Calculating Risk of Down's Syndrome from Maternal Serum alpha-Fetoprotein and HCG

Testing is typically done from 16 to 18 weeks of gestation, but can be done from 15 to 20 weeks.

Step 1: Determine a priori Risk

a prior- risk for Down's syndrome =

= (risk for Down's syndrome based on maternal age)

a priori risk for unaffected pregnancy =

= 1.00 - (a priori risk for Down's syndrome)

Step 2: Calculate the Standard Log-Gaussian Coordinates

standard log-gaussian ordinate for AFP in each condition =

= (LOG10 (AFP MoM) - (mean AFP for condition)) / (standard deviation in AFP for condition)

standard log-gaussian ordinate for HCG in each condition =

= (LOG10 (HCG MoM) - (mean HCG for condition)) / (standard deviation in HCG for condition)

Values for mean and standard deviation vary depending on whether gestational age determined by last normal menstrual period or by ultrasonagraphy (biparietal diameter).

Step 3: Calculate the Relative Frequencies

relative frequency for condition =

= (EXP (A/B)) / C

where:

• A = (-1) * (((standard log-gaussian ordinate for AFP)^2) - (2 * (rho for condition) * (standard log-gaussian ordinate for AFP) * (standard log-gaussian ordinate for HCG)) +  ((standard log-gaussian ordinate for HCG)^2)

• B = 2 * (1 - ((rho for condition) ^2))

• C = 2 * π * (standard deviation for AFP in condition) * (standard deviation for HCG for condition) * SQRT(1 - ((rho for condition) ^2))

Step 4: Calculate the Posterior Risks

risk for condition =

= ((relative frequency condition) * (a priori risk for condition)) / (((relative frequency unaffected) * (a priori risk unaffected)) + ((relative frequency Down's syndrome) * (a priori risk Down's syndrome)))

Interpretation:

• The risk of miscarriage following amniocentesis is about 1 in 190. If the risk for Down's syndrome exceeds that of amniocentesis, then amniocentesis should be considered.