### Description

The risk of a fetus being affected by Down's syndrome can be calculated based on the maternal a priori risk consequent to age, AFP multiple of the mean, and HCG multiple of the mean. The distributions for AFP and HCG are assumed to fit a bivariate log-gaussian distribution in both normal and Down's pregnancies. AFP is typically 30% lower in Down's pregnancies, while HCG is 200% higher.

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)

maternal age

risk of Down's syndrome

risk as decimal

15

1 in 720

0.001389

16

1 in 800

0.001250

17

1 in 900

0.001111

18

1 in 1030

0.000971

19

1 in 1200

0.000833

20

1 in 1200

0.000833

21

1 in 1200

0.000833

22

1 in 1030

0.000971

23

1 in 1030

0.000971

24

1 in 900

0.001111

25

1 in 900

0.001111

26

1 in 850

0.001176

27

1 in 800

0.001250

28

1 in 760

0.001316

29

1 in 720

0.001389

30

1 in 690

0.001449

31

1 in 650

0.001538

32

1 in 550

0.001818

33

1 in 440

0.002273

34

1 in 360

0.002778

35

1 in 280

0.003571

36

1 in 210

0.004762

37

1 in 160

0.006250

38

1 in 130

0.007692

39

1 in 100

0.010000

40

1 in 75

0.013333

41

1 in 60

0.016667

42

1 in 45

0.022222

43

1 in 35

0.028571

44

1 in 30

0.033333

45

1 in 21

0.047619

46

1 in 17

0.058824

47

1 in 13

0.076923

48

1 in 10

0.100000

49

1 in 8

0.125000

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).

by last normal MP

AFP mean

AFP SD

HCG mean

HCG SD

rho

unaffected

0

0.1976

0

0.2419

0.0338

Down's

-0.1427

0.2052

0.3023

0.2681

0.1405

by biparietal diameter

AFP mean

AFP SD

HCG mean

HCG SD

rho

unaffected

0

0.1806

0

0.2372

0.1322

Down's

-0.1427

0.1838

0.3023

0.2638

0.2392

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.