© 2002 Oxford University Press
Human Molecular Genetics, 2002, Vol. 11, No. 6
689–696
Linkage analysis of anorexia nervosa incorporating
behavioral covariates
Bernie Devlin1,*, Silviu-Alin Bacanu1, Kelly L. Klump2, Cynthia M. Bulik3, Manfred M. Fichter4,
Katherine A. Halmi5, Allan S. Kaplan6,7, Michael Strober8, Janet Treasure9, D. Blake
Woodside7, Wade H. Berrettini10 and Walter H. Kaye1
1Department
of Psychiatry, University of Pittsburgh, Pittsburgh, PA 15213-2593, USA, 2Department of Psychology,
Michigan State University, East Lansing, MI, 48824, USA, 3Department of Psychiatry, Virginia Institute for Psychiatric
and Behavioral Genetics, Virginia Commonwealth University, VA 23298-0126, USA, 4Klinik Roseneck, Hospital for
Behavioral Medicine, affiliated with the University of Munich, Prien, Germany, 5New York Presbyterian Hospital,
Weill Medical College of Cornell University, White Plains, NY 10605, USA, 6Program for Eating Disorders and
7Department of Psychiatry, Toronto General Hospital, Toronto, Ontario, M5G 2C4, Canada, 8Department of
Psychiatry and Behavioral Science, University of California at Los Angeles, Los Angeles, CA 90024-1759, USA,
9Eating Disorders Unit, Institute of Psychiatry and South London and Maudsley National Health Service Trust, UK
and 10Center of Neurobiology and Behavior, University of Pennsylvania, Philadelphia, PA 19104, USA
Received November 26, 2001; Revised and Accepted January 18, 2002
Eating disorders, such as anorexia nervosa (AN) and bulimia nervosa (BN), have genetic and environmental
underpinnings. To explore genetic contributions to AN, we measured psychiatric, personality and temperament
phenotypes of individuals diagnosed with eating disorders from 196 multiplex families, all accessed through
an AN proband, as well as genotyping a battery of 387 short tandem repeat (STR) markers distributed across
the genome. On these data we performed a multipoint affected sibling pair (ASP) linkage analysis using a
novel method that incorporates covariates. By exploring seven attributes thought to typify individuals with
eating disorders, we identified two variables, drive-for-thinness and obsessionality, which delimit populations
among the ASPs. For both of these traits, or covariates, there were a cluster of ASPs who have high and concordant values for these traits, in keeping with our expectations for individuals with AN, and other clusters of
ASPs who did not meet those expectations. When we incorporated these covariates into the ASP linkage analysis,
both jointly and separately, we found several regions of suggestive linkage: one close to genome-wide significance on chromosome 1 (at 210 cM, D1S1660; LOD = 3.46, P = 0.00003), another on chromosome 2 (at 114 cM,
D2S1790; LOD = 2.22, P = 0.00070) and a third region on chromosome 13 (at 26 cM, D13S894; LOD = 2.50,
P = 0.00035). By comparing our results to those implemented using more standard linkage methods, we find
the covariates convey substantial information for the linkage analysis.
INTRODUCTION
Eating disorders are classic examples of complex psychiatric
phenotypes having both genetic and environmental determinants.
Some of the environmental underpinnings are well understood
(1,2), being rooted in the reigning western view of the perfect
body; exceptionally thin and fit. Apparently individuals with
anorexia nervosa (AN) are quite sensitive to these cultural
messages and exhibit a dread of body fat that drives, then
sustains an unrelenting avoidance of normal body weight (3).
Still, despite widespread dieting in the western world, only a
small fraction of women (0.1–0.7%) (4–6) and an even smaller
fraction of men ever develop eating disorders.
In addition to environment, liability to eating disorders has a
familial (7–10) and genetic basis. Estimated heritabilities of
liability to eating disorders, based on twin studies, range from
54 to 80% (11–16). Moreover, studies of clinically unaffected
twins find that 40–60% of the variance in liability to abnormal
eating attitudes is attributable to additive genetic effects (17–19).
First-degree relatives of eating disorder probands have an ∼3%
lifetime risk of AN, whereas none of the approximately 1000
first-degree relatives of control probands received the diagnosis
(7,9). Based on these rates, the recurrence risk for first-degree
relatives of an AN proband is likely to be at least 10-fold
higher than the population prevalence.
Psychometric studies (20–32) have consistently linked AN
to a cluster of moderately heritable (33) personality and
temperamental traits, specifically obsessionality, perfectionism,
neophobia and harm avoidance. These traits persist after the
long-term normalization of body weight and menses,
*To whom correspondence should be addressed. Tel: +1 412 624 1432; Fax: +1 412 624 8181; Email: devlinbj@msx.upmc.edu
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supporting the possibility that they influence susceptibility.
Pharmacologic and physiologic studies in people with AN
suggest that these symptoms, as well as pathologic feeding
behavior, are associated with a dysregulation of central
nervous system serotonin pathways (24).
In our ongoing multinational study to determine the genetic
underpinnings of eating disorders (34), we have measured a
wide variety of psychiatric, personality and temperamental
phenotypes on more than 200 affected relative pairs (ARPs),
mostly affected sibling pairs (ASPs). Families in this first
cohort have been recruited through a proband diagnosed with
AN. Affected relatives of the proband have a wider range of
eating disorder diagnoses [i.e. AN, bulimia nervosa (BN) or
eating disorder not otherwise specified (NOS)], although most
individuals have AN. By using a combined approach of
genome-wide linkage analysis, teamed with the analysis of
phenotypes related to eating disorders, we hope to identify
some of the polymorphisms that contribute to eating disorder
liability.
In this paper, we analyze the ASP data using a new method
of linkage analysis that incorporates covariates (35). Whereas
the larger study included numerous potential covariates,
including personality, behavioral and psychiatric traits, we
limit our analysis a priori to attributes thought to typify individuals
with AN. We use several criteria to select these potential
covariates: they must be consistently related to eating
pathology, they must be heritable and they must be indicators
of severity of some aspect of the disorder, or enduring traits
rather than states resulting from the illness itself. Thus, these
traits are unlikely to result from nutritional deficiencies and, in
fact, could underlie the etiology of eating pathology.
Based on these criteria, seven traits have been initially
selected for analysis: harm avoidance and novelty seeking
from the Temperament and Character Inventory (TCI) (36),
trait anxiety from the State Trait Anxiety Inventory (37),
overall perfectionism from the Multidimensional Perfectionism
Scale (MPS) (38), overall obsessiveness/compulsivity from the
Yale–Brown Obsessive Compulsive Scale (Y-BOCS) (39),
overall eating disorder-related obsessiveness/compulsivity from
the Yale–Brown–Cornell Eating Disorder Scale (YBCEDS) (40)
and drive-for-thinness from the Eating Disorders Inventory-2
(EDI-2) (41). All of these traits show phenotypic relationships
with eating disorders. Two of these traits are core measures of
eating disorder pathology (i.e. YBCEDS total score and EDI
drive-for-thinness), whereas the others capture features
commonly associated with AN (25,27,30,42–44).
RESULTS
To estimate marker allele frequency differences among the
families from the seven different recruitment sites, we fit a
Bayesian hierarchical model (45) to the site-specific data. The
estimated degree of differentiation, expressed as a standardized
measure like Wright’s (46) Fst, is 0.0032 for 316 autosomal
loci showing any differentiation. Another 50 autosomal loci
showed no detectable differentiation (i.e. estimated differentiation
is zero). Limited differentiation is to be expected (47)
because almost all participants identified their ancestry as
European. Nonetheless, for our linkage analyses, we use the
site-specific estimates of allele frequencies for each marker,
which arise naturally from the hierarchical model (45) (see
Figure 1. Trait values for ASPs for perfectionism, drive-for-thinness (EDI-DT)
and obsessionality. Trait values are transformed into standard normal deviates,
so the scales are in SD from the population mean.
http://wpicr.wpic.pitt.edu/WPICCompGen for complete,
population-specific allele frequencies). Because we use a likelihood ratio statistic for linkage, log-likelihoods can be
summed over sites to produce a summary statistic.
To implement the ASP linkage analysis with covariates
using the pre-clustering mixture model (35), we sought one or
more covariates that separate ASPs into subpopulations, which
plausibly have different origins for eating disorder liability. To
do so, we first normalize the seven chosen covariates by their
respective normative distributions, derived from convenience
samples from the population (Materials and Methods). For
each trait, we plot the transformed sibling-pair values for each
trait against each other as a diagnostic to identify clusters. Five
of the traits appear to display little discriminatory power; as an
example, we display the values for perfectionism in Figure 1.
While it is clear that individuals with eating disorders generally
are perfectionists, there are no clear-cut populations among
ASPs. Two traits tend to cluster ASPs, however; namely EDI-2
drive-for-thinness (EDI-DT) and Y-BOCS obsessionality (Fig. 1).
For both traits, there is a group of ASPs who are extreme, relative to most individuals in the population, and highly
concordant. This group fits our expectations for individuals with
AN. In contrast a substantial number of ASPs either have
similar but not extreme values for these traits, or the ASPs
show little similarity for these traits. We suspect these ASPs
have different origins for their vulnerability to eating disorders,
compared to those ASPs who are both extreme and concordant.
For our linkage analyses, then, we assume the extreme
concordant ASPs for either trait are typical for the linked
group.
Human Molecular Genetics, 2002, Vol. 11, No. 6
For the pre-clustering model, the probability of membership
in the linked group must be determined. To form two clusters,
we use the mclust function in Splus (48) and both covariates
jointly, as described elsewhere (35); then, to estimate probability
of group membership, we use the Splus quadratic discriminant
analysis (QDA) function. (QDA discriminates between two or
more known groups by assuming that their covariate values
follow normal distributions that differ in their means and
variances.) We also compute these probabilities using one
covariate at a time. If either individual of the ASP had a
missing value for a trait, the ASP is excluded from the linkage
analysis. Missing values are uncommon for obsessionality;
after dropping ASPs due to missing values, the total number of
ASPs we analyzed was 180. Unfortunately, EDI-DT was not
measured in the same way in Munich, Germany, as it was in
the other sites, and therefore we omit all ASPs from Munich for
the obsessionality-based linkage analysis; for obsessionality we
analyzed 143 ASPs. For the analysis incorporating both EDI-DT
and obsessionality, 116 ASPs are available for analysis.
The familial intraclass correlations for EDI-DT and obsessionality are not large; r = 0.17. These correlations, however,
result from a specially selected population, specifically eating
disorder ASPs, and are therefore likely to be different from
those obtained from a random sample from the population.
EDI-DT and obsessionality are weakly correlated (r = 0.21),
but the weights of membership in the linked group are less so
(r = 0.07). Thus we expect the covariates to contribute largely
independent information to the linkage analysis.
Using standard criteria for declared significance of genomewide linkage analysis (49) (i.e. LOD > 3.6 for significant
linkage, LOD > 2.2 for suggestive linkage), linkage analysis
with covariates finds three suggestive linkages (Fig. 2): one on
chromosome 1 that approaches genome-wide significance
(at 210 cM, D1S1660; LOD = 3.46, P = 0.00003); another on
chromosome 2 (at 114 cM, D2S1790; LOD = 2.22; P = 0.00070);
and a third region on chromosome 13 (at 26 cM, D13S894;
LOD = 2.50; P = 0.00035). These results were obtained for
different combinations of covariates: for chromosome 1, both
EDI-DT and obessionality, for chromosome 2, only obsessionality,
and for chromosome 13, only EDI-DT.
Weighting of the ASPs could not be related to any obvious
diagnostic or familial characteristics, regardless of whether the
weightings were derived from both covariates jointly or from
either covariate alone. When we contrast ASPs receiving
weights greater than 0.5 with those receiving weights less than
0.5, there are no significant differences for gender combination
of the ASPs (female–female versus male–female), diagnostic
category (AN–AN, AN–BN or AN–NOS) or number of
affected individuals per family (data not shown). Likewise,
selection of ASPs with complete covariate data cannot account
for the results. Linkage analysis for the sample of 116 ASPs
who have complete data for EDI-DT and obsessionality yields
a maximum LOD = 1.52 in the same 1q region as before. For
the same sample and weights derived from values of EDI-DT
or obsessionality alone, the LOD scores are 1.29 and 1.31
respectively. Thus, insofar as we can discern, the combination of
covariates selects for a critical and presumably homogeneous
subset of ASPs from the larger sample.
The results in Figure 2 are derived by transforming the
P-values from the original likelihood ratio statistic into LOD
scores. The original statistic has a one-sided χ2 distribution,
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Figure 2. LOD scores for the suggestive linkages. Results using both EDI-DT
and obsessionality as covariates are traced by thick, solid lines; results using
EDI-DT as a covariate are traced by thin, solid lines; results using obsessionality
as a covariate are traced by interrupted lines. Horizontal reference line gives
standard criterion for suggestive linkage of a genome-wide scan (49). To see
the results for the entire genome scan, please go to http://wpicr.wpic.pitt.edu/
WPICCompGen.
asymptotically, under the null hypothesis of no linkage (35).
Thus, under the null hypothesis, 50% of the P-values equal 0.5,
and the remaining P-values are distributed uniformly between
0 and 0.5. Our results (Fig. 2) roughly meet this expectation,
except for a slight excess of small P-values, which is the
desired result. On the other hand, while analysis using either
covariate yielded ∼52% P-values at 0.5, only 42% of the
linkage analysis using both covariates did likewise. This result
is not likely to be significant, and in fact we find an even bigger
deviation—in the opposite direction—for standard linkage
analyses on the same sample using GeneHunterPlus (50).
Nonetheless, the tendency for positive results for two covariates,
versus one, could be partially due to the fact that the likelihood
ratio statistic for the pre-clustering model is more variable for
small samples (35), and the use of additional covariates
reduces the effective sample size.
Because chromosome X requires special treatment for
linkage analysis compared to the autosomes, and this treatment
is not yet coded into a computer program for the pre-clustering
model, we took a slightly simpler approach to linkage analysis
for this chromosome. We clustered as described previously;
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Table 1. Best LOD scores, by covariate and position
Drive-for-thinness and obsessionality
Drive-for-thinness
Obsessionality
Positiona
LOD
Chromosome
210
3.46
13
26
2.50
11
37
1.82
10
111
2
159
1.77
11
151
2
88
1.49
1
2
240
1.32
1
1
148
1.19
2
Chromosome
1
Positiona
Positiona
LOD
2
114
2.22
1.68
11
43
1.55
1.53
13
29
1.18
204
1.31
2
184
1.12
110
1.29
4
22
1.10
237
0.94
1
202
1.06
LOD
Chromosome
The values in the table are ‘independent’ LOD scores in the sense that they are associated with well-separated linkage signals.
aPosition in cM on the chromosome.
however, the probabilities of group membership were used as
weights for whole families, whose data were analyzed by
GeneHunterPlus (50). (Because GeneHunterPlus’ NPL scores
are standard normal deviates, it is straightforward to derive the
variance of the sum of weighted deviates.) For both covariates
taken together, the best linkage result occurred at
GATA172D05 (LOD = 0.93; P = 0.039). For either covariate
alone, the best linkage results occurred at the same marker,
GATA10C11, which is ∼3 cM from GATA172D05 on Xq. The
LOD score for obsessionality (LOD = 0.91; P = 0.040) was
slightly larger than EDI-DT (LOD = 0.59; P = 0.099).
In summary, the best linkage signals occurred on the autosomes, and varied by the covariate(s) used in the linkage analysis
(Table 1). Nonetheless, linkage signals for different covariates
overlap in some regions, such as chromosome 1q31 and
chromosome 13q11–12 (Table 1 and Fig. 2). In the 1q region,
information on drive-for-thinness and obsessionality combine to
produce an even more compelling linkage signal. Disappointingly,
the converse is true for the region of overlap on 13q (Fig. 2).
DISCUSSION
We present the results of a genome-wide scan for loci affecting
liability to eating disorders. While we use a standard sampling
scheme, ASPs and a standard set of genetic markers, our
approach deviates from the typical genome scan in several
ways. First, because our study is a multinational collaboration
and ASPs are drawn from disparate locations, we estimate
marker allele differentiation among these populations and
account for the differentiation in the linkage analysis by using
population-specific allele frequency estimates. To do so, we
implement a Bayesian hierarchical model for allele frequencies
(45). As might be expected based on the fact that the majority
of families are of European ancestry (47), the average differentiation among the populations is not large. Thus, the adjustment for population heterogeneity did not have a major impact
on the linkage analysis (unpublished data).
Secondly, we explore various attributes thought to typify
individuals with eating disorders to determine if any of them
might contribute to the linkage analysis. We identify two variables,
EDI-DT and Y-BOCS total score (measuring obsessionality),
which delimit populations among the ASPs in this study, whereas
five others show little discriminatory power (Fig. 1). The
cluster of ASPs who are extreme and concordant with respect
to EDI-DT and obsessionality have prototypical features for
individuals diagnosed with AN.
Thirdly, we combine the information on EDI-DT and obsessionality with linkage analysis using a new method of
multipoint ASP linkage analysis with covariates (35), specifically
the pre-clustering model. Based on standard criteria for significant (LOD > 3.6) and suggestive (LOD > 2.2) linkage (49), we
find three regions showing suggestive linkage, with the results
from one region close to genome-wide significance (LOD = 3.46).
It is worth noting that these criteria are based on complete,
pointwise IBD information; for partial information on identical
by descent (IBD), such as that obtained by this genome scan,
the criterion for significant linkage is lower (51,52).
Our results are substantially better than the results using
more standard methods of analysis. For example, when
GeneHunter (53) was used to analyze the entire data set
reported herein, additional families with ARPs and some larger,
multiplex families, the three best P-values were 0.036, 0.078
and 0.109 (54), which pale in comparison to the results in
Figure 2 for any combination of covariates. Likewise, for
linkage analysis using all ASPs and our model, setting weights
for all families equal 0.99; the best P-values are 0.0010, 0.0076
and 0.0222. Analysis of 38 ASPs who are concordant for AN,
restrictor subtype, produces a finding of suggestive linkage on
chromosome 1, but quite far from our best signal (54). This
suggestive linkage signal (P = 0.00028) at ∼65 cM, obtained
for a dense grid of short tandem repeat (STR) markers across
the region, corresponds to a weaker signal on chromosome 1
for the covariate analyses (Fig. 2). Individuals with AN,
restricting subtype, typically have high EDI-DT and obsessionality. As a group, they are well known for their highly
homogeneous presentation of both illness and behavioral characteristics, something we have also observed in our data (55).
Why do the covariates convey information regarding
linkage? At this time we can only speculate about ultimate
causes, but we assume that drive-for-thinness and obsessionality
differentiate both eating disorder patients themselves and the
genetic loci affecting eating disorder liability. It has long been
observed that certain features typify eating disorder patients,
such as obsession with order, symmetry and exactness,
rigidity, perfectionism, anxiety, and emotional and behavioral
overcontrol. Yet not all individuals display these features, and
diagnostic categories like AN and BN cannot explain the wide
variety of behavioral phenotypes observed in eating disorders,
Human Molecular Genetics, 2002, Vol. 11, No. 6
or vice versa (55). Thus, as befits a general model for a
complex disorder, it would not be surprising to find that
various loci contribute in different ways to eating disorder
liability, and that those loci also affect other traits, such as
compulsive drive-for-thinness and obsessionality. In this
regard, the use of covariates to amplify linkage signals is
becoming increasingly commonplace (56–59).
Given the suggestive linkage findings, it is reasonable to ask
if any of these regions harbor excellent candidate genes for
liability to eating disorders. Like many psychiatric disorders,
the origins of eating disorders are unclear. Nonetheless, ample
research on humans and model organisms (60–71) points to
serotonergic dysregulation as at least one important cause. In
light of our results, recent brain imaging studies are especially
intriguing because they suggest that eating disorders and
obsessive-compulsive disorder (OCD) share frontal-cingulatetemporal-subcortical pathways served, in part, by serotonin
neuronal systems (69,70). The common phenotypic characteristics shared by many AN and OCD patients suggest that these
disorders may share common brain behavioral pathways;
however, the lack of complete overlap suggests that they have
different foci of pathology within those pathways. Thus, we
believe that genes involved in serotonergic regulation are
excellent candidates for liability to eating disorders, and are
plausible targets for follow-up analyses.
We plan to continue our research to identify genes affecting
eating disorder liability in two directions. We will evaluate
candidate genes falling in the regions revealed by our linkage
analyses (Fig. 2), with emphasis on genes having a direct
impact on serotonin regulation. At the same time, we will
begin analyzing a new cohort of almost 400 eating disorder
families. While the new cohort will have some different properties
to the first cohort, largely because families were accessed
through a bulimic rather than anorexic proband, we expect that
covariates common to both cohorts can be used to extract information about etiology in much the same way as the analyses
reported here. Through common covariates, these two samples
should be a powerful means to refine our search for polymorphisms conferring risk for eating disorders.
MATERIALS AND METHODS
Participants and family structure
In a previous report (34), we gave a detailed description of the
sample to be used in our analyses. In brief, 196 probands
meeting modified diagnostic and statistical manual of mental
disorders-fourth edition (DSM-IV) criteria (amenorrhea not
required) for AN, and 237 affected relatives with modified
DSM-IV AN, DSM-IV BN or DSM-IV NOS, were recruited
from seven sites across North America and Europe: Pittsburgh,
New York, Los Angeles, Toronto, London, Munich and Philadelphia. Because we restricted our analyses to ASPs, our initial
sample included 176 families, 61% of which included sibling
pairs who had AN. The remaining 39% included AN–BN (19%)
and AN–NOS (20%) pairs. Of the 176 families with ASPs, 14
had more than two affected siblings. Of these, nine had three
siblings diagnosed with eating disorders and five had four
siblings diagnosed with eating disorders. Most families
consisted of female ASPs; only four ASPs were of opposite
gender.
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Behavioral and personality measures
Below we give a brief description of the measures. Please see
our previous report (34) for more details. All probands and
affected relatives were assessed for these measures.
Temperament and Character Inventory. The personality
constructs harm avoidance (i.e. the tendency to inhibit
behavior to avoid punishment or negative consequences) and
novelty seeking (i.e. the tendency toward behavioral activation
to pursue rewards) were assessed by the 240-item TCI Version
9 (36).
State Trait Anxiety Inventory. This was used to evaluate trait
anxiety (37).
Yale–Brown Obsessive Compulsive Scale. We used the Y-BOCS
(39) to assess participants’ ‘worst lifetime’ obsessions and
compulsions in order to capture lifetime symptoms of greatest
severity.
Yale–Brown–Cornell Eating Disorder Scale. Through the
YBCEDS (40), participants were asked to report their ‘worst
lifetime’ obsessions and compulsions related to eating disorders.
Multidimensional Perfectionism Scale. The MPS (38) measured
overall levels of perfectionism; ‘worst lifetime’ symptom
expression was used.
Eating Disorder Inventory-2. The EDI-2 (41) measured the
drive-for-thinness (i.e. preoccupation with dieting and the
pursuit of thinness), using ‘worst lifetime’ expression.
We transformed these trait values to standard normal deviates
using their corresponding distributions from normative populations, subtracting the observed means and dividing by the
observed SD from the normative population. Normative values
for harm avoidance and novelty seeking (72), perfectionism
(43), trait anxiety (37), drive-for-thinness (41), total Y-BOCS
score (73) and total YBC-EDS score (40) were reported previously.
Genotyping methods
Genomic DNA was extracted from leucocytes using standard
salting procedures (74). DNAs were genotyped for the Weber/
CHLC Screening Set 9 (http://research.marshfieldclinic.org/
genetics/), which consists primarily of tri- and tetranucleotide
repeat markers separated by, on average, ∼10 cM (75). All 387
markers were fluorescently tagged for use with the ABI
sequencer.
Statistical analyses
Error checking. We evaluated markers and pedigrees for
Mendelian errors using the PedCheck program (76). Genotyping errors were set to missing. Nominal and imputed
genetic relationships among individuals from the same family
were contrasted using the Relpair program (77). We excluded
from further analysis three families who appeared to be
composed of genetic half-siblings and three families with
ambiguous relationships among parents and progeny.
Allele frequency estimation. To estimate and account for heterogeneity of marker allele frequencies across the recruitment
sites, we used a Bayesian hierarchical model (45) and implemented in the program AllDist (http://wpicr.wpic.pitt.edu/
WPICCompGen). To estimate population-specific allele
frequency distributions, the observed allele frequencies,
computed by counting genotypes over all individuals from
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each site, were ‘shrunk’ toward the distribution obtained by
pooling subpopulations and toward a prior distribution. For a
prior distribution, we used the CEPH allele distributions
available from the Mammalian Genotyping Service (http://
research.marshfieldclinic.org/genetics/). Using this model, the
level of shrinkage was determined by the data for all STR loci
and prior information on the amount of subpopulation divergence. Because most participants identified themselves as
being of European ancestry, and a few of mixed European and
Asian or Amerindian ancestry, we used 0.003 as an estimate of
population divergence (78). See http://wpicr.wpic.pitt.edu/
WPICCompGen for population-specific allele frequency estimates.
Linkage analysis. To incorporate covariate information into the
linkage analysis, we implemented a new method of analysis (35).
In brief, ASP data were modeled as a mixture distribution,
which assumes a disease mutation is segregating in only a fraction α of the sibships, with 1 – α sibships being unlinked.
Covariate information is used to predict membership within
groups. For an ASP with covariate(s) Z = z and multilocus genotype X = x, the mixture model is α(z)g(x;λ) + [1 – α(z)]g0(x), in
which g0(x) follows the distribution of genotypes under the
null IBD distribution and g(x;λ) allows for increased IBD
sharing. We used the pre-clustering version of this model (35),
which uses only covariate information to assign weights of
membership in the linked and unlinked groups for each ASP
prior to the linkage analysis. Once these weights are determined, they are combined with multipoint IBD estimates, such
as those from standard linkage packages [e.g. GENEHUNTER
(53), Aspex (79)], to test for linkage. As the test statistic for
linkage, we used a likelihood ratio, which has an asymptotic,
one-sided χ2 limiting distribution for the pre-clustering method
under the null hypothesis of no linkage (35).
Fourteen families had more than two affected siblings. For
these families, we formed all possible ASPs for our analyses
after determining the joint IBD status using GENEHUNTER
(53) and after determining the probability of membership in
the linked group. The latter was calculated as described elsewhere (35). We did not correct for these dependent observations because they have little impact on the distribution of the
test statistic under the null hypothesis (80).
ACKNOWLEDGEMENTS
The authors are indebted to the participating families for their
contribution of time and effort in support of this study. The
authors wish to thank the Price Foundation for the support of
the clinical collection of subjects and genotyping, and contribution to the support of data analysis. Data analysis was also
supported by a grant from the National Institute of Health
(MH57881; B.D.).
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