C AND P) / P(P)
Where:
- P(C AND P) is the probability that both the subject has the condition and the test result is positive
- P(P) is the probability of a positive test result
For example, let's say the probability of a man developing cancer is 0.4567 and the probability of a false-positive test result is 0.51. If we assume that the test result is positive, we need to find the probability that the subject actually has cancer. To do this, we substitute the values into the formula:
PPV = (0.4567) / (0.4567 + 0.51)
Simplifying the expression, we get:
PPV = 0.4567 / 0.9667 = 0.4724
So, the positive predictive value for the test is approximately 0.4724, which means that there is a 47.24% chance that the subject has cancer given a positive test result.