Relation

Example of Insensitive of data to causal asymmetry

Example: For a typical 40-year-old woman, the probability of breast cancer in the next year is 1/700, which is a prior probability, P(D). According to the Breast Cancer Surveillance Consortium (BCSC), the sensitivity P(TD)=73P(T | D) = 73%. Using the weighted average to calculate P(T) because the number of healthy 40-year-old women is much higher than the number of sick women, only 1/700 women has the disease and the remainder 699 are healthy. P(T) = (1/700)73% + (699/700)12% = 12.1% --> likelihood ratio = 73% / 12/1% = 6 --> With a positive result, there is, 6(1/700)=6/700, less than a 1 percent chance that this person will actually develop breast cancer.

However, If a woman with a pre-existing family history, the situation would be completely different. Assuming that the prior probability of the patient is 1/20, the updated D probability is =6*(1/20)=3/10. For such women with a high prior probability, the positive test result is very important.

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Updated 2020-03-22

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Data Science