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Statistics for Business and Economics: Excel/Minitab Enhanced
Heinz Kohler
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Statistics in the News: Chapter 12 Estimation

Testing for Colon Cancer

Like all for-profit businesses, health insurance companies seek to achieve given goals, such as the continued health of their subscribers, at the lowest possible cost. But it is rarely obvious how to go about it. Consider screening apparently healthy people for colon cancer, the nation's No. 2 cancer killer. Three possible approaches have been recommended for people aged 50 and above:

  • an annual testing for blood in a patient's stool,
  • a sigmoidoscopy every 5 years, which examines the lower colon,
  • a colonoscopy every 10 years, which examines the entire colon.

Colonoscopy involves the use of a flexible, lighted viewing tube that lets a doctor see a sedated patient's entire colon and immediately remove any growths, but the procedure often costs well over $1,000. In contrast, sigmoidoscopy uses a less-advanced viewing tube, cannot probe the colon's top two-thirds, but can cost as little as $100. The fecal blood test involves taking two stool samples on each of three days and is cheaper still. Which test is best?

Recently, Dr. David A. Lieberman and others concluded an important study that sheds light on the question. The researchers examined 2,885 asymptomatic subjects aged 50 to 75 and performed all three tests on each. (Each test was performed without letting the examiner know the results of the other two tests.) Ultimately, the colonoscopy detected cancer or serious precancerous growths in 306 individuals. The blood test was positive in only 23.9 percent of those cases. Blood test plus sigmoidoscopy were positive in 75.8 percent of them. Thus, the first two tests noted above missed 24.2 percent of the tumors and precancerous growths detected by colonoscopy.

Statisticians will find the details of the study of great interest. While many subjects tested positive for cancer (column 2), significant numbers of these positives turned out to be false (as the colonoscopy later showed). Thus, the numbers of subjects with true positive tests (who actually did have cancer) were smaller (column 3). However, the three types of tests shown here also produced their share of false negatives, thus the total number of subjects with cancer turned out to be higher than 232, equal to 306, which accounts for column (4). Finally, note the confidence intervals in column (5).

Table A. Sensitivity of Alternative Screening Programs

Type of Test


Subjects With Positive Tests


Subjects With

True Positive Tests


Ratio of Subjects With True Positive Tests to All Subjects With Cancer


Associated 95% Confidence Interval


Blood test only



(73/306) = 23.9%


Sigmoidoscopy only



(215/306) = 70.3%

65.2% to 75.4%

Blood test first, followed by sigmoidoscopy



(232/306) = 75.8%

71.0% to 80.6%

Postscript: Insurers have been reluctant to pay for colonoscopy, despite the fact that it may well be in their long-run interest to provide such coverage. (Ultimately paying for cancer treatment may be much more expensive than the occasional colonoscopy that may prevent the development of the disease.) Medicare added coverage in July 2001; at the time, the Canadian Ministry of Health did not provide it.

Sources: Adapted from "Study Rates Colonoscopy as Far Superior Test, " The New York Times, August 23, 2001, p. A13; David A. Lieberman, "One-Time Screening for Colorectal Cancer with Combined Fecal Occult-Blood Testing and Examination of the Distal Colon," The New England Journal of Medicine, August 23, 2001, and A. S. Detsky, "Screening for Colon Cancer – Can We Afford Colonoscopy?" The New England Journal of Medicine, August 23, 2001.

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