Biomath Imperfect Testing
Nancy Crisler, Tasha Fingerlin, Tom Fleetwood & Landy Godbold With contributions from: Jim Kupetz
This—and other BioMath Modules under development—arose from a
conference in April, 2005, held at the Center for Discrete Mathematics and
Theoretical Computer Science (DIMACS) at Rutgers University, organized
by Fred Roberts and Margaret Cozzens (both now at DIMACS at Rutgers
University). The conference explored methods to establish connections
between mathematics and biology, bringing together those who have tried
it, those who have made it work on the undergraduate level, and those who
know how to get new programs into the schools.
From that conference arose the NSF-sponsored Bio-Math Connection
(BMC). It develops innovative classroom materials that highlight connections between mathematics and biology and helps teachers use
at various grade levels, in either biology or mathematics classes (or both).
The main BMC products are 24 teaching/learning Modules (including
this one), together with a book (containing some of the Modules) intended
for a one-semester senior-level non-calculus-based course that will satisfy
part of state requirements for a fourth year of mathematics or science. These
materials are developed primarily for an audience of high school students,
but with little adaptation they are suitable for college students too.
BMC is seeking topics, writers, reviewers, and users for further Modules.
If you are interested, please contact COMAP
This Module uses an interrupted case study approach to answer the following
• What do the results of an imperfect medical test actually mean?
• How does one measure the effectiveness of a particular medical test or
• How does this information affect public policy or personal decisionmaking?
The results of a mammogram, like those of many tests, are not always
correct. A false positive test result may create unnecessary anxiety, while a
false negative test result may result in a false sense of security.
In this Module, students are presented with the case of an adult female
who learns that her mammography test is positive. They then use real data
to calculate the probabilities of receiving true (or false) test results and discuss
the possible implications of a positive test result, given the properties
of the test. These properties, which include sensitivity and specificity, can
be used to help determine the rates of incorrect test results. The importance
of disease prevalence is also investigated.
Next, the womanhas a genetic test, through which she learns she has the
BRCA gene mutations associated with breast cancer. The students investigate
what it means to have this mutation and how scientists are working
on medical treatments that can be tailored to a particular genetic profile.
Finally, knowing that their mother is positive for the BRCA mutation
leads to a dilemma for her daughters, who must then decide if they will
be tested for this BRCA allele, since results from testing do not definitively
determine whether or not a woman will develop breast cancer.
This Module is divided into three sections to allow for flexibility in
implementation and differentiation between classes or ability levels:
• The first section introduces the case study and deals with the topics of
imperfect testing and cancer. All classes should complete this section
(Bayes’ Rule can be used as an extension).
• The second section teaches students about pharmacogenetics and treatments
tailored to a particular patient.
• The third section gives students a chance to take various perspectives
and practice debate and decision-making.
The second and third sections are independent.
Optional informationalhandoutsare providedoncancer, mammograms,