Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL) using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent (IBD) scoring methods. Each method used all marker data for all markers on a chromosome. Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL, corroborating previously published results. However, these results were not replicated in a classical linkage analysis of the data or by using IBD scoring methods. We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method accommodating genetically complex traits and linkage heterogeneity, validation of these signals remains elusive

Basu, Saonli

George, Andrew W

Li, Na

Rothstein, Joseph H

Sieberts, Solveig K

Stewart, William

Thompson, Elizabeth A

Wijsman, Ellen M

BMC Genetics

English

PubMed

Andrew W George

Saonli Basu

Na Li

Joseph H Rothstein

Solveig K Sieberts

William Stewart

Ellen M Wijsman

Elizabeth A Thompson

Springer - Publisher Connector

Approaches to mapping genetically correlated complex traits

Crossref

BioMed CentralBMC Genetics
ssOpen AcceProceedings
Approaches to mapping genetically correlated complex traits
Andrew W George*1, Saonli Basu1, Na Li2, Joseph H Rothstein2, 
Solveig K Sieberts1, William Stewart1, Ellen M Wijsman2,3 and 
Elizabeth A Thompson1
Address: 1Department of Statistics, University of Washington, Seattle, USA, 2Department of Biostatistics, University of Washington, Seattle, USA 
and 3Division of Medical Genetics, Department of Medicine, University of Washington, Seattle, USA
Email: Andrew W George* - andrew-george@uiowa.edu; Saonli Basu - saonli@stat.washington.edu; Na Li - lina@u.washington.edu; 
Joseph H Rothstein - joe419@u.washington.edu; Solveig K Sieberts - solly@stat.washington.edu; William Stewart - babar@stat.washington.edu; 
Ellen M Wijsman - wijsman@u.washington.edu; Elizabeth A Thompson - thompson@stat.washington.edu
* Corresponding author    
Abstract
Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham
Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with
covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL)
using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent
(IBD) scoring methods. Each method used all marker data for all markers on a chromosome.
Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL,
corroborating previously published results. However, these results were not replicated in a
classical linkage analysis of the data or by using IBD scoring methods.
We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but
interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method
accommodating genetically complex traits and linkage heterogeneity, validation of these signals
remains elusive.
Background
The aim of our analyses was to detect and localize trait loci
associated with quantitative traits logtriglyceride (lnTG)
and high-density lipoprotein cholesterol (HDL) in the
Framingham Heart Study data. Based primarily on Shear-
man et al. [1], we focused our search on certain chromo-
somes. By using Markov chain Monte Carlo analysis
(MCMC), we were able to perform linkage analyses of
data collected on large and sometimes complex pedigrees,
using information from many marker loci simultane-
ously. Here we report multipoint linkage results from sev-
eral approaches to analyzing the data.
Methods
Pedigree and map analysis
We first did routine analysis and investigation, removing
uninformative individuals. Based on data availability, we
decided for later analyses to use time point 11 for Cohort
1 and time point 1 for Cohort 2. For a few covariates una-
vailable at time point 11 for Cohort 1, the information
was taken from time point 10 or 12. The program
ECLIPSE was used to investigate pedigree uncertainties or
errors on the basis of all available marker data. We also
estimated sex-averaged and sex-specific recombination
frequencies via an expectation maximization (EM)
from Genetic Analysis Workshop 13: Analysis of Longitudinal Family Data for Complex Diseases and Related Risk Factors
New Orleans Marriott Hotel, New Orleans, LA, USA, November 11–14, 2002
Published: 31 December 2003
BMC Genetics 2003, 4(Suppl 1):S71
<supplement> <title> <p>Genetic Analysis Workshop 13: Analysis of Longitudinal Family Data for Complex Diseases and Related Risk Factors</p> </title> <editor>Laura Almasy, Christopher I Amos, Joan E Bailey-Wilson, Rita M Cantor, Cashell E Jaquish, Maria Martinez, Rosalind J Neuman, Jane M Olson, Lyle J Palmer, Stephen S Rich, M Anne Spence, Jean W MacCluer</editor> </supplement>
This article is available from: http://www.biomedcentral.com/1471-2156/4/s1/S71Page 1 of 6
(page number not for citation purposes)
BMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S71algorithm based on the MCMC program lm_auto in the
MORGAN package (URL information below).
Trait definition and segregation analyses
We analyzed quantitative traits using the MORGAN EM
program PolyEM for fitting multivariate polygenic mod-
els. We used the phenotypic traits and covariates shown in
Table 1. As a result of these analyses, we focused on HDL
and lnTG for further study, defining the traits HDLA,
lnTGA, and HDLAA as shown in Table 1.
Two approaches were used to obtain models for HDLAA
to be used in linkage analysis. Loki [2], the Bayesian
MCMC program for oligogenic models, provided some
initial models. Also, normal mixtures were fitted to the
adjusted trait values in a commingling analysis assuming
Hardy-Weinberg equilibrium. Several binary traits were
defined, with cutoffs at -10, +10, and +27.6 for both
HDLAA and HDLA, this corresponding to 21% (23%),
19% (20%), and 3% (3%) of the observed individuals
having the low, high, or very high HDLAA (HDLA) phe-
notype. An ordinal trait with 15 ordered categories was
also used. Penetrances were defined for the binary trait
and ordinal traits: for HDLAA the model was based on the
commingling analysis and for HDLA on Loki output.
Linkage detection and mapping
Our linkage studies focused primarily on chromosome 7.
Linkage signals have been reported on chromosome 7 for
lnTG, HDL, and log(HDL/TG) [1,2], which we hoped to
replicate. Additional analyses were carried out on chro-
mosomes 3, 4, 9, 11, 16, and 20, either to attempt replica-
tion of reported signals or as a negative control. Except
where indicated, our results and discussion refer only to
chromosome 7.
We used Loki to analyze several quantitative traits based
on HDL and lnTG. The binary HDLA and HDLAA traits
were subjected to IBD scoring linkage detection methods
based on lm_auto [3]. We used the MORGAN multipoint
LOD score program SCHNELL [4] on the quantitative
HDLAA trait. A few single-marker LOD scores for the
quantitative HDLA trait at chromosome 7 markers were
checked using FASTLINK [5]. Both the binary and ordinal
HDLA and HDLAA were also analyzed with the MORGAN
MCMC program lm_bayes, a pseudo-Bayesian approach
to the estimation of multipoint LOD scores [6]. All
reported analyses used the Haldane genetic map dis-
tances, and all multipoint analyses used all markers on a
chromosome simultaneously. Except where stated, we
used sex-averaged maps. All pedigrees were used
unbroken.
Results
Pedigree and map analysis
An ECLIPSE analysis of putative sib trios identified indi-
vidual 590513 in pedigree 27096 as being an unlikely
member of the stated sibship. Whereas true sib trios give
log-likelihood differences in the range 40 to 80 relative to
half-sib alternatives, trios including this individual gave
values close to 0. This pedigree has substantial missing
marker data, suggesting there may have been Mendelian
errors. The data set that was left after removing 35 individ-
uals with no data, 593 unobserved founder couples each
with only one offspring, and the individual 590513, con-
sisted of 3470 individuals in 362 pedigree components,
ranging in size from 1 to 74. Two pedigrees contained
loops due to sibship exchanges, and several had more
than one founder couple. Our segregation and joint link-
age/segregation analyses used the reduced data set of 3470
potentially informative individuals. Genome sharing,
map re-estimation, and LOD score methods used the sub-
set of 3444 individuals in non-singleton pedigrees.
Re-estimated maximum likelihood recombination fre-
quencies were obtained for chromosome 7. The genetic
distance from marker 7_1 to marker 7_22 increased from
191 cM (given) to 205 cM (estimated). Overall, there were
few large differences between the given and estimated sex-
averaged and sex-specific maps. Marker intervals 7_13–
14, 7_18–19 and 7_19–20 showed the highest relative
increase in sex-averaged recombination rates: 37%, 45%,
and 58%, respectively.
Trait definition and segregation analyses
The results of two polygenic segregation analyses are
shown in Table 2. Joint analysis of HDLA and lnTGA
showed substantial narrow-sense heritability for each trait
(45% and 46%, respectively) and large negative genetic
and environmental correlations. Adjusting HDLA for
lnTG to define the HDLAA trait had little impact on the
HDLA model parameters. Relative to an environmental
model, the log-likelihood increases for a model including
additive genetic effects were 141 and 73, under the bivar-
iate and univariate analyses, respectively.
Linkage detection and mapping
Bayesian analyses using Loki detected one main signal on
chromosome 7 around marker 7_21. Figure 1a shows the
log-intensity ratios (logIR) [7] for various traits. HDL and
HDLA gave the strongest signals. The signal is weaker
when HDL is adjusted for lnTG, suggesting that this signal
is, at least in part, a TG linkage signal. lnTG and log(TG/
HDL) showed weaker signals centered around marker
7_17. Additional positive signals were observed at 3_18–
19 for HDLAA (logIR = 0.5), at 16_7 for HDLA with cov-
ariates CV2 and lnTG (logIR = 0.3) and 20_6 for lnTG
with covariates CV1 and CV2 (logIR = 1.3).Page 2 of 6
(page number not for citation purposes)
BMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S71The strength of Loki signals was sensitive to the prior dis-
tribution assumed for QTL effects. It was also sensitive to
changes in the marker genetic map: the MCMC EM esti-
mated map resulted in reductions in the peak IR, relative
to the supplied map, of 11.6% and 17.3% for HDLA and
lnTGA, respectively. As shown in Figure 1b, the realized
QTL in the region 7_19 to 7_22 having non-negligible
trait contributions were used to help define trait models
for HDLA and HDLAA LOD score analyses.
Using the IBD S-pairs scoring statistic of [8], lm_auto gave
weak signs of linkage in the region 7_11 and 7_21 for
very-high HDLAA trait, with weaker signals for low
HDLAA (Figure 2a). For HDLA, the signal in the region
7_21 was reduced (Figure 2b). Very high HDLAA also gave
a signal at 3_18, consistent with the Loki signal.
Using penetrances based on commingling and Loki anal-
yses, LOD scores for the "very-high" binary and ordinal
HDLA and HDLAA traits were computed using lm_bayes
(Figure 3). Although estimated LOD scores were barely
positive, the curves do show the greater discriminating
power provided by an ordinal compared to binary trait,
and by not adjusting HDLA for lnTGA. SCHNELL also
failed to obtain positive multipoint LOD scores for the
quantitative HDLAA trait. No multipoint LOD score pro-
gram found consistent positive signals for linkage, and
there was sensitivity of LOD scores both to genetic map
and model parameters. For example, analyzing the binary
HDLAA trait under a sex-averaged map as apposed to a
sex-specific map resulted in more negative multipoint
LOD scores, with a drop of 2 LOD score units in some
places. Interestingly, lm_bayes for the ordinal HDLA trait
and FASTLINK for the quantitative HDLA trait gave single-
marker LOD scores just above 1.0 close to marker 7_21.
Table 1: Definition of phenotypes used in reported analyses
Phenotype Notation Definition or Computation Trait (T) and/or Covariate (C)
HDL Fasting HDL cholesterol (mg/dl) T
TG Fasting triglycerides (mg/dl) T
lnTG Loge(TG) T/C
BMI 707 × Weight/(height2) C
Smk Number of cigarettes smoked/day C
Drk Number of grams of alcohol/day C
Gl Fasting glucose (mg/dl) C
CV1 Covariate set 1: age, sex, cohort C
CV2 Covariate set 2: Drk, BMI C
HDLA & lnTGA HDL and lnTG adjusted for CV1 T
HDLAA HDLA adjusted for CV2 and lnTG T
Table 2: PolyEM Analysis of HDLA and lnTGAA
Bivariate Analysis Univariate Analysis of 
HDLA
HDLA lnTGA
Overall Mean 0.242 -0.011 0.15
Variance Additive Genetic 71 0.13 68
88 0.15 90
Correlation Additive Genetic -0.46
Residual -0.23
Covariates used in trait preadjustment CV1 CV1
Covariates used within trait analysis BMI, Smk, Drk, Gl Drk, CV2
ABivariate PolyEM Analysis for HDLA and lnTGA, and analysis of HDLA. Residuals in the latter analysis define the HDLAA trait. Covariate 
categories are defined as follows: BMI (<18.5, 18.5–25, 25–30, >30); Smk (<1, 1–10, 11–20, >20); Drk (<1, 1–6, 7–18, >18); Gl (<82, 82–94, 95–101, 
>101); lnTG (< ln(200), > ln(200)).Page 3 of 6
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BMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S71Results from LokiFig re 1
Results from Loki Chromosome 7 results from Loki. (a) Log10 IR for HDL (heavy dashed); HDLA (heavy solid); HDLAA 
(light solid); log(TG/HDL) with covariates CV1 and CV2 (dotted); HDLA with covariates CV2 and lnTG (dash-dot); and lnTG 
with CV1 and CV2 (double dashed). (b) Difference in genotype values for the heterozygote vs. AA homozygote (AB-AA) and 
BB homozygote vs. AA homozygote (BB-AA) for all iterations with QTL located between 175 and 195 cM, for a run based on 
HDLA (Table 1). Dashed lines indicate positions of dominant models. Positions of markers 11–22 are indicated along the top.
S-pairs standardized statistics at marker locus positions on chromosome 7Figu e 2
S-pairs standardized statistics at marker locus positions on chromosome 7 S-pairs standardized statistics at marker 
locus positions on chromosome 7: (a) HDLAA, (b) HDLA. Solid line: very high (>27.6). Semi-dashed line: low (≤10). Dashed 
line: high (>10).Page 4 of 6
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BMC Genetics 2003, 4 http://www.biomedcentral.com/1471-2156/4/s1/S71Multipoint LOD scores on chromosome 7Figure 3
Multipoint LOD scores on chromosome 7 LOD scores on chromosome 7 for the very-high (>27.6) binary trait and the 
15-category ordinal trait for (a) HDLAA and (b) HDLA. Dashed line, binary trait; solid line, ordinal trait.Page 5 of 6
(page number not for citation purposes)
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Conclusions
In combination, our segregation and linkage analysis
results suggest both oligogenic inheritance of HDLA and
lnTGA, and a negative genetic correlation, which may be
the result of loci affecting these traits at chromosome 7-
qter. The chromosome 7 signals were consistently
stronger for HDLA than for HDLAA, the latter trait being
adjusted for lnTG. For genetically correlated traits, adjust-
ment may weaken the signal, whereas the ratio-trait of
Shearman et al. [1] will reinforce the signal in the presence
of a negative genetic correlation. Adjustments for geneti-
cally correlated covariates should be applied cautiously.
The weak signals of the model-free analyses of binary
traits may be due to low power, and the problems of the
multipoint LOD score analyses due to model sensitivity.
In the presence of oligogenic inheritance, Loki can detect
weak signals, imputing linked QTL only in certain
families and modeling other heritable variation with
unlinked QTL. However, interpretation of the strength of
the signal provided by Loki remains an open question.
Thus, in the absence of a LOD score method accommo-
dating genetically complex traits and linkage heterogene-
ity, validation of these signals remains elusive.
Acknowledgments
Research supported in part by NIH grant GM 46255.
The MORGAN, ECLIPSE and Loki packages are available at http://
www.stat.washington.edu/thompson/Genepi/pangaea.shtml
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