Question

Patients with breast cancer sometimes die for other reasons. In a​ Nurses’ Health​ study, women with breast cancer were followed for 10 years and​ 2.5% had incidence of heart disease. Suppose the baseline​ 10-year incidence rate of heart disease in the general population is​ 2%. Assume a study is to be undertaken tracking women with breast cancer to see if there is a difference in the heart disease rate from the general population.

Assuming the true heart disease incidence rate for women with breast cancer is​ 2.5%, what is the power of this test if the investigators are able to track​ 6,000 women with breast​ cancer?

Answer 1

Null hypothesis H0: Incidence rate of heart disease women with breast cancer, p = 2%

Alternative hypothesis Ha: Incidence rate of heart disease women with breast cancer, p 2%

Standard error of proportion, p = = 0.0018

Assuming significance level of 0.05, critical z value is 1.96

Critical value to reject H0 is less than 0.02 - 1.96 * 0.0018 or greater than 0.02 + 1.96 * 0.0018

=> < 0.016472 or > 0.023528

Power of the test = P(Reject H0 | p = 0.025)

= P( < 0.016472 | p = 0.025) + P( > 0.023528 | p = 0.025)

= P[z < (0.016472 - 0.025) / 0.0018] + P[z > (0.023528 - 0.025) / 0.0018]

= P[z < -4.74] + P[z > -0.82]

= 0 + 0.7933

= 0.7933