Journal of Genetic Counseling, Vol. 16, No. 1, February 2007 ( c
2007)
DOI: 10.1007/s10897-006-9040-9
Professional Issues
Bayesian Risk Assessment in Genetic Testing for Autosomal
Dominant Disorders with Age-Dependent Penetrance
Shuji Ogino,
Robert B. Wilson,
Bert Gold,
and Pamela Flodman
Published Online: 13 February 2007
Risk assessment is an essential component of genetic counseling and testing, and the accu-
racy of risk assessment is critical for decision making by consultands. However, it has been
shown that genetic risk calculations may have high error rates in practice. Risk calculations
for autosomal dominant disorders are frequently complicated by age-dependent penetrance
and sensitivities of less than 100% in genetic testing. We provide methods of risk calcula-
tion for prototypical pedigrees of a family at risk for an autosomal dominant disorder with
age-dependent penetrance. Our risk calculations include scenarios in which the sensitivity
of genetic testing is less than 100%, and in which the sensitivity of genetic testing varies for
different family members at risk. Our Bayesian methods permit autosomal dominant disease
probabilities to be calculated accurately, taking into account all relevant information. Our
methods are particularly useful for hereditary cancer syndromes, in which genetic testing can
seldom achieve 100% sensitivity. Our methods can be applied to many different scenarios,
including those where the sensitivity of genetic testing varies for different family members at
risk.
KEY WORDS: bayes; bayesian; genetic risk; risk assessment; genetic counseling; autosomal dominant;
hereditary cancer; penetrance; sensitivity.
1
The content of this publication does not necessarily reflect the
views or policies of the Department of Health and Human Ser-
vices, nor does mention of trade names, commercial products, or
organizations imply endorsement by the U.S. Government.
2
Department of Medical Oncology, Dana-Farber Cancer Institute,
Boston, MA, USA.
3
Department of Pathology,
Brigham and Women’s Hospital,
Harvard Medical School, Boston, MA, USA.
4
Department of Pathology and Laboratory Medicine, University
of Pennsylvania Medical Center, Philadelphia, PA, USA.
5
Human Genetics Section, Laboratory of Genomic Diversity, Na-
tional Cancer Institute at Frederick, Frederick, MD, USA.
6
Department of Pediatrics, University of California Irvine, Irvine,
CA, USA.
7
Correspondence should be directed to Shuji Ogino, MD, PhD,
Department of Pathology,
Brigham and Women’s Hospital,
Harvard Medical School, 75 Francis St., Boston, MA 02115,
USA; e-mail: shuji ogino@dfci.harvard.edu.
INTRODUCTION
Risk assessment is an essential component of
genetic counseling and testing, and Bayesian analy-
sis plays a central role in complex risk calculations
(Bridge,
; Hodge and Flodman,
; Ogino and
Wilson,
; Young,
). However, a recent study,
in which only 20 of 112 respondents correctly es-
timated genetic risks for all three questions of rel-
atively simple to moderately complex calculations,
suggests that there may be high error rates in ge-
netic risk calculations by health care professionals in
clinical genetics (Bonke et al.,
). Clear and com-
prehensible descriptions of risk calculation methods
are needed. We previously developed methods of
Bayesian risk calculations for autosomal recessive
disorders, which are particularly useful for cystic fi-
brosis (CF) (Ogino et al.,
; Ogino et al.,
). We also developed methods to calculate genetic
29
1059-7700/07/0200-0029/0
C
2007 National Society of Genetic Counselors, Inc.
30
Ogino, Wilson, Gold, and Flodman
risks for autosomal recessive spinal muscular atro-
phy (SMA), where differences in gene copy number
and deficiencies of full-length encoded protein are
pathogenic (Ogino et al.,
; Ogino and Wilson,
).
Risk calculations for autosomal dominant dis-
orders are frequently complicated by incomplete,
age-dependent penetrances and sensitivities of less
than 100% for genetic testing. This is particularly
true for hereditary cancer syndromes in which var-
ious loss-of-function mutations in specific genes are
pathogenic and current testing fails to detect all pre-
disposing mutations. Methods to calculate the risk
of carrying a mutation associated with a particular
autosomal dominant condition have been reported
(Bonke et al.,
; Otto and Maestrelli,
For example, Otto and Maestrelli describe a compre-
hensive and generalized approach for families with
isolated cases of disorders with incomplete pene-
trance (Otto and Maestrelli,
). However, these
published methods were only applied to limited sce-
narios in which penetrances were age-independent
(Otto and Maestrelli,
), or in which test sensi-
tivities were 100% (Bonke et al.,
). The
penetrance of many autosomal dominant disorders is
age-dependent, and the sensitivity of genetic testing
is often less than 100%; thus, risk-calculation meth-
ods that take these additional aspects into account
are needed.
In this manuscript, we provide methods of risk
calculation for prototypical pedigrees of a family at
risk for an autosomal dominant hereditary cancer
syndrome with age-dependent penetrance. Our risk
calculations include scenarios in which the sensitiv-
ity of genetic testing is less than 100%, and in which
the sensitivity of genetic testing varies for differ-
ent family members at risk. Our Bayesian methods
allow autosomal dominant disease probabilities to
be calculated accurately, taking into account all rele-
vant information. These methods can be modified for
many different scenarios, including other autosomal
dominant disorders.
METHODS AND RESULTS
We provide various prototypical examples of ge-
netic risk calculations for autosomal dominant disor-
ders with age-dependent penetrance. We described
previously the principles of Bayesian analysis used to
calculate genetic risk (Ogino and Wilson,
). To
perform a Bayesian risk analysis, one must first set
I-1
II-1
I-2 Classic cancer syndrome
Age 50
Asymptomatic
Negative for mutations
Fig. 1.
Pedigree for Scenario 1.
out the problem in a format that allows the neces-
sary calculations to be specified, either by using prob-
ability tables, as presented and illustrated in our pre-
vious articles (Ogino et al.,
), or by graphi-
cally depicting all pedigree structures and available
information, as in the unified approach described by
Hodge (Hodge,
). Second, one must determine
the prior probabilities and conditional probabilities
to be included in the table or pedigrees. Third, one
must calculate the joint and posterior probabilities.
In the risk calculation scenarios described herein, we
designate the penetrance, P(x), as a function of age
x. We assume that the de novo mutation rate(s) for
the disease gene(s) is approximately 0, and that the
disease or syndrome in question is sufficiently rare
that the carrier risk of individuals unrelated to the
proband is approximately 0. We designate the sen-
sitivity of genetic testing for carrier detection as S;
i.e., the test detects the fraction S of all disease alleles
in the general population. We assume that the speci-
ficity of genetic testing in our scenarios is 100%; i.e.,
non-carrier individuals lack disease-associated muta-
tions and test negative. The posterior probabilities
are given in the text rather than in the Bayesian anal-
ysis tables themselves. To obtain the posterior prob-
ability for any given column, one simply divides the
joint probability for that column by the sum of all the
joint probabilities. Excel spreadsheets to facilitate
the posterior-probability calculation for each column
in each Bayesian table are available upon request.
Scenario 1: Autosomal dominant disorder with
age-dependent penetrance and a negative test result
Figure
shows a simple pedigree of a family at
risk for an autosomal dominant hereditary cancer
syndrome. I-2 had characteristic features of the
syndrome and died of cancer. We assume that I-2
is heterozygous for a disease allele; that I-1 is a
non-carrier; and that non-carriers do not develop
Autosomal Dominant Disease Risk Calculations
31
Table I.
Bayesian Analysis for Autosomal Dominant Cancer
Syndrome (Scenario 1)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
Conditional probability of
no symptoms at age 50
1
− P(50)
1
Conditional probability of
a negative test result
1
− S
1
Joint probability
1/2
× {1 − P(50)}
× (1 − S)
1/2
Column
A
B
symptoms. II-1, the son of I-2, is 50 years old and
asymptomatic. P(50) designates the penetrance at
age 50. II-1 tests negative by a genetic test with sensi-
tivity S. What is the probability that II-1 is a carrier?
Table
shows the Bayesian analysis for this scenario.
Before we obtain clinical and testing information on
II-1, the probability that II-1 is a carrier or a non-
carrier is 1/2 or 1/2, respectively (prior probability).
If II-1 is a carrier, the conditional probability that
II-1 is asymptomatic at age 50 is 1
− P(50), and the
conditional probability that II-1 tests negative is
1
− S. If II-1 is a non-carrier, the conditional prob-
ability that II-1 is asymptomatic at age 50 is 1, and
the conditional probability that II-1 tests negative is
1. When P(50) and S are 0.6 and 0.7, respectively,
the joint probabilities of columns A and B are 0.06
and 0.5, respectively. The posterior probability that
II-1 is a carrier is the joint probability of column A
divided by the sum of the joint probabilities, or 0.11.
Scenario 2: Calculating the probability that an
asymptomatic at-risk individual becomes
symptomatic
In Scenario 1, what is the probability that II-1
will become symptomatic by age 60, given that he is
asymptomatic at age 50? Table
shows the Bayesian
analysis for this scenario. P(50) and P(60) desig-
nate the penetrances at age 50 and 60, respectively.
Figure
illustrates the calculations to obtain the con-
ditional probability that an asymptomatic carrier at
age 50 will become symptomatic by age 60. When
P(50), P(60) and S are 0.6, 0.7 and 0.7, respectively,
the joint probabilities of columns A, B and C are
0.015, 0.045 and 0.5, respectively. The posterior prob-
ability that II-1 will become symptomatic by age 60 is
the joint probability of column A divided by the sum
of the joint probabilities, or 0.027. Alternatively, one
Symptomatic; P(50) = 0.6
Symptomatic; P(60) = 0.7
By age 60
1 – P(50)
Probability that this person becomes symptomatic
by age 60, given asymptomatic at age 50
= {P(60) – P(50)} / {1 – P(50)}
P(60) – P(50)
By age 50
Fig. 2.
Age-Dependent Penetrance Determines the Probability
that an At-Risk Asymptomatic Individual Becomes Symptomatic.
I-1
II-2
II-1
I-2 Classic cancer syndrome
III-1
Age 35
No symptoms
Died at age 50
No symptoms
Fig. 3.
Pedigree for Scenario 3.
could first calculate II-1’s carrier risk as in Scenario 1,
and then multiply that risk by the probability that II-
1 will become symptomatic by age 60, given that he is
an asymptomatic carrier at age 50. However, to min-
imize the risk of errors, particularly in more complex
scenarios, we recommend the use of one comprehen-
sive Bayesian analysis table.
Scenario 3: Autosomal dominant disorder with
age-dependent penetrance and a negative test result
in a three-generation pedigree
Figure
shows a pedigree of a family at risk for
an autosomal dominant hereditary cancer syndrome.
I-2 had characteristic features of the syndrome and
died of cancer. II-1, the son of I-2, died at age 50 with-
out any evidence of the syndrome, and tested neg-
ative by a genetic test with sensitivity S. P(50) and
P(35) designate penetrances at age 50 and 35, respec-
tively. What are the probabilities that II-1 and III-1
are carriers? Table
shows the Bayesian analysis
for this scenario. Each column represents a particular
32
Ogino, Wilson, Gold, and Flodman
Table II.
Bayesian Analysis Calculating the Probability of Becoming Symptomatic (Scenario 2)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
Conditional probability of
no symptoms at age 50
1
− P(50)
1
Conditional probability of
a negative test result
1
− S
1
Status at age 60
Symptomatic
Asymptomatic
Asymptomatic
{P(60) − P(50)}/{1 − P(50)}
{1 − P(60)}/{1 − P(50)}
1
Joint probability
1/2
× {P(60) − P(50)}(1 − S)
1/2
× {1 − P(60)}(1 − S)
1/2
Column
A
B
C
Table III.
Bayesian Analysis for Autosomal Dominant Cancer Syndrome (Scenario 3)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
Conditional probability of
no symptoms at age 50
1
− P(50)
1
Conditional probability of
a negative test result
1
− S
1
III-1
Carrier
Non-carrier
Non-carrier
Conditional probability of
inheriting alleles
1/2
1/2
1
Conditional probability of
no symptoms at age 35
1
− P(35)
1
1
Joint probability
1/4
× {1 − P(50)} {1 − P(35)} (1 − S)
1/4
× {1 − P(50)} (1 − S)
1/2
Column
A
B
C
combination of possibilities. For example, column A
represents the situation in which II-1 is a carrier, II-1
is asymptomatic at age 50, II-1 tests negative for mu-
tations, III-1 is a carrier; and III-1 is asymptomatic at
age 35. When P(50), P(35) and S are 0.6, 0.3 and 0.7,
respectively, the joint probabilities of columns A, B
and C are 0.021, 0.03 and 0.5, respectively. The pos-
terior probabilities of columns A, B and C are 0.038,
0.054 and 0.91, respectively. III-1’s carrier risk is the
posterior probability of column A, or 0.038, and II-1’s
carrier risk is the sum of the posterior probabilities of
column A and B, or 0.093.
Scenario 4: Multiple at-risk family members
negative for different panels of mutations
Because of advances in molecular-diagnostic
technologies, it is not uncommon for two or more
at-risk individuals in a given family to undergo
genetic testing at different times and/or at different
institutions, often with testing panels that differ in
the disease-causing mutations detected. In a modi-
fication of Scenario 3, II-1 tests negative by Test 1,
a mutation panel with sensitivity S
1
, and III-1 tests
Sensitivity S
1
Sensitivity S
2
Test 2
1 – S
1
Sensitivity of Test 2 for the detection of mutations that
cannot be detected by Test 1 = (S
2
– S
1
) / (1 – S
1
)
S
2
– S
1
Test 1
Fig. 4.
Test 2 Detects More Mutations Than Test 1.
negative by Test 2, an expanded mutation panel
(with sensitivity S
2
) that include the Test 1 mutation
panel. The sensitivity of Test 2 for the detection of
mutations undetectable by Test 1 is (S
2
− S
1
)/(1
− S
1
)
(Fig.
). In addition to the fraction S
1
of all mutations
detectable by Test 1, Test 2 detects an additional
fraction (S
2
− S
1
) of all mutations. For mutations
undetectable by Test 1
{i.e., the fraction (1 − S
1
)
of all mutations
}, the sensitivity of Test 2 is
Autosomal Dominant Disease Risk Calculations
33
Table IV.
Bayesian Analysis for Autosomal Dominant Cancer Syndrome with Two At-Risk Individuals Testing
Negative by Different Mutation Panels (Scenarios 4 and 5)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
Conditional probability of
no symptoms at age 50
1
− P(50)
1
Conditional probability of
a negative test result
(Test 1)
1
− S
1
1
III-1
Carrier
Non-carrier
Non-carrier
Conditional probability of
inheriting alleles
1/2
1/2
1
Conditional probability of
no symptoms at age 35
1
− P(35)
1
1
Conditional probability of
a negative test result
(Test 2)
1
− (S
2
− S
1
)/(1
− S
1
)
1
1
Joint probability
1/4
× {1 − P(50)}{1 − P(35)}(1 − S
2
)
1/4
× {1 − P(50)}(1 − S
1
)
1/2
Column
A
B
C
(S
2
− S
1
)/(1
− S
1
), and the conditional probability
that III-1 is negative by Test 2 (if II-1 and III-1
are carriers and if II-1 tests negative by Test 1) is
{1 − (S
2
− S
1
)/(1
− S
1
)
} = (1 − S
2
)/(1
− S
1
). Table
shows the Bayesian analysis for this scenario. When
P(50), P(35), S
1
and S
2
are 0.6, 0.3, 0.7 and 0.8,
respectively, the joint probabilities of columns A,
B and C, are 0.014, 0.03 and 0.5, respectively. The
posterior probabilities of columns A, B, and C, are
0.026, 0.055, and 0.92, respectively. The carrier risk
of II-1 is the sum of the posterior probabilities of
columns A and B, or 0.081. The carrier risk of III-1
is the posterior probability of column A, or 0.026.
If III-1 and II-1 test negative by the same muta-
tion panel (i.e., S
2
= S
1
), then the test result for III-1
does not change the risk calculations. The probabil-
ity that III-1 has a mutation detectable by the test is
0, even if III-1 is a carrier. If Test 1 detects more mu-
tations than Test 2 (i.e., S
1
>
S
2
), then the test result
on III-1 again does not change the risk calculations.
The probability that III-1 has a mutation detectable
by Test 2 is 0, even if III-1 is a carrier.
Scenario 5: Both of two different testing panels
contain mutations that are not included in the other
panel, in addition to mutations that are included in
both panels
In a modification of Scenario 4 (Fig.
), if Test 1
panel and Test 2 panel contain overlapping muta-
tions as well as mutations that are not included in
Sensitivity 75%
Sensitivity 65%
Test 2
10%
Sensitivity of Test 2 for the detection of mutations that
cannot be detected by Test 1 = 15%/(15%+10%) = 0.6
15%
Test 1
25%
50%
Fig. 5.
Both Test 1 and Test 2 Can Detect Mutations That Are
Not Included in the Other Testing Panel.
the other panel, how does it affect risk calculations?
In this case, both Test 1 and Test 2 can detect mu-
tation(s) that cannot be detected by the other test
(Fig.
). Consider that the overlapping mutations in
both panels consist 50% of all mutant alleles in the
general population; that mutations in Test 1 panel
that are not included in Test 2 panel consist 25%
of all mutant alleles; that mutations in Test 2 panel
that are not included in Test 1 panel consist 15% of
all mutant alleles; and that the remaining 10% of all
mutant alleles cannot be detected by either Test 1
or Test 2 (Fig.
). The sensitivities of Test 1 and
Test 2 for the detection of carriers in a previously
untested family would be 75% (
= 50% + 25%) and
65% (
= 50% + 15%), respectively. In this scenario,
34
Ogino, Wilson, Gold, and Flodman
I-1
II-2
II-1
I-2 Classic cancer syndrome
III-4
III-3 Age 30
III-2 Age 35
III-1
IV-3 Age 5
IV-2 Age 4
IV-1 Age 7
Died at age 50
Fig. 6.
Pedigree for Scenarios 6 through 11.
the sensitivity of Test 2 for the detection of mutations
undetectable by Test 1 is 0.6
{ = 15%/(15% + 10%)}.
Thus, the “conditional probability of a negative test
result (Test 2)” (the third row from the bottom in
Table
) in column A is (1
− 60%) = 0.4. The “con-
ditional probability of a negative test result (Test 1)”
(the forth row from the top) for columns A and B is
(1
− 75%) = 0.25. When P(50) and P(35) are 0.6 and
0.3, respectively, the joint probabilities of columns
A, B and C, are 0.007, 0.025 and 0.5, respectively.
The posterior probabilities of columns A, B and C,
are 0.013, 0.047, and 0.94, respectively. The carrier
risk of II-1 is the sum of the posterior probabilities of
columns A and B, or 0.060. The carrier risk of III-1
is the posterior probability of column A, or 0.013.
Scenario 6: Autosomal dominant disorder with
age-dependent penetrance in a complex pedigree
Figure
shows a more complex pedigree of a
family at risk for an autosomal dominant hereditary
cancer syndrome. I-2 had characteristic features of
the syndrome and died of cancer. II-1, the son of I-2,
died at age 50 without any evidence of the syndrome.
III-2 and III-3, a son and daughter of II-1, are now
age 35 and 30, respectively, and are both asymp-
tomatic. IV-1 and IV-2 are the son (seven years old)
and daughter (four years old), respectively, of III-2.
IV-3 is a daughter of III-3 and is 5 years old. We as-
sume that I-1, II-2, III-1, and III-4 are non-carriers.
P(50), P(35) and P(30) designate the penetrances of
this syndrome at age 50, 35 and 30, respectively. Pen-
etrances at age 7 and 5 years old are essentially 0.
What are the probabilities that II-1, III-2, III-3, IV-1,
IV-2, and IV-3 are carriers? Table
shows the
Bayesian analysis for this scenario. Because the ages
of at-risk individuals without symptoms modify the
carrier risks of all other at-risk family members, it is
important to incorporate all relevant family informa-
tion in one table. Each column represents a particular
combination of possibilities. For example, column A
represents the situation in which II-1 is a carrier; II-1
is asymptomatic at age 50, III-2 is a carrier, III-2 is
asymptomatic at age 35, III-3 is a carrier; and III-3
is asymptomatic at age 30. When P(50), P(35) and
P(30) are 0.6, 0.3 and 0.2, respectively, then the joint
probabilities of columns A, B, C, D, and E, are 0.028,
0.035, 0.04, 0.05, and 0.5, respectively. The posterior
probabilities of columns A, B, C, D, and E, are 0.043,
0.054, 0.061, 0.077, and 0.77, respectively. The carrier
risk of II-1 is the sum of the posterior probabilities
of columns A through D, or 0.23. The carrier risk of
III-2 is the sum of the posterior probabilities of
columns A and B, or 0.096. The carrier risk of III-
3 is the sum of the posterior probabilities of columns
A and C, or 0.10. The carrier risk of IV-1 and IV-2 is
half of III-2’s carrier risk, or 0.048, and IV-3’s carrier
risk is half of III-3’s carrier risk, or 0.052.
Scenario 7: A complex pedigree with an at-risk
family member negative for mutations
Suppose one of the at-risk individuals tests neg-
ative for disease-associated mutations. For exam-
ple, in the Fig.
pedigree, III-2 tests negative by a
mutation panel with sensitivity S. Table
shows
the Bayesian analysis for this scenario. Note that
the analysis incorporates the sensitivity of genetic
testing, which modifies the risks accordingly. When
P(50), P(35), P(30) and S are 0.6, 0.3, 0.2 and 0.7, re-
spectively, the joint probabilities of columns A, B, C,
D, and E, are 0.0084, 0.0105, 0.04, 0.05, and 0.5, re-
spectively. The posterior probabilities of columns A,
B, C, D, and E, are 0.014, 0.017, 0.066, 0.082, and 0.82,
respectively. The carrier risk of II-1 is the sum of the
posterior probabilities of columns A through D, or
0.18. The carrier risk of III-2 is the sum of the poste-
rior probabilities of columns A and B, or 0.031. The
carrier risk of III-3 is the sum of the posterior proba-
bilities of columns A and C, or 0.079.
Scenario 8: A complex pedigree with multiple at-risk
family members testing negative for mutations
Suppose two of the at-risk individuals test
negative for disease-associated mutations. For ex-
ample, in the Fig.
pedigree, III-2 and III-3 test
Autosomal Dominant Disease Risk Calculations
35
Table V.
Bayesian Analysis for Autosomal Dominant Cancer Syndrome (Scenario 6)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
II-1 asymptomatic
1
− P(50)
1
III-2
Carrier
Non-carrier
Non-carrier
1/2
1/2
1
III-2 asymptomatic
1
− P(35)
1
1
III-3
Carrier
Non-carrier
Carrier
Non-carrier
Non-carrier
1/2
1/2
1/2
1/2
1
III-3 asymptomatic
1
− P(30)
1
1
− P(30)
1
1
Joint probability
1/8
× {1 − P(50)}
{1 − P(35)}{1 − P(30)}
1/8
× {1 − P(50)}
{1 − P(35)}
1/8
× {1 − P(50)}
{1 − P(30)}
1/8
× {1 − P(50)}
1/2
Column
A
B
C
D
E
Table VI.
Bayesian Analysis of Autosomal Dominant Cancer Syndrome with a Negative Genetic Test Result (Scenario 7)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
II-1 asymptomatic
1
− P(50)
1
III-2
Carrier
Non-carrier
Non-carrier
1/2
1/2
1
III-2 asymptomatic
1
− P(35)
1
1
III-2 negative for
mutations
1
− S
1
1
III-3
Carrier
Non-carrier
Carrier
Non-carrier
Non-carrier
1/2
1/2
1/2
1/2
1
III-3 asymptomatic
1
− P(30)
1
1
− P(30)
1
1
Joint probability
1/8
× {1 − P(50)}
{1 − P(35)}{1 − P(30)}
(1
− S)
1/8
× {1 − P(50)}
{1 − P(35)}(1 − S)
1/8
× {1 − P(50)}
{1 − P(30)}
1/8
× {1 − P(50)}
1/2
Column
A
B
C
D
E
Table VII.
Bayesian Analysis of Autosomal Dominant Cancer Syndrome with Negative Genetic Test Results (Scenario 8)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
II-1 asymptomatic
1
− P(50)
1
III-2
Carrier
Non-carrier
Non-carrier
1/2
1/2
1
III-2 asymptomatic
1
− P(35)
1
1
III-2 negative for
mutations
1
− S
1
1
III-3
Carrier
Non-carrier
Carrier
Non-carrier
Non-carrier
1/2
1/2
1/2
1/2
1
III-3 asymptomatic
1
− P(30)
1
1
− P(30)
1
1
III-3 negative for
mutations
1
1
1
− S
1
1
Joint probability
1/8
× {1 − P(50)}
{1 − P(35)}{1 − P(30)}
(1
− S)
1/8
× {1 − P(50)}
{1 − P(35)} (1 − S)
1/8
× {1 − P(50)}
{1 − P(30)}
(1
− S)
1/8
× {1 − P(50)}
1/2
Column
A
B
C
D
E
negative by a mutation panel with sensitivity S.
Table
shows the Bayesian analysis for this
scenario. When P(50), P(35), P(30) and S are 0.6,
0.3, 0.2 and 0.7, respectively, the joint probabilities
of columns A, B, C, D, and E, are 0.0084, 0.0105,
0.012, 0.05, and 0.5, respectively. Note that for
column A, the conditional probability that III-3
tests negative is 1. This is because in the column A
situation, III-2 is a carrier and tests negative, indi-
cating that the mutation is undetectable by the test.
36
Ogino, Wilson, Gold, and Flodman
Table VIII.
Bayesian Analysis of Autosomal Dominant Cancer Syndrome with Two At-Risk Individuals Testing Negative for Differ-
ent Mutation Panels (Scenario 9)
II-1
Carrier
Non-carrier
Prior probability
1/2
1/2
II-1 asymptomatic
1
− P(50)
1
III-2
Carrier
Non-carrier
Non-carrier
1/2
1/2
1
III-2 asymptomatic
1
− P(35)
1
1
III-2 negative for
mutations by Test 1
1
− S
1
1
1
III-3
Carrier
Non-carrier
Carrier
Non-carrier
Non-carrier
1/2
1/2
1/2
1/2
1
III-3 asymptomatic
1
− P(30)
1
1
− P(30)
1
1
III-3 negative for
mutations by Test 2
1
− (S
2
− S
1
)/ (1
− S
1
)
1
1
− S
2
1
1
Joint probability
1/8
× {1 − P(50)}
{1 − P(35)}{1 − P(30)}
(1
− S
2
)
1/8
× {1 − P(50)}
{1 − P(35)} (1 − S
1
)
1/8
× {1 − P(50)}
{1 − P(30)}
(1
− S
2
)
1/8x
{1 − P(50)}
1/2
Column
A
B
C
D
E
On the other hand, for column C, the conditional
probability that III-3 is tests negative is (1
− S).
This is because in the column C situation, III-2 is a
non-carrier and the mutation has not been shown
to be undetectable. The posterior probabilities of
columns A, B, C, D, and E, are 0.014, 0.018, 0.021,
0.086, and 0.86, respectively. The carrier risk of II-1
is the sum of the posterior probabilities of columns
A through D, or 0.14. The carrier risk of III-2
is the sum of the posterior probabilities of columns
A and B, or 0.032. The carrier risk of III-3 is the sum
of the posterior probabilities of columns A and C, or
0.035.
Suppose that, in addition to III-2 and III-3, IV-1
is tested by the same genetic test. Note that the risk
calculations would be unchanged. This is because
III-2 tested negative, indicating that the mutation, if
present in III-2 and IV-1, is undetectable.
Scenario 9: A complex pedigree with multiple at-risk
family members testing negative by different
mutation panels
As noted above, because of advances in
molecular-diagnostic technologies, it is not uncom-
mon for two or more at-risk individuals in a given
family to undergo genetic testing at different times
and/or at different institutions, often with testing
panels that differ in the disease-causing mutations
detected. In the Fig.
pedigree, for example, sup-
pose that III-2 tests negative by Test 1, a mutation
panel with sensitivity S
1
, and III-3 tests negative by
Test 2, an expanded mutation panel with sensitivity
S
2
. Table
I shows the Bayesian analysis for this
scenario. Column A represents a situation in which
III-2 is a carrier with a mutation undetectable by
Test 1, and III-3 is a carrier with a mutation un-
detectable by Test 2. What is the probability that
III-3, who carries a mutation undetectable by Test
1, tests negative by Test 2? As illustrated in Fig.
in addition to the fraction S
1
of all mutations de-
tectable by Test 1, Test 2 detects an additional frac-
tion (S
2
− S
1
) of all mutations. For mutations unde-
tectable by Test 1
{i.e., the fraction (1 − S
1
) of all mu-
tations
}, the sensitivity of Test 2 is (S
2
− S
1
)/(1
− S
1
),
and the conditional probability that III-3 is nega-
tive by Test 2 (column A; if II-1, III-2, and III-3
are all carriers and if III-2 tests negative by Test 1)
is
{1 − (S
2
− S
1
)/(1
− S
1
)
} = (1 − S
2
)/(1
− S
1
). When
P(50), P(35), P(30), S
1
and S
2
are 0.6, 0.3, 0.2, 0.7 and
0.8, respectively, the joint probabilities of columns A,
B, C, D, and E, are 0.0056, 0.0105, 0.008, 0.05, and 0.5,
respectively. The posterior probabilities of columns
A, B, C, D, and E, are 0.0098, 0.018, 0.014, 0.087, and
0.87, respectively. The carrier risk of II-1 is the sum
of the posterior probabilities of columns A through
D, or 0.13. The carrier risk of III-2 is the sum of the
posterior probabilities of columns A and B, or 0.028.
The carrier risk of III-3 is the sum of the posterior
probabilities of columns A and C, or 0.024. The car-
rier risk of IV-1 and IV-2 is half of III-2’s carrier risk,
or 0.014, and IV-3’s carrier risk is half of III-3’s car-
rier risk, or 0.012.
Autosomal Dominant Disease Risk Calculations
37
Table IX.
Bayesian Analysis of Autosomal Dominant Cancer Syndrome with Three At-Risk Individuals Testing Negative by Two
Different Mutation Panels (Scenario 9)
II-1
Carrier
Non-
carrier
Prior probability
1/2
1/2
II-1
asymptomatic
1
− P(50)
1
III-2
Carrier
Non-carrier
Non-
carrier
1/2
1/2
1
III-2
asymptomatic
1
− P(35)
1
1
III-2 negative for
mutations by
Test 1
1
− S
1
1
1
III-3
Carrier
Non-carrier
Carrier
Non-carrier
Non-
carrier
1/2
1/2
1/2
1/2
1
III-3
asymptomatic
1
− P(30)
1
1
− P(30)
1
1
III-3 negative for
mutations by
Test 2
1
− (S
2
− S
1
)/(1
− S
1
)
1
1
− S
2
1
1
IV-1
Carrier
Non-carrier
Carrier
Non-carrier
Non-carrier
Non-carrier
Non-
carrier
1/2
1/2
1/2
1/2
1
1
1
IV-1 negative for
mutations by
Test 2
1
1
1
− (S
2
− S
1
)/(1
− S
1
)
1
1
1
1
Joint probability
1/16
× {1 − P(50)}
{1 − P(35)}
{1 − P(30)}
(1
− S
2
)
1/16
×
{1 − P(50)}
{1 − P(35)}
{1 − P(30)}
(1
− S
2
)
1/16
× {1 − P(50)}
{1 − P(35)}
(1
− S
2
)
1/16
× {1 − P(50)}
{1 − P(35)}
(1
− S
1
)
1/8
×
{1 − P(50)}
{1 − P(30)}
(1
− S
2
)
1/8
×
{1 − P(50)}
1/2
Column
A
B
C
D
E
F
G
Suppose IV-1, the son of III-2, tests nega-
tive by Test 2. Table
shows the Bayesian anal-
ysis for this scenario. As in the example above,
the conditional probability that III-3 is a carrier
and tests negative by Test 2, if III-2 carries a
mutation undetectable by Test 1 (columns A and
B), is
{1 − (S
2
− S
1
)/(1
− S
1
)
} = (1 − S
2
)/(1
− S
1
). The
conditional probability that IV-1 tests negative by
Test 2, if III-2 carries a mutation undetectable by
Test 1 and if III-3 is a non-carrier (column C),
is
{1 − (S
2
− S
1
)/(1
− S
1
)
} = (1 − S
2
)/(1
− S
1
). On the
other hand, the conditional probability that IV-1 is
a carrier and tests negative by Test 2, if III-3 car-
ries a mutation undetectable by Test 2 (column A),
is 1. When P(50), P(35), P(30), S
1
and S
2
are 0.6,
0.3, 0.2, 0.7 and 0.8, respectively, the joint probabil-
ities of columns A, B, C, D, E, F and G are 0.0028,
0.0028, 0.0035, 0.00525, 0.008, 0.05, and 0.5, respec-
tively. The posterior probabilities of columns A, B,
C, D, E, F and G are 0.0049, 0.0049, 0.0061, 0.0092,
0.014, 0.087 and 0.87, respectively. The carrier risk
of II-1 is the sum of the posterior probabilities of
columns A through F, or 0.13. The carrier risk of III-
2 is the sum of the posterior probabilities of columns
A through D, or 0.025. The carrier risk of III-3 is the
sum of the posterior probabilities of columns A, B
and E, or 0.024. The carrier risk of IV-1 is the sum
of the posterior probabilities of columns A and C, or
0.011. The carrier risk of IV-2 is half of III-2’s carrier
risk, or 0.013, and IV-3’s carrier risk is half of III-3’s
carrier risk, or 0.012.
Scenario 10: Penetrance reaches 100%
A penetrance that reaches 100% for an at-risk
individual in a pedigree simplifies risk calculations.
For example, in Scenario 6, if II-1 lived to the age
38
Ogino, Wilson, Gold, and Flodman
of 80, and if the penetrance at age 80 were 100%,
then the joint probability of columns A through D in
Table
would be 0. The only possibility that remains
is that II-1, III-2 and III-3 are all non-carriers.
Scenario 11: Test sensitivity reaches 100%.
A genetic-test sensitivity of 100% for an at-risk
individual in a pedigree simplifies risk calculations.
For example, in Scenario 7 (Table
), if the test
sensitivity for III-2 were 100% (S
= 1), then the joint
probability of columns A and B would be 0, and III-
2’s carrier risk would be 0. In Scenario 8 (Table
if the test sensitivity for III-2 and III-3 were 100%
(S
= 1), then the joint probability of columns A, B,
and C would be 0.
DISCUSSION
We conducted this study to provide comprehen-
sive means to calculate genetic risks for autosomal
dominant disorders with age-dependent penetrance
for which genetic testing cannot achieve 100% sen-
sitivity. Risk calculations for autosomal dominant
disorders are frequently complicated by incomplete
penetrance and sensitivities of less than 100% in ge-
netic testing. This is particularly true for hereditary
cancer syndromes in which various loss-of-function
mutations in specific genes are pathogenic and cur-
rent testing fails to detect all predisposing mutations.
Our risk calculations include scenarios in which the
sensitivity of genetic testing is less than 100%, and in
which the sensitivity of genetic testing varies for dif-
ferent family members at risk.
Bayesian analysis plays an essential role in cal-
culations of genetic risk (Bridge,
; Ogino and
Wilson,
; Ogino and Wilson,
; Young,
Accurate risk assessment is critical for decision mak-
ing by consultands, yet a recent study suggests that
there may be high error rates in genetic risk cal-
culations by health care professionals in clinical ge-
netics (Bonke et al.,
). In practice, risk calcula-
tions, particularly in complicated scenarios, should
be checked independently by a second geneticist
to prevent errors (Hodge and Flodman,
). We
abide by this rule ourselves. Even in the best of cir-
cumstances, clinicians must be alert to the limita-
tions inherent in genetic risk calculations (Biesecker,
). These limitations include uncertainties in clin-
ical diagnoses, pedigree information, and/or allelic
frequencies; unrecognized abortuses; gonadal mo-
saicism; and de novo mutations.
Because of advances in molecular-diagnostic
technologies, it is not uncommon for two or more
at-risk individuals in a given family to undergo ge-
netic testing at different times and/or at different
institutions, often with testing panels that differ in
the disease-causing mutations detected. Discrepant
sensitivities of genetic tests for different at-risk in-
dividuals in the same pedigree are not infrequently
encountered, given the rapid advances in molecular-
diagnostic technologies and the decreasing costs of
detecting a given panel of mutations become less ex-
pensive.
In risk calculations, particularly in more com-
plex scenarios, it is important not to rely on intuition
(Flodman and Hodge,
). To assess all relevant
information systematically, and thereby minimize er-
rors, we recommend the use of one comprehensive
Bayesian analysis table. In addition, because infor-
mation regarding at-risk individuals can modify the
risks of all other at-risk family members, it is impor-
tant to incorporate all relevant family information.
The use of one comprehensive Bayesian analysis ta-
ble decreases the likelihood of missing relevant fam-
ily and testing information, and provides results for
all interrelated risk calculations at once.
We admit that genetic risk calculations in gen-
eral have limitations. We can apply our methods to
scenarios where a consultand and/or relative(s) have
either negative or positive results by genetic tests.
In genetic testing such as a DNA sequencing test
for a hereditary cancer syndrome, however, it is not
uncommon to find a genetic sequence variant with
unknown clinical significance. Unless the probability
that such a variant is actually a disease causing muta-
tion is known, it is not possible to provide a precise
risk estimate. It is also difficult to precisely calculate
specificity (though it is close to 1), and some genetic
tests such as DNA sequencing may have a substan-
tial frequency of such uncertain results. However, in
practice, one can use specificity equaling 1 for many
genetic tests.
In conclusion, we have developed Bayesian
analysis methods to calculate genetic risks for auto-
somal dominant disorders with age-dependent pene-
trance. Our methods can be applied to many differ-
ent scenarios, including those where the sensitivity of
genetic testing is less than 100% and where the sen-
sitivity of genetic testing varies for different family
members at risk.
Autosomal Dominant Disease Risk Calculations
39
ACKNOWLEDGMENTS
This project has been funded in part with Fed-
eral Funds from the National Cancer Institute, Na-
tional Institutes of Health. We thank Lindsay Mid-
delton and Mei-Chiung Shih for critical reading of
the manuscript.
REFERENCES
Biesecker, L. (2005). Accuracy and precision in Bayesian analysis.
Am J Med Genet A, 134, 111.
Bonke, B., Tibben, A., Lindhout, D., Clarke, A. J., & Stijnen, T.
(2005). Genetic risk estimation by healthcare professionals.
Med J Aust, 182, 116–118.
Bonke, B., Tibben, A., Lindhout, D., & Stijnen, T. (2002).
Favourable mutation test outcomes for individuals at risk for
Huntington disease change the perspectives of first-degree
relatives. Hum Genet, 111, 297–298.
Bonke, B., Tibben, A., Lindhout, D., & Stijnen, T. (2006). Calcu-
lating risk changes after negative mutation test outcomes for
autosomal dominant hereditary late-onset disorders. Hered-
ity, 96, 259–261.
Bridge, P. J. (1997). The Calculation of Genetic Risks: Worked Ex-
amples in DNA Diagnostics. Second Edition edn. The Johns
Hopkins University Press, Baltimore.
Flodman, P., & Hodge, S. E. (2001). A genetic risk calculation sur-
prise. Am J Med Genet, 100, 169–171.
Hodge, S. E. (1998). A simple, unified approach to Bayesian risk
calculations. J Genet Couns, 7, 235–261.
Hodge, S. E., & Flodman, P. L. (2004). Risk calculations: still es-
sential in the molecular age. Am J Med Genet, 129A, 215–
217.
Ogino, S., Flodman, P., Wilson, R. B., Gold, B., & Grody, W. W.
(2005). Risk calculations for cystic fibrosis in neonatal screen-
ing by immunoreactive trypsinogen and CFTR mutation
tests. Genet Med, 7, 317–327.
Ogino, S., Leonard, D. G., Rennert, H., Ewens, W. J., & Wilson, R.
B. (2002). Genetic risk assessment in carrier testing for spinal
muscular atrophy. Am J Med Genet, 110, 301–307.
Ogino, S., & Wilson, R. B. (2002). Genetic testing and risk assess-
ment for spinal muscular atrophy (SMA). Hum Genet, 111,
477–500.
Ogino, S., & Wilson, R. B. (2004). Bayesian Analysis and Risk As-
sessment in Genetic Counseling and Testing. J Mol Diagn, 6,
1–9.
Ogino, S., Wilson, R. B., Gold, B., Hawley, P., & Grody, W. W.
(2004a). Bayesian analysis for cystic fibrosis risks in prenatal
and carrier screening. Genet Med, 6, 439–449.
Ogino, S., Wilson, R. B., & Grody, W. W. (2004b). Bayesian risk
assessment for autosomal recessive diseases: fetal echogenic
bowel with one or no detectable CFTR mutation. J Med
Genet, 41, e70.
Otto, P. A., & Maestrelli, S. R. (2000). Heterozygosity probabil-
ities for normal relatives of isolated cases affected by in-
completely penetrant conditions and the calculation of recur-
rence risks for their offspring. I. Autosomal dominant genes.
Am J Med Genet, 95, 43–48.
Young, I. D. (1999). Introduction to risk calculation in genetic
counseling. 2nd edn. Oxford University Press, Oxford.
Wyszukiwarka
Podobne podstrony:
fulltext286 id 181306 Nieznany
fulltext106 id 181301 Nieznany
fulltext id 181296 Nieznany
fulltext873 id 181318 Nieznany
fulltext329 id 181307 Nieznany
fulltext895 id 181321 Nieznany
fulltext476 id 181310 Nieznany
fulltext878 id 181320 Nieznany
fulltext286 id 181306 Nieznany
Abolicja podatkowa id 50334 Nieznany (2)
4 LIDER MENEDZER id 37733 Nieznany (2)
katechezy MB id 233498 Nieznany
metro sciaga id 296943 Nieznany
perf id 354744 Nieznany
interbase id 92028 Nieznany
Mbaku id 289860 Nieznany
Probiotyki antybiotyki id 66316 Nieznany
miedziowanie cz 2 id 113259 Nieznany
LTC1729 id 273494 Nieznany
więcej podobnych podstron