4. For a variety of reasons, self-reported disease outcomes are frequently used without verification in epidemiologic research. In a study by Parikh-Patel et al. (A-12), researchers looked at the relationship between self-reported cancer cases and actual cases. They used the self-reported cancer data from a California Teachers Study and validated the cancer cases by using the California Cancer Registry data. The following table reports their findings for breast cancer:
Cancer Reported (A) Cancer in Registry (B) Cancer Not in Registry Total
Yes 2991 2244 5235
No 112 115849 115961
Total 3103 118093 121196
a) Let A be the event of reporting breast cancer in the California Teachers Study. Find the probability of A in this study.
b) Let B be the event of having breast cancer confirmed in the California Cancer Registry. Find the probability of B in this study.
c) Find the probability of A and B and A or B.
d) Find P(A/B) and P(B/A)
e) Find the sensitivity of using self-reported breast cancer as a predictor of actual breast cancer in
the California registry.
f) Find the specificity of using self-reported breast cancer as a predictor of actual breast cancer in the California registry.
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