Case 6.4 Maternal Serum Screening Test for Down syndrome
Please keep in mind that I do not have a Math back ground so this is brand new to me and like a foreign language that I have never seen nor heard spoken before. Thank you for your help in advance.
Pregnant women are screened for a birth defect called Down syndrome. Down syndrome babies are mentally and physically challenged. Some mothers choose to abort the fetus when they are certain that their baby will be born with the syndrome. The most common screening is maternal Serum screening, a blood test that looks for markers in the blood to indicate whether the birth defects may occur. The false- positive and false- Negative rates vary according to the mother.
Mothers age false positive rate false negative rate
Under 30 .04 .376
30-34 .082 .290
35-37 .178 .269
Over 38 .343 .029
The probability that the baby has Down syndrome is primarily a function of the mother’s age. The probabilities are listed here.
Age Probability of Down Syndrome
25 1/1300
30 1/900
35 1/350
40 1/100
45 1/25
49 1/12
a) For each of the ages 25, 30, 35, 40, 45, and 49, determine the probability of Down syndrome if the maternity serum screening produces a positive result.
b) Repeat the negative result
To determine the probability of Down syndrome given a positive or negative result from the maternal serum screening test, we need to multiply the probability of Down syndrome for a specific age group with the corresponding false positive or false negative rates.
a) Probability of Down syndrome given a positive result:
1. For age 25:
Probability = (Probability of Down syndrome at age 25) * (False positive rate for age under 30)
Probability = (1/1300) * (0.04)
2. For age 30:
Probability = (Probability of Down syndrome at age 30) * (False positive rate for age 30-34)
Probability = (1/900) * (0.082)
3. For age 35:
Probability = (Probability of Down syndrome at age 35) * (False positive rate for age 35-37)
Probability = (1/350) * (0.178)
4. For age 40:
Probability = (Probability of Down syndrome at age 40) * (False positive rate for age over 38)
Probability = (1/100) * (0.343)
5. For age 45:
Probability = (Probability of Down syndrome at age 45) * (False positive rate for age over 38)
Probability = (1/25) * (0.343)
6. For age 49:
Probability = (Probability of Down syndrome at age 49) * (False positive rate for age over 38)
Probability = (1/12) * (0.343)
b) Probability of Down syndrome given a negative result:
To calculate the probabilities when the result is negative, we need to use the false negative rates instead of the false positive rates.
Repeat the above calculations using the false negative rates for the corresponding age groups.
Note: It's important to understand that these calculations are based on the given data and assumptions. The actual probability of Down syndrome can vary, and it is recommended to consult with a medical professional for accurate and personalized information.