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 Source: Arti Parikh-Patel, Mark Allen, William E. Wright, and the California Teachers Study Steering Committee,

“Validation of Self-reported Cancers in the California Teachers Study,” American Journal of Epidemiology, 157 (2003), 539–545.

(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 PðA \ BÞ

(d) Find ð Þ A j B

(e) Find PðB j AÞ

(f) Find the sensitivity of using self-reported breast cancer as a predictor of actual breast cancer in the California registry.

(g) Find the specificity of using self-reported breast cancer as a predictor of actual breast cancer in the California registry.