Complex diseases are often reported along with disease-related traits (DRT). Sometimes investigators consider both disease and DRT phenotypes separately and sometimes they consider individuals as affected if they have either the disease or the DRT, or both. We propose instead to consider the joint distribution of the disease and the DRT and do a linkage analysis assuming a pleiotropic model. We evaluated our results through analysis of the simulated datasets provided by Genetic Analysis Workshop 14. We first conducted univariate linkage analysis of the simulated disease, Kofendrerd Personality Disorder and one of its simulated associated traits, phenotype b (fear/discomfort with strangers). Subsequently, we considered the bivariate phenotype, which combined the information on Kofendrerd Personality Disorder and fear/discomfort with strangers. We developed a program to perform bivariate linkage analysis using an extension to the Elston-Stewart peeling method of likelihood calculation. Using this program we considered the microsatellites within 30 cM of the gene pleiotropic for this simulated disease and DRT. Based on 100 simulations of 300 families we observed excellent power to detect linkage within 10 cM of the disease locus using the DRT and the bivariate trait

Ji, Fei

Lee, Dayoung

Mendell, Nancy Role

BMC Genetics

English

PubMed

Fei Ji

Dayoung Lee

Nancy Mendell

Springer - Publisher Connector

BioMed CentralBMC Genetics
ssOpen AcceProceedings
A power study of bivariate LOD score analysis of a complex trait 
and fear/discomfort with strangers
Fei Ji*†1, Dayoung Lee2 and Nancy Role Mendell*†2
Address: 1Statistical Genetics Laboratory, Rockefeller University, 1230 York Ave, New York, NY 10021 USA and 2Department of Applied Math and 
Statistics, Stony Brook University, Stony Brook, NY 11794 USA
Email: Fei Ji* - fji@rockefeller.edu; Dayoung Lee - dylee250@gmail.com; Nancy Role Mendell* - nmendell@notes.cc.sunysb.edu
* Corresponding authors    †Equal contributors
Abstract
Complex diseases are often reported along with disease-related traits (DRT). Sometimes
investigators consider both disease and DRT phenotypes separately and sometimes they consider
individuals as affected if they have either the disease or the DRT, or both. We propose instead to
consider the joint distribution of the disease and the DRT and do a linkage analysis assuming a
pleiotropic model. We evaluated our results through analysis of the simulated datasets provided
by Genetic Analysis Workshop 14. We first conducted univariate linkage analysis of the simulated
disease, Kofendrerd Personality Disorder and one of its simulated associated traits, phenotype b
(fear/discomfort with strangers). Subsequently, we considered the bivariate phenotype, which
combined the information on Kofendrerd Personality Disorder and fear/discomfort with strangers.
We developed a program to perform bivariate linkage analysis using an extension to the Elston-
Stewart peeling method of likelihood calculation. Using this program we considered the
microsatellites within 30 cM of the gene pleiotropic for this simulated disease and DRT. Based on
100 simulations of 300 families we observed excellent power to detect linkage within 10 cM of the
disease locus using the DRT and the bivariate trait.
Introduction
Due to the complexity of the transmission of complex dis-
eases, more researchers are paying attention to disease-
related traits (DRT), or endophenotypes. We define a DRT
as an abnormality that 1) appears more frequently in cases
(diseased individuals) than in the population, and 2) has
a higher frequency in unaffected siblings of cases than in
the population. There can be different explanations of the
relationship between the disease and the DRT. One expla-
nation is that the traits are determined by a pleiotropic
gene, a gene that controls more than one trait. For
instance, a single gene mutation may cause an enzyme
deficiency, which in turn may affect more than one tissue
in one individual [1]. Alternatively a pleiotropic allele
may cause both the disease and a DRT abnormality.
The DRT, phenotype b, fear/discomfort with strangers
(FDS), appears at a greater frequency in Kofendrerd Per-
sonality Disorder (KPD) affected individuals than in the
general population. Additionally, the trait FDS appears
more frequently in unaffected siblings of KPD individuals
than in the general population. Moreover, according to
Greenberg [2], both trait and disease are results of an
allele at the D1 locus on chromosome 1. Thus, D1 is a
major gene for FDS and one of several genes for KPD. We
thus consider it to be an ideal candidate for bivariate
genetic analysis assuming a pleiotropic model. It turns out
that if one is considering a categorical DRT with two out-
comes, the bivariate analysis of a disease and DRT reduces
to a univariate linkage analysis of a trait with 4 pheno-
types. Thus, the extension of standard linkage techniques
from Genetic Analysis Workshop 14: Microsatellite and single-nucleotide polymorphism
Noordwijkerhout, The Netherlands, 7-10 September 2004
Published: 30 December 2005
BMC Genetics 2005, 6(Suppl 1):S113 doi:10.1186/1471-2156-6-S1-S113
<supplement> <title> <p>Genetic Analysis Workshop 14: Microsatellite and single-nucleotide polymorphism</p> </title> <editor>Joan E Bailey-Wilson, Laura Almasy, Mariza de Andrade, Julia Bailey, Heike Bickeböller, Heather J Cordell, E Warwick Daw, Lynn Goldin, Ellen L Goode, Courtney Gray-McGuire, Wayne H ning, ail Jarvik, Brion S Maher, Nancy Mendell, Andrew D Paterson, John Rice, Glen Satten, Brian Suar z, Veronica Vieland, Marsha Wilcox, Heping Zhang, Andre s Ziegler and Jean W MacCluer</editor> <note>Proceedings</note> </suppleme t>Page 1 of 5
(page number not for citation purposes)
BMC Genetics 2005, 6:S113to a pleiotropic gene is quite straightforward. In this study
we report the power of analyses done using this approach
in contrast to what one would obtain upon considering
the disease and DRT separately.
Subjects
The study was conducted on nuclear pedigree datasets col-
lected from Aipotu, Karangar, and Danacaa, respectively,
and the combination of these three datasets. The simu-
lated data from each city contained 100 nuclear families
averaging about 7 members per family. There was no
missing phenotype or marker data. Each dataset was sim-
ulated 100 times [2].
In order to demonstrate that FDS was a DRT we investi-
gated its distribution in offspring of these nuclear fami-
lies. For our sample of probands, we used all offspring in
these families who had KPD. All offspring who did not
have KPD were considered unaffected siblings of
probands. Upon doing this we noted that in Karangar
47% of the probands had FDS, 3% of the unaffected sib-
lings of KPD probands had FDS; the rate of FDS in Kara-
ngar was 2% [2]. A slightly stronger association between
FDS and KPD was observed in Aipotu, with 66% of
probands with KPD having FDS, 4% of unaffected siblings
of KPD probands having FDS, and a population preva-
lence of 2%. The strongest association between FDS and
KPD was observed in Danacaa, however, where 100% of
the probands with KPD had FDS, 8% of the unaffected
siblings of probands had FDS, and the population rate
was 2%.
Univariate and bivariate trait linkage analysis
We noted first that the two binary traits could be consid-
ered as a single trait with 4 phenotypes, which we defined
as follows: 1) KPD positive and FDS positive, KPD+ FDS+;
2) KPD positive and FDS negative, KPD+ FDS- ; 3) KPD
negative and FDS positive, KPD- FDS+; 4) KPD negative
and FDS negative, KPD- FDS-.
There are then 12 penetrance values in penetrance matrix
ψB, with entries gu(x). Here gu(x) denotes the penetrance
of the phenotype x for the uth genotype, for u = 1, 2, 3 and
x = 1, 2, 3, 4, where . A nuclear family dataset
is composed of information on family size, the phenotype
of interest, and the marker genotype for each individual.
We used disease locus allele frequencies, and marker allele
frequencies provided by Genetic Analysis Workshop 14
(GAW14) [2].
Conditional on the genetic parameters and the joint dis-
tribution of the 4 phenotypes and marker genotypes in
family members, we calculated the LOD score for the
bivariate trait for a given nuclear family as follows:
Here, as in Elston and Stewart [3], pstu denotes the proba-
bility that an offspring has genotype u at the disease/DRT
locus given that the parents disease/DRT genotypes are s
and t; gu(xi) denotes the probability of having trait pheno-
type x (x = 1, 2, 3, 4) given that the disease/DRT genotype
is u for the ith offspring in the nuclear family; n denotes the
number of offspring; pfm (pmm) denotes the probability
that the father's marker (mother's marker) genotype is fm
(mm); pt (ps) denotes the probability that the father
(mother) has disease/DRT genotype s (t).
The algorithm described above was implemented in a C++
program, GAWBI [4,5], which can be used to yield LOD
scores of univariate traits and bivariate traits for any arbi-
trary nuclear family pedigree dataset.
We computed the bivariate LOD score for the combined
city samples of 300 nuclear families and the average of
these bivariate LOD scores over 100 replicates (bivariate
ELOD). This value was then compared to the average LOD
score obtained on considering the disease status alone
(ELOD-disease) and the trait status alone (ELOD-DRT)
using the usual univariate LOD score method and using
the marginal penetrance values of KPD and FDS assumed
in the bivariate analysis. We then calculated the frequency
of the bivariate LOD ≥ 3.0 out of 100 replicates and
g xu
x
∑ =( ) 1
Bivariate LOD Log=






==
∑∏
10
1
3
1
p g x p g x p gstu u i
ui
n
s s t t( ) ( ) ( ) ,
( )
,
x p p
p g x p g
fm mm
s t
stu u i
ui
n
s














=
==
∑
∑∏
1
3
1
3
1
θ
s t t fm mm
s t
x p g x p p( ) ( ) , /
.
,








=















=
∑
1
3
1 2θ
( )1
Table 1: Penetrances of univariate (KPD, FDS) and bivariate (KPD/FDS) traits
Genotypes Phenotypes
KPD+ FDS+ KPD+ FDS- KPD- FDS+ KPD- FDS- KPD+ FDS+
AA 0.12 0.08 0.24 0.56 0.20 0.36
AB 0.12 0.08 0.24 0.56 0.20 0.36
BB 0.006 0.004 0.0 0.99 0.006 0.006Page 2 of 5
(page number not for citation purposes)
BMC Genetics 2005, 6:S113referred to this value as the bivariate power. Power was
similarly obtained for disease and DRT.
We used the gene frequencies given by GAW14 [2] as the
values in the analysis model. We did not know the pene-
trance values for the combined KPD-FDS phenotypes nor
did we know the penetrance values for KPD or FDS sepa-
rately. We read the information on these two traits and
used this to make an educated guess as to these penetrance
values. In Table 1 we indicate the genotype phenotype
penetrance matrix that we used for our analysis.
The markers in the region close to locus D1 contained in
the microsatellite files were investigated. The number of
alleles at each marker varied from 4 to 9.
Results
The ELOD results for the linkage analysis of the samples
of 300 families are presented in Figure 1A. Figure 1A gives
the ELOD for considering 1) bivariate analysis of the joint
distribution of KPD and FDS, or equivalently a 4-pheno-
type univariate trait (bivariate ELOD), 2) analysis of trait
FDS alone (ELOD-DRT), and 3) analysis of the disease,
KPD alone (ELOD-disease). All three approaches show
high ELOD values for the markers very close to the suscep-
tibility locus, D1, which is between D01S0021 and
D01S0023. The ELOD obtained through analysis of FDS
appears to be consistently higher than the ELOD obtained
through analysis of KPD alone or through the analysis of
the bivariate trait KPD/FDS. The ELOD obtained through
analysis of the bivariate KPD/FDS trait is always higher
than that obtained through analysis of KPD alone.
In Figure 1B, we present the power to detect linkage using
a critical value of observed LOD ≥ 3.0. We observe very
high power (>90%) to detect linkage for loci within 10 cM
of the KPD/FDS locus D1 on analysis of FDS alone and/or
using the bivariate analysis. We also observe essentially no
difference in power for analyses based on FDS as com-
pared to KPD/FDS.
In Figures 2, we present corresponding ELOD and power
results for analysis of 100 replicates of the 100 families in
Aipotu dataset. In this case the ELOD, as expected, is
much lower than that observed in analyses of the three cit-
ies combined. However, it has a similar pattern to that
Linkage analysis of disease, DRT, and bivariate trait with the Aipotu dat set: ELOD (A) and power (percentage (LOD>3)) (B)F gur 2
Linkage analysis of disease, DRT, and bivariate trait with the 
Aipotu dataset: ELOD (A) and power (percentage (LOD>3)) 
(B).
A
B
14
4
6
8
10
12
ELOD-Diseeas
ELOD-DRT
ELOD-Bivariate
E
LO
D
2
0
D01S0019D01S0020D01S0021D01S0025D01S0026D 1S0022D 1S0023D01S0024
Marker Positions on Chromosome 
10
20
30
40
50
60
70
80
90
100
P
er
ce
nt
ag
e 
(L
O
D
>3
)
power_Disease
power_DRT
power_Bivariate
0
D01S0019D01S0020D01S0021D01S0025D01S0026D01S0022D01S0023D01S0024
Marker Positions on Chromosome 
Linkage analysis of disease, DRT, and bivariate trait with the three cities dataset: ELOD (A) and power (p rcen age (LOD>3)) (B)Figur 1
Linkage analysis of disease, DRT, and bivariate trait with the 
three cities dataset: ELOD (A) and power (percentage 
(LOD>3)) (B).
A
B
14
12
10
8
E
LO
D
6
4
2 ELOD-Disease
ELOD-DRT
0
D01S0019D01S0020D01S0021D01S0025D01S0026
ELOD-Bivariate
D 1S0022D 1S0023D01S0024
Marker Positions on Chromosome 
100
90
80
P
er
ce
nt
ag
e 
(L
O
D
>3
) 70
60
50
40
30
20
power_Disease
0
10 power_DRT
power_Bivariate
D01S0019D01S0020D01S0021D01S0025D01S0026D 1S0022D 1S0023D01S0024
Marker Positions on Chromosome Page 3 of 5
(page number not for citation purposes)
BMC Genetics 2005, 6:S113shown in Figure 1A. The corresponding power plot (Fig-
ure 3A) shows that considering the DRT alone appears to
have greater power than the bivariate approach. Similar
results were observed with the Karangar data (not shown).
However, the ELOD and power for Karangar data were
even lower than the values obtained for the Aipotu data.
In Figure 3, we present corresponding results for analysis
of 100 replicates of the 100 families in Danacaa. In this
case the ELOD and power obtained in the bivariate anal-
ysis are the same as those obtained upon the analysis of
FDS alone.
In all ELOD and power figures, the highest values are
observed at marker position D01S0023, which is the clos-
est marker to D1 (the major susceptibility gene).
Discussion and Conclusions
The results observed for the linkage analysis of FDS/KPD
appear at first to be counterintuitive. We would expect
that the bivariate approach would result in greater power
than consideration of a single trait. This is indeed what we
observed in comparing the two approaches under a wide
range of generating models [4]. However Ji [4] considered
the situation in which the analysis model parameter val-
ues were always correct. There are 12 penetrance values (9
of which are functionally independent) and 1 gene fre-
quency parameter involved. In the case of analysis of a
single dichotomous trait there are 6 penetrance values (3
of which are functionally independent) and 1 gene fre-
quency parameter. In this analysis we only have accurate
information on the allele frequencies. We also have a sit-
uation in which these penetrance values are not the same
in all 3 cities so there is not 1 set of correct values for the
combined sample of 3 cities.
We did have a rough estimate of the generating model and
perhaps did make a better than average guess than one
could do in reality. However Ji [4] investigated the robust-
ness of the analysis to using analysis parameter values
which were not equal to the correct ones and obtained a
slight reduction in power.
Our results indicate that the power of the bivariate analy-
sis appears to be more sensitive to the accuracy of the pen-
etrance values assumed than the analysis of the DRT
alone. Ji [4] did note many situations in which analysis
based on the DRT was as powerful as analysis based on the
bivariate trait. However, she did not observe any pene-
trance parameter value for which analysis of the DRT was
more powerful than analysis of the bivariate trait. In Dan-
acaa the criterion for designating an individual as KPD+
was much narrower than the other two cities, resulting in
all KPD+ individuals also being FDS+. This may be a situ-
ation where analysis of the DRT is as powerful as the
bivariate analysis. Additionally, there was less genetic het-
erogeneity in the Danacaa sample.
These findings indicate the need to consider several anal-
ysis model parameter values with a correction for the
number of parameter values considered as is done in LOD
score analysis of a single binary phenotype. We also need
to realize that there are going to be some situations in
which analysis of the trait alone might be as powerful as
analysis of the bivariate trait.
The bivariate analysis discussed in this study was done
using software (GAWBI) developed by Ji and Yoo [4,5];
however, simple manipulation of the data can allow one
to calculate the bivariate trait using LINKAGE [6] with 4
liability classes. In the pedigree input file for the LINKAGE
program, we set the affection status of all subjects to 2;
that is, every person is affected. The liability class is
decided based on the subject's bivariate phenotype j, j = 1,
2, 3, or 4. In the parameter input file, the penetrances of
each liability class are set to equal P(j|genotype), where
genotypes are disease/DRT genotypes. A simple dataset
was tested using both LINKAGE and GAWBI, and identi-
cal results were obtained.
Linkage analysis of disease, DRT, and bivariate trait with the Dan caa d ta et: ELOD (A) and power (perc nt ge (LOD>3)) (B)Figur 3
Linkage analysis of disease, DRT, and bivariate trait with the 
Danacaa dataset: ELOD (A) and power (percentage 
(LOD>3)) (B).
A
B
14
12
10
ELOD-Disease
E
LO
D ELOD-DRT8
ELOD-Bivariate
6
4
2
0
D01S0019D01S0020D01S0021D01S0025D01S0026D 1S0022D 1S0023D01S0024
Marker Positions on Chromosome 
0
10
20
30
40
50
60
70
80
90
100
P
er
ce
nt
ag
e 
(L
O
D
>3
)
power_Diseeas
power_DRT
power_Bivariate
D01S0019D01S0020D01S0021D01S0025D01S0026D 1S0022D 1S0023D01S0024
Marker Positions on Chromosome 1Page 4 of 5
(page number not for citation purposes)
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Abbreviations
DRT: Disease-related traits
FDS: Fear/discomfort with strangers
GAW14: Genetic Analysis Workshop 14
KPD: Kofendrerd Personality Disorder
Authors' contributions
NRM and FJ conceived the study, participated in its design
and coordination, and drafted the manuscript. NRM pre-
sented this work. FJ developed GAWBI, the bivariate LOD
score analysis program for this study. FJ and DL carried
out all the genetic analyses and statistical analyses.
Acknowledgements
We thank Dr. Derek Gordon for reviewing the manuscript and for his help-
ful comments. FJ's research was supported by NIH grant MH44292.
References
1. Vogel F, Motulsky AG: Human Genetics, Problems and Approaches Third
edition. Berlin: Springer; 1997. 
2. Greenberg DA, Zhang J, Shmulewitz D, Strug LJ, Zimmerman R, Singh
V, Marathe S: Construction of the model for Genetic Analysis
Workshop 14 simulated data: genotype-phenotype relation-
ships, gene interaction, linkage, association, disequilibrium,
and ascertainment effects for a complex phenotype.  BMC
Genet 2005, 6(Suppl 1):S3.
3. Elston RC, Stewart J: A general model for the genetic analysis
of pedigree data.  Hum Hered 1971, 21:523-542.
4. Ji F: Linkage analysis of a disease related trait using pleio-
tropic genes.  In Doctoral dissertation Stony Brook University, Depart-
ment of Applied Mathematics and Statistics; 2004. 
5. Yoo YJ: Power study of likelihood based linkage statistics.  In
Doctoral dissertation Stony Brook University, Department of Applied Math-
ematics and Statistics; 2004. 
6. Lathrop GM, Lalouel JM, Julier C, Ott J: Strategies for multilocus
analysis in humans.  Proc Natl Acad Sci USA 1984, 81:3443-3446.Page 5 of 5
(page number not for citation purposes)


A power study of bivariate LOD score analysis of a complex trait and fear/discomfort with strangers

A general model for the genetic analysis of pedigree data. Hum Hered

Linkage analysis of a disease related trait using pleiotropic genes.

Marathe S: Construction of the model for Genetic Analysis Workshop 14 simulated data: genotype-phenotype relationships, gene interaction, linkage, association, disequilibrium, and ascertainment effects for a complex phenotype.

Motulsky AG: Human Genetics, Problems and Approaches Third edition.

Power study of likelihood based linkage statistics.

Strategies for multilocus analysis in humans.

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A power study of bivariate LOD score analysis of a complex trait and fear/discomfort with strangers

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