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UTILITY AND DECISION MAKING 569

MANAGEMENT SCIENCE IN ACTION

Medical Screening Test at Duke University Medical Center
new medical screening test developed at the newborns. Thus, the prior probability of a deficiency
A Duke University Medical Center (USA) involved was 1/250 000 ¼ 0.000004. Based on judgements
using blood samples from newborns to screen for about the probabilities of false-positive and false-
metabolic disorders. A positive test result indicated negative test results, Bayes’ theorem was used to
that a deficiency was present, while a negative test calculate the posterior probability that a newborn
result indicated that a deficiency was not present. with a positive test result actually had a deficiency.
However, it was understood that the screening test This posterior probability was 0.074. Thus, while a
was not a perfect predictor; that is, false-positive test positive test result increased the probability the new-
results as well as false-negative test results were born had a deficiency from 0.000004 to 0.074, the
possible. A false-positive test result meant that the probability that the newborn had a deficiency was
test detected a deficiency when in fact no deficiency still relatively low (0.074). The probability information
was present. This case resulted in unnecessary fur- was helpful to doctors in reassuring worried parents
ther testing as well as unnecessary worry for the that even though further testing was recommended,
parents of the newborn. A false-negative test result the chances were greater than 90 per cent that a
meant that the test did not detect the presence of an deficiency was not present. After the assignment of
existing deficiency. Using probability and decision costs to the eight possible outcomes, decision anal-
analysis, a research team analyzed the role and ysis showed that the decision alternative to conduct
value of the screening test. the test provided the optimal decision strategy. The
A decision tree with six nodes, 13 branches and expected cost criterion established the expected
eight outcomes was used to model the screening cost to be approximately $6 per test.
test procedure. A decision node with the decision Decision analysis helped provide a realistic
branches Test and No Test was placed at the start of understanding of the risks and costs associated with
the decision tree. Chance nodes and branches were the screening test. In 1998, the test was given to
used to describe the possible sequences of a pos- every child born in the state of North Carolina.
itive test result, a negative test result, a deficiency
Based on James E. Smith and Robert L. Winkler, ‘Casey’s Problem:
present and a deficiency not present.
Interpreting and Evaluating a New Test’, Interfaces 29, no. 3 (May/June
The particular deficiency in question was rare, 1999): 63–76.
occurring at a rate of one case for every 250 000

We will see that in cases where expected monetary value does not lead to the
most preferred decision alternative, expressing the value (or worth) of an outcome
in terms of its utility will permit the use of expected utility to identify the most
desirable decision.

The Meaning of Utility

Utility is a measure of the total worth of a particular outcome; it reflects the decision
maker’s attitude toward a collection of factors such as profit, loss and risk. As an
example of a case where utility can help in selecting the best decision alternative, let
us consider the problem faced by Swofford, a relatively small real estate investment
firm. Swofford currently has two investment opportunities that require approxi-
mately the same cash outlay. The cash requirements necessary prohibit Swofford
from making more than one investment at this time. Consequently, three possible
decision alternatives may be considered.

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