the chapter discusses the probability of a mammogram being positive as a PPV
and the #2 question from problem set 6 asks:
what is the probability of a “positive” McIsaac Score? I interpret this as the same as the discussion I refer to in chp 2. Can you help clarify this for me
The mammogram example says:
10. Now you can get posterior probability from the table by reading across in the appropriate row and dividing the number with disease by the total number in the row with that result. So the posterior probability if the mammogram is positive (positive predictive value) = 21/719 = 2.9%, and our 45-year-old woman with a positive mammogram has only about a 2.9% chance of breast cancer!
The probability that the mammogram is positive is 719/10,000 = 0.0719. In probability notation, this is P(T+).
The PPV is P(D+|T+). In this case, it is the probability that the patient has breast cancer given a positive mammogram. This is 21/719 = 0.029 .
Another way, to calculate this is P(D+|T+) = P(T+ & D+)/P(T+). This is the definition of conditional probability.
In the example, P(T+ & D+) = 21/10,000 = 0.0021. As above, P(T+) = 0.0719, so P(T+&D+)/P(T+) = 0.0021/0.0719 = 0.029
The probability of a positive McIsaac Score is exactly analogous to the probability of a positive mammogram (719/10,000 = 0.0719). The 2x2 table in the PSet 6 answer key (that I will post tonight) will have 425 out of 1000 positive McIsaac Scores, so P(T+) = 425/1000 = 0.425.
