Bayesian Analysis: A pedigree of a family with two individuals affected by autis

ID: 178519 • Letter: B

Question

Bayesian Analysis: A pedigree of a family with two individuals affected by autism is shown below. How would you determine the risk that the unborn child carried by IV-1 will be affected by autism?

This is the way I did it. Is it correct?

1. Scenarios:

A. IV-1 is a carrier & V is not a carrier

B. IV-1 and V are both carriers

C. IV-1 is not a carrier and therefore V is not a carrier

2. Assign Prior and Conditional Probabilities

A. If IV-1 is a carrier, she is 1/2. The child (V) then has a 1/2 chance of getting the disease from her mom.

B. If they are both carriers, IV-1 and V are both 1/2

C. If IV-1 is not a carrier, she is 1 and therefore because IV-1 is not a carrier, her child (V) is also not a carrier which is also 1

3. Calculate Joint & Posterior Probabilities

Joint

A. (1/2 from IV-1) (1/2 from child) = 1/4

B. 1/4 again

C. (1)(1) = 1

Posterior: Joint/Joint + Joint + Joint

A. 1/4 / (1/4 + 1/4 + 1) = 1/6

B. 1/6 again

C. 1 / (1/4 + 1/4 + 1) = 2/3

Therefore, the probability V is affected by autism is 1/6 or 17% (B scenario only based on scenario)

Autism 16 wk

Explanation / Answer

The approach is verified and results are found correct