Question

Cancer Screening ~ Breast cancer is the most common cancer in females in the United States and throughout the world. Digital mammography test (the process of using low-energy X-rays to examine the human breast for diagnosis and screening) is one of the typical techniques for early detection of breast cancer in recent years. According to a study, digital mammography test has a sensitivity of 0.97, and a specificity of 0.63 for breast cancer detection.

Round all numeric answers to four decimal places.

1. Given a theoretical population of 10,000, assume that the base rate of this population is 0.06. Complete the table below for this scenario. .

	Test Positive	Test Negative	Total
Have Breast Cancer
Do not have Breast Cancer
Total			10,000

2. In what proportion of cases do we expect the test will indicate the patient does not have breast cancer?

3. Among the cases where the test indicates the patient has breast cancer, what proportion of patients would we expect to actually have the disease?

4. Among the cases where the test indicates the patient does not have breast cancer, what proportion of patients would we expect to actually be healthy?

5. Consider a second scenario with a base rate of 0.14, does the probability of actually having breast cancer if someone tests positive increase, decrease or remain the same?

Answer 1