2. Women with breast cancer are first treated by removing the tumor surgically.

Question

2. 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 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 RecurrenceObserved Yes Yes in 6 years Frequency therapy Yes Yes 0 0 28 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 corresponding relative risk of recurrence and odds ratio for recurrence, and summarize the results verbally.

Explanation / Answer

For question 2, we would use the chi-square test and the null and alternate hypothesis would be as follows: -

H0: 1 = 2 (Recurrence amongst women treated with radiation and without radiation is the same)

H1: 1 2 (Recurrence amongst women treated with radiation and without radiation is not the same)

Critical value for (r-1)(c-1) degrees of freedom would be 3.841 and hence reject the null hypothesis because computed value is greater than critical value

Observed Radiation Recurrence Yes No Total Yes 55 441 496 No 28 111 139 Total 83 552 635 Expected Radiation Recurrence Yes No Total Yes 64.83149606 431.1685039 496 No 18.16850394 120.8314961 139 Total 83 552 635 (O-E)^2/E Radiation Recurrence Yes No Total Yes 1.490916001 0.224177587 1.715093588 No 5.32010314 0.799943045 6.120046184 Total 6.81101914 1.024120632 7.835139772

Critical value for (r-1)(c-1) degrees of freedom would be 3.841 and hence reject the null hypothesis because computed value is greater than critical value

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.