Chapter 6.4, Problem 34E

Delayed diagnosis of cancer is a problem because it can delay the start of treatment. The paper "Causes of Physician Delay in the Diagnosis of Breast Cancer" (Archives of Internal Medicine [2002]: 1343-1348) examined possible causes for delayed diagnosis for women with breast cancer. The accompanying table summarizes data on the initial written mammogram report (benign or suspicious) and whether or not diagnosis was delayed for 433 women with breast cancer.

Consider the following events:

B = the event that the mammogram report says benign

S = event that the mammogram report says suspicious

D = event that diagnosis is delayed

1. a. Assume that these data are representative of the larger group of all women with breast cancer. Use the data in the table to estimate and interpret the following probabilities. (Hint: See Example 6.15.)
   1. i. P(B)
   2. ii. P(S)
   3. iii. P(D|B)
   4. iv. P(D|S)
2. b. Remember that all of the 433 women in this study actually had breast cancer, so benign mammogram reports were, by definition, in error. Write a few sentences explaining whether this type of error in the reading of mammograms is related to delayed diagnosis of breast cancer.