|
|
Carrier
|
Noncarrier
|
|
prior probability
|
(risk)
|
1 - (risk)
|
|
conditional probability
|
(conditional risk carrier)
|
(conditional risk noncarrier)
|
|
joint risk
|
(risk) * (conditional risk carrier)
|
(1 - (risk)) * (conditional risk noncarrier)
|
where:
• The prior probability for being a carrier in many genetic conditions if one parent is a known carrier is 0.5.
• The conditional probability for being a noncarrier is 1 if offspring are normal.
posterior probability of being a carrier =
= ((risk) * (conditional risk carrier)) / (((risk) * (conditional risk carrier)) + ((1 - (risk)) * (conditional risk noncarrier)))
posterior probability of being a noncarrier =
= ((1 - (risk))* (conditional risk noncarrier)) / (((risk) * (conditional risk carrier)) + ((1 - (risk)) * (conditional risk noncarrier)))
For the situation where previous offspring are all normal (conditional risk for noncarrier = 1):
posterior probability of being a carrier =
= ((risk) * (conditional risk carrier)) / (((risk) * (conditional risk carrier)) + (1 - (risk))) =
= ((risk) * (conditional risk carrier)) / (((risk) * ((conditional risk carrier) - 1)) + 1)
posterior probability of being a noncarrier =
= (1 - (risk)) / (((risk) * (conditional risk carrier)) + (1 - (risk))) =
= 1 - (posterior risk of being a carrier)
