Answer to Question #207176 in Calculus for Arwa

Question

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.

(b) Let B be the event of having breast cancer confirmed in the California Cancer Registry. Find the probability of B in this study.

Answer 1

$P(B)=\frac{B}{N}\\ P(B)=\frac{2991}{3103}\\ P(B)=0.9639$