Slide 1
Bayesian Calculation
Application to Medical Genetics
Dr. Larsen
Session id = Larsen
Slide 2
Objectives
• Apply that Bayesian calculation is done when both
of the two conditions are met:
– presence of doubt on carrier risk of a person, and
– presence of additional information influencing the risk
for that person
• Demonstrate ability to include Bayesian calculation
into risk calculation of genetic pedigrees including
information from offspring phenotype, lab values or
physical examination, or reduced penetrance
• Sample questions in Canvas
• Reading: Emery’s elements of medical genetics p94
Slide 3
When to Use?
• When doubt about risk exists, and
• When there is additional information
• Most often additional information is
–
–
–
–
Phenotype of the person itself
Phenotype of offspring
Test results (uncertain)
Penetrance different from 100%
In other words: if a person has a 0% or a 100% risk for something (certainty) then Bayesian
analysis is not relevant. Bayesian analysis is only relevant for in between values.
Slide 4
Simple Examples
• Sister of a hemophilia patient has a risk of 1/2 for
being a carrier; what happens if she has an affected
boy?
• Her risk changes to 1 (she is for sure a carrier)
• In a family with an albino, an unborn sibling has a risk
of ¼ for becoming an albino, and of ½ for being a
heterozygote; what happens after birth of a baby with
normal phenotype?
• The baby’s risks become 0 for being an albino and 2/3
for being a heterozygote
These are both things you know from previously. The relevance here is that there is a step wise
progression: you have one risk, then an additional observation occurs leading to a recalculation
of the risk. There is, however, no reason to use a formal framework for these two cases, they
are easy enough that you can do them without. The rest of the lecture is about how to use a
framework to handle slightly more complex cases.
Slide 5
Example 1: healthy sons for
X-linked recessive
Slide 6
DMD sons: what is the risk that
the daughter is a carrier?
No other known
cases in family
1.
2.
3.
4.
5.
1
1/2
1/3
1/8
1/4
Slide 7
X-linked recessive trait
(e.g., DMD)
• II-2 has two healthy and
no affected sons; what is
her risk of being carrier?
I will go through this calculation in class. The next slide contains the same calculation, but
seeing it developed in a stepwise fashion might be valuable.
Slide 8
Calculating the Last Risk
Possibilities
II-2 is a carrier
(Xx)
II-2 is not a carrier
(XX)
Prior probability
1/2
(before birth) [Prior]
1/2
Observation (she has ½ x ½ = ¼
two healthy
sons)[Conditional]
1
1/8
Product, adjust to
common base [Joint]
1/2 = 4/8
(sum=5/8)
Throw away divisor, 1/5
divide by sum
[posterior]
4/5
Notice that final result is the probability for II-2 herself being a carrier, it does not say anything
about passing the bad allele on. In other words, the number circled at the bottom is the new
value for the text at the top of the column.
The statistical designations for these rows are: prior, conditional, joint, and posterior.
Slide 9
The Second Row
(conditional/observation)
• The value is the Probability(observation
given the genotype listed above the
column)
• In the previous slide for the first column,
that would be Probability (healthy sons
when genotype is Xx)
Slide 10
Continued: what is the risk that
her child will have the disease?
• II-2 had carrier risk
of 1/5
• Passing on would be
½
• And probability of
son would be ½
• Result 1/20
Multiply all rows together. Reminder from semester 1: the reason we use ½ for son is that
daughters do not become affected (or at least only have a few % risk of doing so, something we
ignore in Bayes calculations)
Slide 11
Example 2
reduced penetrance for AD
Slide 12
Reduced penetrance: AD gene, 80%
penetrance. What would be the risk of an
offspring for having the disease?
1.
2.
3.
4.
5.
6.
0.5
1.0
~0
0.4
0.8
0.2
Slide 13
What is the risk for the offspring
(III-1) for being affected?
1.
2.
3.
4.
5.
6.
1/4
1/6
~0
2/9
1/15
1/12
Slide 14
Strategy
• First calculate the risk that II-1 is a carrier
(Bayes)
• Secondly, calculate the risk of passing on
times risk of being affected
Slide 15
Bayes table for that example
II-1
Carrier
Non-carrier
Prior
½
½
Healthy (conditional)
2/10
1
Joint/product
1/10
5/10
Posterior
1/6
(5/6)
Sum
6/10
Remember that 1/6 is the new carrier risk; it has not taken
into account probability for passing on or for fetus
becoming affected
Slide 16
Example 3
disease with late onset and
physical exam/lab results
Slide 17
Bayes Formula: Integrating Other
Observations
• Mr. Jones is offspring of a person with
Huntington Disease (HD)
• Mr. Jones is 38 and does not show any signs
of HD
• How likely is it that Mr. Jones has the gene
for HD?
Slide 18
HD and Age of Onset
Not
affected
Affected
In an exam question, expect a written presentation of the results rather than a graph. It will
almost always take the form of “the risk for being carrier and affected is X”. Because the person
you are interested in is healthy, no affected, the value you need is risk for being carrier and
healthy, which is 1 – X.
Slide 19
Calculating the Risk
Possibilities
Mr. Jones is a
carrier (Aa)
Mr. Jones is not a
carrier (aa)
Prior probability (from 1/2
known dominant
inheritance)
1/2
Observation (Mr.
Jones has no
symptoms)
1/3
1
Product, adjust to
common base
1/6
1/2 = 3/6
sum=4/6
Throw away divisor,
divide by sum
1/4
3/4
Slide 20
Example 4
Two different observations
Slide 21
Two different observations
• E.g., lab data and offspring
• Use two lines for observation and multiply
both with the prior
Slide 22
Two people are affected with DMD. II-2 has normal
CK (70% of DMD carriers have elevated CK). What
is her risk of being a carrier?
1.
2.
3.
4.
5.
3/43
5/32
1/16
7/62
7/47