One of my classmates ask this question and it wasn't answered so now I am asking it and of course we are all struggling with no strong Math background
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, you need to use the false-positive and false-negative rates provided in the table, along with the probabilities of Down syndrome based on the mother's age.
a) Probability of Down syndrome given a positive result:
1. For the age of 25:
- False-positive rate: 0.04 (from the table)
- Probability of Down syndrome: 1/1300 (from the given probabilities)
To calculate the probability of Down syndrome given a positive result, we need to use a conditional probability formula:
Probability of Down syndrome given a positive result = (False-positive rate) x (Probability of Down syndrome)
For an age of 25, the calculation would be:
Probability of Down syndrome given a positive result = 0.04 x (1/1300) = 0.04/1300 = 0.00003
Repeat these calculations for each age given:
- Age 30: False-positive rate = 0.082, Probability of Down syndrome = 1/900
- Age 35: False-positive rate = 0.178, Probability of Down syndrome = 1/350
- Age 40: False-positive rate = 0.343, Probability of Down syndrome = 1/100
- Age 45: False-positive rate = 0.343, Probability of Down syndrome = 1/25
- Age 49: False-positive rate = 0.343, Probability of Down syndrome = 1/12
Perform the same calculation for each age to find the probability of Down syndrome given a positive result using the formula:
Probability of Down syndrome given a positive result = (False-positive rate) x (Probability of Down syndrome)
b) Probability of Down syndrome given a negative result:
To calculate the probability of Down syndrome given a negative result, you will need to use the false-negative rate instead.
1. For the age of 25:
- False-negative rate: 0.376 (from the table)
- Probability of Down syndrome: 1/1300 (from the given probabilities)
To calculate the probability of Down syndrome given a negative result, use the formula:
Probability of Down syndrome given a negative result = (False-negative rate) x (Probability of Down syndrome)
Repeat these calculations for each age given:
- Age 30: False-negative rate = 0.29, Probability of Down syndrome = 1/900
- Age 35: False-negative rate = 0.269, Probability of Down syndrome = 1/350
- Age 40: False-negative rate = 0.029, Probability of Down syndrome = 1/100
- Age 45: False-negative rate = 0.029, Probability of Down syndrome = 1/25
- Age 49: False-negative rate = 0.029, Probability of Down syndrome = 1/12
Perform the same calculation for each age to find the probability of Down syndrome given a negative result using the formula:
Probability of Down syndrome given a negative result = (False-negative rate) x (Probability of Down syndrome)
Keep in mind that these calculations are based on the given data, and the actual probabilities may vary depending on other factors.