Women with breast cancer are first treated by removing the t

Women with breast cancer are first treated by removing the tumor surgically. Often, radiation therapy is used afterwards to kill any residual cancer cells that might cause a recurrence of the cancer. However, such radiation treatments are severe and have serious side effects, so they are not always used and it is important to assess whether they effectively reduce the probability of a recurrence of the breast cancer.

A case-control study was done in which women receiving radiation therapy after breast cancer surgery were matched with women who had not received radiation therapy after their surgery. The women were followed for 6 years, and classified as to whether or not they had a recurrence of breast cancer. These data were obtained:

Radiation therapy

Recurrence in 6 years

Observed Frequency

Yes

Yes

55

Yes

No

441

No

Yes

28

No

No

111

a. Organize these data into a contingency table.

b. Use a hypothesis test appropriate for determining whether the probability of a recurrence differs for women treated with radiation versus those not treated with radiation. State the null and alternative hypotheses clearly, both verbally and with symbolic notation. State the conclusion of your hypothesis test.

c. Calculate the estimated conditional probability for a recurrence when radiation therapy is used after surgery and the estimated conditional probability for a recurrence when radiation therapy is not used. Calculate the corresponding relative risk of recurrence and odds ratio for recurrence, and summarize the results verbally.

d. Calculate the relative risk and odds ratio.

Solution