Interpreting the Accuracy of Detection of Down Syndrome with the Triple Test using Bayes’ Theorem
Down syndrome (also called trisomy 21), a genetic disorder, is caused when irregular cell division results in extra genetic material from chromosome 21. Approximately 1 in 1000 pregnancies result in Down Syndrome. To date, the most accurate test for down syndrome requires a trial involving the removal and testing of a sample of cells from the amniotic fluid surrounding the fetus. However, this test carries a significant risk of miscarriage (approximately one in 200). A less risky but less reliable method is the triple test, which screens for hormone levels in maternal blood. This test sometimes produces false negatives and false positives.
The accuracy of a triple test (the probability that a fetus with down syndrome will be correctly identified for the detection of down syndrome) is 0.60. The false-positive rate (the likelihood that a test would say incorrectly that a fetus without down syndrome has down syndrome) is 0.05 (Newberger 2000).
These probabilities may look “OK,” however, with Bayes’ Theorem, we can get more revealing quantitative data that can help us interpret this deceiving probability… We will utilize Bayes’ theorem to discover the probability that a fetus has down syndrome, given that the triple test has a positive result.
Pr[Down syndrome|positive] = (Pr[Down syndrome] Pr[positive])/Pr[positive]
Pr[positive] = (Pr[positive] Pr[Down syndrome]) + (Pr[positive|no down syndrome] Pr[no down syndrome]) = (0.6 x .0001) + .05(1 – .001) ) = .05055
Pr[down syndrome|positive] = (.6 x .001)/.05055 = .012
This means that there is 1.2% probability that a fetus that is detected as positive actually has down syndrome!
Unfortunately, this frequency of false-positive ratio is typical. Many diagnostic tests have high proportions of false positives among the positive cases. In this case, we should be cautious when determining if the result is appropriate because when the triple test returns a positive outcome, we can then verify it with amniocentesis and weigh additional factors such as a family history of down syndrome, age of conceiving, etc…
Newberger, D. S. 2000. Down syndrome: prenatal risk assessment and diagnosis. American Family Physician 62: 825–832.