1. Baye’s Rule and Medical Screening Tests

2. Baye’s Rule
Baye’s Rule is used in medicine and epidemiology to calculate the probability that an individual has a disease, given that they test positive on a screening test.
Example: Down syndrome is a variable combination of congenital malformations caused by trisomy 21. It is the most commonly recognized genetic cause of mental retardation, with an estimated prevalence of 9.2 cases per 10,000 live births in the United States. Because of the morbidity associated with Down syndrome, screening and diagnostic testing for this condition are offered as optional components of prenatal care.
Many studies have been conducted looking at the effectiveness of screening methods used to identify “likely” Down syndrome cases.

3. Study of “Triple Test” Effectiveness
The results of a study looking at the effectiveness of the “triple-test” are presented below:
How well does the triple-test perform?

4. Triple-Test Performance
What conditional probabilities would be good measures of the performance of the triple-test?

5. Test Result  What??
Now suppose you are have just been given the news the results of the “triple test” are positive for Down syndrome.
What do you want to know now?
You probably would like to know what the probability that your unborn child actually has Down syndrome.
To answer this question we need to use Baye’s Rule to “reverse the conditioning”.

6. Baye’s Rule
This requires prior knowledge about the probability of having the disease, P(D+), and hence the probability of not having the disease, P(D-).
This probability is called the positive predictive value (PPV) of the triple-test.

7. Negative Predictive Value
This also requires prior knowledge of the probabilities of having and not having the disease.

8. Example: PPV for Triple-Test
Prior knowledge about Down’s Syndrome suggests P(D+) =
or roughly 1 in 1,000 (i.e. P(D+) = .001).
We also now from our earlier work that…
P(T +|D+) = P(T -|D+) = .2627
P(T -|D -) = P(T +|D -)=.0499

9. Example: PPV for Triple-Test
Prior knowledge about Down’s Syndrome suggests P(D+) =
or roughly 1 in 1,000 (i.e. P(D+) = .001).
We also now from our earlier work that…
P(T +|D+) = P(T -|D+) = .2627
P(T -|D -) = P(T +|D -)=.0499