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
(1)
|
Subjects With Positive Tests
(2)
|
Subjects With
True Positive Tests
(3)
|
Ratio of Subjects With True Positive
Tests to All Subjects With Cancer
(4)
|
Associated 95% Confidence Interval
(5)
|
Blood test only
|
239
|
73
|
(73/306) = 23.9%
|
|
Sigmoidoscopy only
|
566
|
215
|
(215/306) = 70.3%
|
65.2% to 75.4%
|
Blood test first, followed by sigmoidoscopy
|
719
|
232
|
(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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