Biomath Imperfect Testing

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 the materials 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 questions:

• What do the results of an imperfect medical test actually mean?

• How does one measure the effectiveness of a particular medical test or compare tests?

• 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, and probability.