Rare-Variant Extensions of the Transmission Disequilibrium Test: Application to Autism Exome Sequence Data
Many population-based rare-variant (RV) association tests, which aggregate variants across a region, have been developed to analyze sequence data. A drawback of analyzing population-based data is that it is difficult to adequately control for population substructure and admixture, and spurious associations can occur. For RVs, this problem can be substantial, because the spectrum of rare variation can differ greatly between populations. A solution is to analyze parent-child trio data, by using the transmission disequilibrium test (TDT), which is robust to population substructure and admixture. We extended the TDT to test for RV associations using four commonly used methods. We demonstrate that for all RV-TDT methods, using proper analysis strategies, type I error is well-controlled even when there are high levels of population substructure or admixture. For trio data, unlike for population-based data, RV allele-counting association methods will lead to inflated type I errors. However type I errors can be properly controlled by obtaining p values empirically through haplotype permutation. The power of the RV-TDT methods was evaluated and compared to the analysis of case-control data with a number of genetic and disease models. The RV-TDT was also used to analyze exome data from 199 Simons Simplex Collection autism trios and an association was observed with variants in ABCA7. Given the problem of adequately controlling for population substructure and admixture in RV association studies and the growing number of sequence-based trio studies, the RV-TDT is extremely beneficial to elucidate the involvement of RVs in the etiology of complex traits.
of the Transmission Disequilibrium Test:
Application to Autism Exome Sequence Data
Brian J. O’Roak,
Joshua D. Smith,
Regie Lyn P. Santos-Cortez,
Deborah A. Nickerson,
Evan E. Eichler,
and Suzanne M. Leal
Many population-based rare-variant (RV) association tests, which aggregate variants across a region, have been developed to analyze
sequence data. A drawback of analyzing population-based data is that it is difﬁcult to adequately control for population substructure
and admixture, and spurious associations can occur. For RVs, this problem can be substantial, because the spectrum of rare variation
can differ greatly between populations. A solution is to analyze parent-child trio data, by using the transmission disequilibrium test
(TDT), which is robust to population substructure and admixture. We extended the TDT to test for RV associations using four commonly
used methods. We demonstrate that for all RV-TDT methods, using proper analysis strategies, type I error is well-controlled even when
there are high levels of population substructure or admixture. For trio data, unlike for population-based data, RV allele-counting asso-
ciation methods will lead to inﬂated type I errors. However type I errors can be properly controlled by obtaining p values empirically
through haplotype permutation. The power of the RV-TDT methods was evaluated and compared to the analysis of case-control data
with a number of genetic and disease models. The RV-TDT was also used to analyze exome data from 199 Simons Simplex Collection
autism trios and an association was observed with variants in ABCA7. Given the problem of adequately controlling for population
substructure and admixture in RV association studies and the growing number of sequence-based trio studies, the RV-TDT is extremely
beneﬁcial to elucidate the involvement of RVs in the etiology of complex traits.
Complex-trait rare-variant association studies of exome
or whole-genome sequence data have been facilitated by
next-generation sequencing (NGS).
The vast majority of
NGS association studies of complex traits have been popu-
lation-based studies of qualitative and quantitative traits.
However, these studies are vulnerable to population
substructure and admixture, which can greatly increase
false-positive rates. The observation of spurious associa-
tions due to population substructure has been shown to
be an even greater problem for rare variants than for
Even for European populations, unlike
for common variants, there can be considerable differences
in the rare allelic spectrum from one European ethnic
group to another. These differences can be even more
extreme when studying admixed populations such as
African-Americans and Hispanics. Although it has been
demonstrated for association studies of common variants
in European populations that principal components
analysis (PCA) can adequately control for population
it is debated whether PCA is adequate to
control for population substructure when rare variants
For admixed populations, performing PCA
to globally control for population admixture can be insuf-
ﬁcient, even for the association analysis of common
For population-based studies in the presence of either
population substructure or admixture, spurious associa-
tions can be detected as a result of sampling artifacts
because of differences in allele frequencies between popu-
lations. What is desired is to detect an association due to a
difference in the genotype frequencies (e.g., between cases
and controls, individuals with high and low quantitative
trait values) at the causal variant or variants in linkage
disequilibrium (LD) with the causal variant. Family-based
analysis can avoid the problem of spurious associations
due to population substructure and admixture, and signif-
icant ﬁndings always imply association due to the causal
variant or LD with the causal variant. The study of trios
is the most basic family-based design for association
testing, using genotype data from an affected proband
and his parents. Since the trio design was ﬁrst proposed
by Falk and Rubinstein in 1987 to control for population
admixture and substructure,
a number of adaptations
have been developed including the method that is pre-
dominantly used to date, the transmission disequilibrium
For the TDT, only parents that are heterozy-
gous at the marker locus are informative, and it tests
whether or not the frequency of transmitted alleles is the
same as the alleles not transmitted to an affected child.
The only assumption for the TDT is Mendelian transmis-
sion, and an excess of an allele of one type transmitted
to the affected offspring indicates a disease-susceptibility
Center for Statistical Genetics, Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX 77030, USA;
Genome Sciences, University of Washington School of Medicine, Seattle, WA 98195, USA
Present address: Department of Molecular and Medical Genetics, Oregon Health and Science University, Portland, OR 97239, USA
http://dx.doi.org/10.1016/j.ajhg.2013.11.021. 2014 by The American Society of Human Genetics. All rights reserved.
The American Journal of Human Genetics 94, 33–46, January 2, 2014 33
locus for the trait that is both linked and associated with
Both linkage and association between the trait
and the marker are required to reject the null hypothesis.
This dual-alternative hypothesis protects the TDT from
spurious associations where an association is observed
but linkage is not present, which can occur in the presence
of population admixture and/or substructure.
The cost of
recruiting probands and their relatives and performing
NGS used to be a bottleneck in performing family-based
rare-variant association studies. Currently in order to study
the role of de novo mutations in genetic diseases, NGS data
are being generated for a large number of trios.
The traditional TDT can be used to perform rare-variant
association analysis by analyzing single variants. However,
it has been shown that association analysis of individual
rare variants (minor allele frequency [MAF] % 1%) is un-
as a result of the small number of observa-
tions for a rare variant and a stringent multiple-testing
correction. In order to analyze rare variants, many associa-
tion methods have been developed speciﬁcally to enrich
the association signal and reduce the multiple-testing pen-
alty. All of these methods group information across multi-
ple variants within a genomic region, which is usually a
In addition to aggregating rare variants within
a region, these methods include (1) weighting each variant
by either the frequency in controls
or the complete sam-
or by predicted functionality of the variants
maximizing the test statistic over all variants or variant
These methods can improve power to
detect rare-variant associations compared to single variant
analysis. Methods that combine the beneﬁts of rare-variant
association analysis and family-based tests provide a robust
and powerful approach to identify and characterize rare
We incorporated four commonly used rare-variant
association methods into the TDT framework: Combined
Multivariate and Collapsing (CMC),
Weighted Sum Sta-
Burden of Rare Variants (BRV),
a revised version of Gene- or Region-based Analysis of Var-
iants of Intermediate and Low frequency (GRANVIL),
and Variable Threshold (VT).
We also compared the po-
wer of these methods to the previously described Family
Based-Sequence Kernel Association Test (FB-SKAT).
using simulated genetic data, we demonstrate that type I
errors are well-controlled for all extended rare-variant
(RV)-TDT methods, even when applied to admixed or sub-
structured populations. However, in the presence of LD
between variants, there are some caveats in properly con-
trolling type I errors.
The power of the four RV-TDT methods to detect associ-
ations varies only slightly and the most powerful method
is dependent on the underlying disease model. However,
all RV-TDT methods are more powerful than FB-SKAT.
The power of the RV-TDT methods were also compared
to population-based rare-variant association methods.
In order to further illustrate the application of the RV-TDT
methods with NGS data, 199 autism spectrum disorder
(ASD) trios from the Simons Simplex Collection were
ASD, a heterogeneous disorder with substantial
heritability, is deﬁned by impaired social communication,
deﬁcits in language development, and the presence of
restricted interests and/or stereotyped repetitive behav-
Genome-wide association, de novo mutation, and
copy-number-variant studies have reported more than
100 different genes and genomic regions to be associated
with this complex trait,
but for at least 70% of autism cases
the underlying genetic component remains unexplained.
This motivates great interest in investigating the role of low-
frequency and rare variants in the etiology of ASD. Applica-
tion of our RV-TDT methods identiﬁed an association with
rare variants within ABCA7 (MIM 605414), which encodes
ATP-binding cassette subfamily A member 7 protein and
might be involved in the etiology of autism.
Material and Methods
Transmission Disequilibrium Test
The TDT was performed in the manner described by Spielman
by using a 2 3 2 table to tally all possible transmission
events (Figure 1). For the TDT, only the transmission of alleles
from parents who are heterozygous is of interest; for those geno-
types where the parent is homozygous the meiosis is uninforma-
tive. Transmission events from homozygous parents fall into cells
a and d, which are not used in the test statistic. The informative
meioses from heterozygous parents are where
(1) the minor allele is transmitted to the proband and
the major allele is not transmitted, which we deﬁne as
a minor-allele-transmitted event. These observations are
tallied in cell c; and
(2) the major allele is transmitted to the proband and the
minor allele is not transmitted, which we deﬁne as a ma-
jor-allele-transmitted event. These observations are tallied
in cell b.
The null hypothesis holds when the proportions b=ðb þ cÞ and
c=ðb þ cÞ are comparable with probabilities 0.5 and 0.5 (i.e., b ¼ c ).
The hypothesis is tested by using a 1-degree of freedom asymptot-
test, McNemar’s test,
and the c
statistic is deﬁned as
ðb þ cÞ
: (Equation 1)
For the RV-TDT methods a one-sided test is performed, because
only the overtransmission of the minor allele to the affected child
Figure 1. Two-by-Two Table for the McNemar’s Test
Displays the manner in which transmission and nontransmission
of the parental minor alleles are counted for the transmission
34 The American Journal of Human Genetics 94, 33–46, January 2, 2014
is of interest. For all RV-TDT methods, a de novo event is consid-
ered to be a minor-allele-transmission event.
Rare-Variant Association Methods
Four commonly used rare-variant association methods are incor-
porated into the TDT framework to detect the association between
rare variants and the phenotype of interest.
The CMC method uses an indicator variable to denote the pres-
ence or absence of rare variant(s) and tests the association between
the phenotype and rare-variant carrier status. For every parent, for
each informative variant site we count whether or not a minor-
allele-transmitted event occurs. For parent j with variant i,we
deﬁne indicator variables c
1; if a minor-allele-transmitted event
occurs for parent j with variant i
1; if a major-allele-transmitted event
occurs for parent j with variant i
Then, for a genetic region L, the total minor-allele-transmitted
events and major-allele-transmitted events for parent j are given by
: (Equation 3)
For the TDT-CMC method, for a data set with n trios (2n par-
ents), the c and b quadrants in the 2 3 2 table for gene L above
are given by
; b ¼
: (Equation 4)
Then Equation 1 will be used to attempt to reject the null
hypothesis of no linkage or association between the genetic region
and the disease. This approach will ensure every informative
parent contributes a score of 1 to the McNemar’s test. There are
a few rare situations where phasing is required for the TDT-
CMC, because each informative parent can only contribute a score
of 1, for example, if the proband, mother, and father are all hetero-
zygous at the same rare-variant site and the mother is heterozy-
gous at an additional rare variant site. In this situation, if both
of the mother’s rare variants are on the same haplotype, then
she is scored 1 for a major-allele-transmitted event (quadrant b)
and the father is scored 1 for a minor-allele-transmitted event
(quadrant c). On the other hand, if the mother’s rare variants are
on different haplotypes, she is scored
for a major-allele-trans-
mitted event (quadrant b) and
for a minor-allele-transmitted
event (quadrant c), whereas the father is scored 1 for a major-
allele-transmitted event (quadrant b). Therefore, for the applica-
tion of the TDT-CMC, haplotypes must be phased.
The TDT-BRV method counts the number of minor-allele-trans-
mitted events and major-allele-transmitted events from every
informative parent to the affected proband. Therefore unlike the
TDT-CMC where each informative parent can only contribute a
score of 1 to the McNemar’s test, for the TDT-BRV each informative
parent contributes a score that is equivalent to the number of
informative sites within the region, e.g., 1, 2, 3.
The same analysis is used as for the TDT-CMC, except Equation 4
above is given in the form of
; b ¼
: (Equation 5)
Because each site within an informative region can be counted
independently of the other sites, it is not necessary to phase the
data before performing the TDT-BRV, when analytical p values
are obtained. However to control type I errors in the presence of
LD, empirical p values should be estimated via haplotype permu-
tation, which requires phasing the trio data.
For the TDT-WSS, each variant site is weighted by the estimated SD
of the number of variants in the parental haplotypes that are not
transmitted to the offspring
; (Equation 6)
is the allele frequency of variant i in parental haplo-
types that are not transmitted to the offspring. The remaining
analysis is similar to the TDT-BRV, except the c and b in Equation 4
above are given in the form of
; b ¼
Because internal information is applied to obtain the weights,
p values must be obtained empirically by using permutation to
avoid spurious associations.
For the TDT-VT, the test statistic is maximized over allele fre-
quencies and therefore a variable allele frequency threshold is
applied, instead of a ﬁxed MAF cut-off. The TDT-VT can be imple-
mented by using either the TDT-CMC or TDT-BRV coding. The
TDT-VT avoids the implicit assumption about the relationship
between allele frequency and odds ratio. Because the test statistic
is maximized over allele frequencies, to correct for multiple
testing, p values must be obtained empirically.
We also compared the power of the RV-TDT methods to FB-
SKAT. FB-SKAT is an extension of the family-based association
test (FBAT) to detect rare-variant associations by using a variance
component test. More details about this method can be found in
Ionita-Laza et al.
Simulation Based on Population Demographic Models
To evaluate type I error rates and the power of the RV-TDT
methods, we generated population genetic data by using forward
Two population demographic models were
For the Kryukov model, a con-
ventional four-parameter model was used to describe the demo-
graphic history (i.e., bottleneck and exponential expansion) of
the European population. Purifying selection, which affects the
rare-variant site frequency spectrum, is also modeled for nonsy-
nonymous variants. Details on the population genetic model’s
parameters can be found in Kryukov et al.
For the Boyko model,
a simple two-epoch and a six-parameter complex bottleneck
models were used to model population demographic changes for
Africans and Europeans, respectively. Details for these population
genetic models can be found in Boyko et al.,
The American Journal of Human Genetics 94, 33–46, January 2, 2014 35
on the choice of parameters have been previously described by Liu
For each population genetic model, 500 haplotype
pools were generated, each consisting of 200,000 haplotypes of
1,500 bp in length, which is the average size of a human gene.
This 1,500 bp ‘‘gene’’ represents only the coding regions and con-
sists of sites deemed to be either synonymous or nonsynonymous.
Generation of Trio Data
One haplotype pool is randomly selected for each replicate. The
genotypes for the proband are obtained by pairing two randomly
drawn haplotypes. When genetic data are generated under the
alternative hypothesis, a penetrance model is used to determine
whether the inherited pair of haplotypes will cause the
proband to be ‘‘affected.’’ When an affected proband is obtained,
one haplotype is selected to be the maternal haplotype and the
other chosen to be the paternal haplotype. The remaining
maternal and paternal haplotypes are obtained by randomly
selecting two additional haplotypes from the same haplotype
pool. When genetic data are generated under the null hypothesis,
the same procedure is performed, except that the proband’s
genotypes are composed solely from two randomly sampled
To generate African and European admixed trios, we generated
haplotype pools by using African and European population
demographic models, and the haplotypes were sampled from
both the African and European pools. The proportion of African
and European admixture is determined by the probability that is
used to select from either the African or European haplotype
pool. Various degrees of population admixture are examined,
i.e., 75% African and 25% European, 50% African and 50% Euro-
pean, and 25% African and 75% European, with the assumption of
random mating. By using these probabilities, the two proband
haplotypes are either selected both from the African pool, both
from the European pool, or one haplotype is selected from the
European pool and the other from the African pool. Each one of
the proband’s haplotypes is assigned to a parent and then, by
using the admixture probabilities, it is determined whether the
second haplotype for each parent should be selected from an
African or European haplotype pool.
To generate trios in the presence of population substructure,
the proband’s haplotypes were constructed by sampling from
haplotype pools that were either African or European, and the
parents’ haplotypes were drawn from a haplotype pool of the
same ancestry. Population substructure was created by analyzing
together ‘‘African’’ and ‘‘European’’ trios with the proportions
75% African and 25% European, 50% African and 50% European,
and 25% African and 75% European.
To evaluate the effect of intermarker LD on type I error, we
generated trio haplotypes with perfect LD. To create a pool, we
selected 20 haplotypes that have two or more variant sites and
no one variant site could be found on more than one haplotype
background. Additionally, to evaluate haplotype reconstruction
when there is perfect LD and population substructure, two pools
were created each with 20 nonoverlapping haplotypes. Haplo-
types were drawn from these two pools with either equal probabil-
ity or 25% of haplotypes were sampled from one pool and 75%
from the other haplotype pool.
Generation of Case-Control Data
In order to compare the power of the RV-TDT methods to the
analysis of population-based data by using the original versions
of the rare-variant association methods, variant data were
generated by the Kryukov model. Two haplotypes were sampled
from a haplotype pool and by using the penetrance model
described below it was determined whether the haplotype pair
should be assigned ‘‘case’’ or ‘‘control’’ status. The process was
repeated until the desired numbers of cases and controls were
Generation of Phenotype Data
The disease status for a pair of haplotypes is assigned based upon
their multisite genotypes consisting only of rare nonsynonymous
variant sites (MAF % 1%). Power is evaluated when 100%, 75%,
and 50% of the nonsynonymous variant sites are causal. Those
sites within the gene region that are nonsynonymous were
randomly deemed to be causal based upon the predetermined
proportions, whereas the remaining rare-variant sites are
noncausal with no phenotypic effect. An odds ratio (OR) > 1is
assigned to each causal variant, and the disease probabilities of
all variants within a gene are computed based upon an additive
mode of inheritance.
Two different disease models were applied,
both using a disease prevalence of 1%: the equal-effect model
where the ORs of causal variants are constant and the variable-
effects model where the ORs of causal variants are inversely
correlated with their MAFs. For the equal-effect model, those
variant sites that are deemed to be causal were evaluated by
using four ORs ¼ 1.8, 2.0, 2.2, and 2.5. For the variable-effects
model, those variant sites which were deemed to be causal with
the lowest observed allele frequency were assigned OR
while those variant sites with the highest allele frequency were
. Interpolation was used to obtain the effect
size of all causal variants with allele frequency between the high-
est and lowest MAF. The power was evaluated for four variable-
effects models OR
¼ 1.5–2.5, 1.5–3.0, 1.5–3.5 and
For the TDT-CMC, TDT-BRV, and FB-SKAT, only rare variants with
a MAF % 1% were analyzed, whereas for the TDT-WSS, TDT-VT-
CMC, and TDT-VT-BRV both rare and low frequency variants
(MAF % 5%) were analyzed. For evaluating the effect of LD on
the RV-TDT methods, a MAF of % 5% was used for all tests. All var-
iants meeting the MAF criteria were analyzed whether or not they
were deemed to be ‘‘causal.’’ For TDT-CMC and TDT-BRV, p values
were obtained both analytically and empirically, whereas for TDT-
WSS, TDT-VT-CMC, and TDT-BRV, p values were only obtained
empirically through genotype and haplotype permutation. For
the FB-SKAT method, p values were obtained by moment match-
ing approach with 10,000 Monte Carlo simulations. For the anal-
ysis of population-based data with the rare-variant association
methods BRV, WSS, and VT, p values were obtained empirically,
whereas for the CMC, p values were obtained both empirically
Genotype and haplotype permutation methods were evaluated.
For genotype permutation, genotypes are shufﬂed at every variant
site between each parental pair, and then a paternal and maternal
haplotype were randomly chosen to form the offspring’s geno-
types. For haplotype permutation, the haplotypes are phased
and then the parental haplotypes within each trio are shufﬂed,
36 The American Journal of Human Genetics 94, 33–46, January 2, 2014
and the offspring’s genotypes are obtained by pairing a randomly
selected paternal and maternal haplotype.
For the TDT-CMC, TDT-VT-CMC and haplotype permutation,
haplotypes must be phased. In order to evaluate how well haplo-
types could be phased in the presence of African and European
population admixture, the phase of the generated data was
ignored and phasing was performed with BEAGLE.
haplotype data were generated with perfect LD, and the haplotype
phases were ignored and then reconstructed with BEAGLE. By
using 10,000 replicates, the proportion of times parental haplo-
types could be correctly phased was evaluated.
Evaluating Type I Error and Power
To evaluate type I errors, we generated 20,000 replicates each with
1,500 trios. For RV-TDT methods where p values were obtained
empirically, 10,000 permutations were performed. Power was eval-
uated for an a ¼ 0.05. Two thousand replicates were generated to
evaluate power for samples of 800, 1,000, 1,200, 1,500, and 1,800
trios, and to obtain p values empirically, 2,000 permutations were
performed. Additionally, to compare power for the RV-TDT
methods to the analysis of population-based data, 2,000 replicates
were generated for three different scenarios: 1,500 trios, 1,500
cases/1,500 controls, and 1,000 cases/1,000 controls. P values
were obtained empirically by performing 2,000 permutations.
Application to Autism Data
From the Simons Simplex Collection, 199 autism spectrum disor-
der trios were analyzed. Previously, 189 of these trios were
analyzed to detect de novo events.
An additional 10 trios, which
have not been described, were also analyzed.
All samples and phenotypic data were collected under the direc-
tion of the Simons Simplex Collection by its 12 research clinic
sites: Baylor College of Medicine; Children’s Hospital Boston and
Harvard University; Columbia University; Emory University;
McGill University; Vanderbilt University; Yale University; Univer-
sity California Los Angeles (UCLA); University of Illinois at
Chicago; University of Michigan; University of Missouri; and Uni-
versity of Washington. Parents consented and children assented as
required by each local institutional review board. Participants were
de-identiﬁed before distribution. Research was also approved by
the University of Washington Human Subject Division under
nonidentiﬁable biological specimens/data.
Exome Capture and Genotype-Calling
Genomic DNA was extracted from whole blood.
captured by using NimbleGen EZ Exome V2.0 and reads were map-
ped to a custom reference genome assembly (GRC build37). All
exomes met the completed criteria of R83 read depth in 90% of
the capture target and R203 read depth in 80% of capture target.
Additional details on exome sequencing of the autism trio data
can be found in O’Roak et al.
Variants were selected if they passed the following GATK ﬁlters:
AB (allele balance for hets [ref/(refþalt)]) % 0.75, HRun (largest
contiguous homopolymer run of variant allele in either direction)
%5.0, QD (variant conﬁdence/quality by depth) R5, SB (strand
bias) %0.10, QUAL (sequencing quality) >30, and SnpCluster
(at least 3 variants clustered within 10 bp).
tion Tools (VAT) software was used to remove genotypes with
a read depth <103 and also to select variants for analysis.
Gene regions were assigned based upon RefSeq deﬁnition and
was used to annotate variant sites. Only variant sites
that were either nonsynonymous or putative splice site variants
Phasing Trios Data
Before phasing, Mendelian inconsistencies were identiﬁed and
removed with the PLINK software.
Phased genotypes were
obtained with BEAGLE software.
For missing genotype data,
BEAGLE imputes missing data and only provides the most likely
genotype. We observed that analyzing the most likely genotype
can increase false-positive rates for trio data (data not shown).
Therefore the imputed variant calls were removed from the anal-
ysis. Additionally to avoid spurious associations, those regions of
the exome containing copy-number variants or pseudogenes
were removed from the analysis. Genes on the autosomal chromo-
somes with R4 variant sites were analyzed, and 8,441 genes were
included in the analysis.
Evaluation of Type I Error
Type I error rates were estimated by the proportion of
replicates with p values % 0.05 or % 0.005. Additionally,
Quantile-Quantile (QQ) plots were generated. When the
data were generated without LD, no type I error inﬂation
was observed for any of the RV-TDT methods (Table 1;
see Figure S1 available online). For both the TDT-CMC
and TDT-BRV when p values were obtained analytically,
the type I error is well-controlled and the p values are
slightly conservative (Table 1; Figures S1A and S1D). Like-
wise, when p values were obtained empirically through
either genotype or haplotype permutation, type 1 error is
well-controlled (Table 1; Figure S1). However, when the
haplotypes with perfect intermarker LD, i.e., r
¼ 1 were
analyzed, extreme inﬂation in type I error was observed
(Table 1; Figure 2) under several conditions. For p values
that were obtained analytically for the TDT-BRV, type I
error is extremely inﬂated, but for the TDT-CMC, the
type I errors are well-controlled and even slightly conserva-
tive (Table 1 ; Figure 2A). For example, for the TDT-BRV
when haplotypes with the variants in perfect LD were
analyzed, an a level of 0.05 has a type I error rate of 0.20.
This inﬂation of type I error is not resolved through geno-
type permutation (Figure 2B). Haplotype permutation
resolves the problem and type I error is well-controlled
(p value ¼ 0.05) (Figure 2C). For the TDT-WSS, TDT-VT-
CMC, and TDT-VT-BRV, p values must be obtained empir-
ically to properly control type I errors, and when there
is intermarker LD, although genotype permutation leads
to inﬂated type I errors (Table 1; Figure 2B), haplotype
permutation properly controls type I error rates (Table 1;
To demonstrate that the RV-TDT methods can
adequately control for population admixture, admixed
African and European populations were generated
following the Boyko population demographic models
using different ratios of African and European admix-
ture. For all methods, haplotype permutation provided
The American Journal of Human Genetics 94, 33–46, January 2, 2014 37
control of type I errors. Also for the TDT-CMC, when
p values were obtained analytically, type I error was
well-controlled (Table 1; Figure 3). Similar results were ob-
tained for substructured populations (data not
shown). These ﬁndings strongly support that RV-TDT
methods are robust to both population admixture and
For all methods for which type I error is well-controlled,
haplotypes need to be reconstructed. We examined the
ability to reconstruct haplotypes for trio data, where infor-
mation from the proband can aid in the reconstruction.
In the presence of population admixture, even with no
LD, when a ratio of 50% African and 50% European was
used, 99.95% (SD 0.12%) of the haplotypes could be recon-
structed correctly. Likewise, when the ratio was changed to
75% African and 25% European, 99.93% (SD 0.23%) of the
haplotypes were correctly reconstructed. The results were
very similar when data were generated under population
substructure. For example, for population substructure
where 50% of the population was African and 50% Euro-
pean, 99.88% (SD 0.40%) of the haplotypes were correctly
Power of RV-TDT Methods
The power of the RV-TDT methods were evaluated for a
variety of sample sizes and effect sizes, and also compared
to the power of FB-SKAT. The difference in power between
the RV-TDT methods is small, although TDT-BRV and
TDT-CMC are slightly more powerful than other methods
under the equal-effect model (Figure 4; Figure S2); how-
ever, there is a clear difference in power between the
RV-TDT methods and FB-SKAT, with the RV-TDT methods
being considerably more powerful. The power of the
RV-TDT methods, as a function of genetic effect size and
sample size, is shown in Figure 4 and Figure S3, respec-
tively. For example, when 75% of all nonsynonymous
rare-variant sites were causal and the OR for causal variants
is 2.5, the power of TDT-CMC and TDT-BRV is 71.15% and
Table 1. Type I Error for RV-TDT Methods at a Levels of 0.05 and 0.005
Kyrukov Boyko LD
a ¼ 0.05 a ¼ 0.005 a ¼ 0.05 a ¼ 0.005 a ¼ 0.05 a ¼ 0.005
0.0493 0.0032 0.0468 0.0033 0.1996
0.0427 0.0042 0.0396 0.0034 0.1992 0.0934
0.0432 0.004 0.0396 0.0034 0.051 0.0033
TDT-CMC Analytical 0.0492 0.0032 0.0467 0.0033 0.0472 0.0034
Genotype 0.043 0.004 0.0397 0.0035 0.1082 0.0265
Haplotype 0.0431 0.0039 0.0396 0.0034 0.0519 0.0041
TDT-VT-BRV Genotype 0.0448 0.0037 0.0423 0.0039 0.2795 0.1269
Haplotype 0.0445 0.0039 0.0424 0.0038 0.0487 0.004
TDT-VT-CMC Genotype 0.0447 0.0038 0.0423 0.004 0.1086 0.0188
Haplotype 0.0442 0.0039 0.0425 0.0039 0.0445 0.0047
TDT-WSS Genotype 0.0459 0.0042 0.0441 0.0038 0.1846 0.081
Haplotype 0.0449 0.0041 0.0446 0.0037 0.0509 0.0041
Proportion of African and European Admixture
0.75/0.25 0.5/0.5 0.25/0.75
a ¼ 0.05 a ¼ 0.005 a ¼ 0.05 a ¼ 0.005 a ¼ 0.05 a ¼ 0.005
TDT-BRV Haplotype 0.0509 0.0044 0.0489 0.0047 0.0483 0.0050
TDT-CMC Analytical 0.0416 0.0040 0.0463 0.0043 0.0481 0.0037
Haplotype 0.0470 0.0041 0.0483 0.0043 0.0504 0.0047
TDT-VT-BRV Haplotype 0.0491 0.0058 0.0483 0.0051 0.0518 0.004
TDT-VT-CMC Haplotype 0.0495 0.0055 0.0489 0.0054 0.0520 0.0042
TDT-WSS Haplotype 0.0519 0.0050 0.0498 0.0056 0.0527 0.0048
p values obtained analytically.
Inﬂated type I errors are highlighted in bold font.
p values obtained with 10,000 genotype permutations.
p values obtained with 10,000 haplotype permutations.
38 The American Journal of Human Genetics 94, 33–46, January 2, 2014
71.10%, respectively, whereas the power for TDT-WSS,
TDT-VT-CMC, and TDT-VT-BRV is 67.25%, 66.00%, and
66.10%, respectively. For the same scenario, the power
for FB-SKAT is 53.90% (Figure 4E). When 75% of the
variant sites are causal and the OR for causal variant is
between 1.5 and 4.0, the power of TDT-CMC, TDT-BRV,
TDT-WSS, TDT-VT-CMC, and TDT-VT-BRV is 68.25%,
68.05%, 70.25%, 70.05%, and 70.20%, respectively, while
for the same scenario the power for FB-SKAT is 35.88%
To further evaluate the power of the RV-TDT methods,
we compared their power to the corresponding rare-
variant association methods for population-based data.
In Figure 5, the comparison of the power between the
TDT-BRV and BRV is shown, used to analyze trio and
case-control data, respectively. As previously observed for
the analysis of common variants per genotyped individ-
uals, the case-control design is slightly more powerful
than the trio design. For example, when 75% of all nonsy-
nonymous rare-variant sites are causal with OR ¼ 2.0, the
power of BRV when 1,500 cases and 1,500 controls
were analyzed is 45.85% and the power of TDT-BRV
when 1,000 trios were analyzed is 43.25%. However, if
only 1,000 cases and 1,000 controls are analyzed using
the BRV, the power is 33.00% (Figure 5B). Similar results
were observed for the other TDT extensions (data not
Applications to Autism Data Set
We applied the RV-TDT methods to analyze 199 trios from
the Simons Simplex collection that had available whole-
exome sequence data. The QQ plots for TDT-CMC, TDT-
BRV, TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS indicate
that there is no inﬂation of type I error (Figure S3). None
of the detected associations meet exome-wide signiﬁcance
of 5.92 3 10
, i.e., an a level of 0.05 Bonferroni corrected
for testing 8,441 genes. ABCA7 showed the strongest evi-
dence of being associated with autism (OR ¼ 8.5 5 0.75
stdev) with all RV-TDT methods.
Results from the
TDT-RV methods were similar: TDT-BRV (p value ¼
1.4 3 10
), TDT-CMC (p value ¼ 1.6 3 10
(analytical) (p value ¼ 2.9 3 10
(p value ¼ 1.5 3 10
), TDT-VT-CMC (p value ¼ 2.3 3
), and TDT-WSS (p value ¼ 2.8 3 10
). None of
the variants that were observed in ABCA7 are de novo
events. Ten missense variants in ABCA7 with MAF % 1%
were observed in 18 trios with a total of 19 minor
alleles observed in the parental generation (Table 2). There
were 17 minor-allele-transmitted events and 2 major-
allele-transmitted events. For seven missense variants,
only a single minor-allele-transmitted event was observed.
Three missense variants had multiple transmission events:
c.2629G>A (p.Ala877Thr) had a minor-allele-transmitted
event in ﬁve trios and a major-allele-transmitted event in
one trio, c.5435G>A (p.Arg1812His) had a minor-allele-
transmitted event in three trios and a major-allele-
transmitted in one trio, and c.4795G>A (p.Val1599Met)
had a minor-allele-transmitted event in two trios (Table 2).
Only in one trio, two transmission events were observed
in ABCA7, c.1534C>G (p.Arg512Gly), and c.4795G>A
(p.Val1599Met). Of the ten missense variant sites, ﬁve
occurred at conserved nucleotides (both PhyloP and
GERP scores > 1) and were deemed damaging by at least
three of four bioinformatics tools, and therefore could
be potentially causal (Table 2). Three of the damaging
missense variants were observed in the NHLBI GO
Exome Sequencing Project (ESP)
with MAF 0.0002-
0.004, while two variants are not previously reported in
Figure 2. QQ Plot of Negative Natural Log p Values Obtained for Trio Data under the Null Hypothesis of No Association when the
Variant Sites that Are Tested Are in Perfect LD
For each scenario, a total of 1,500 trios were analyzed and 20,000 replicates were generated. For the TDT-CMC and TDT-BRV, variants
with MAF % 1% were analyzed while for the TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS, variants with MAF % 5% were analyzed.
(A) Displays the results for the TDT-BRV and TDT-CMC when p values were obtained analytically (Anal).
(B) Displays the results for the TDT-BRV, TDT-CMC, TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS. All p values were obtained empirically by
performing 10,000 genotype (Geno) permutations for each replicate.
(C) Displays the results for the TDT-BRV, TDT-CMC, TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS. All p values were obtained empirically by
performing 10,000 haplotype (Haplo) permutations for each replicate.
The American Journal of Human Genetics 94, 33–46, January 2, 2014 39
publically available databases including 1000 Genomes.
For the additional ﬁve ABCA7 variants, only one was
not previously reported in publically available databases
In this work, we incorporated rare-variant association
analysis into the TDT framework to analyze sequence
data, in particular rare variants. The simulation results
demonstrate that our RV-TDT methods are robust to both
population substructure and admixture, which highlights
the potential beneﬁts of their application to the analysis
of sequence data. Current methods to control for popula-
tion substructure and admixture might not be sufﬁcient
to avoid spurious associations when analyzing rare vari-
ants, in particular for admixed populations such as Afri-
can-Americans and Hispanics.
The RV-TDT framework
can control for both admixture and substructure and
thus avoid spurious associations. Additionally proper
control of population substructure and admixture can
also decrease type II error and lead to an increase in power.
Although the accuracy of NGS technologies has greatly
improved, there is still ~1% false-positive call rate even
for high read-depth sequence data.
An additional advan-
tage of analyzing trio data is that it is possible to improve
the accuracy of variant calls, by using variant callers that
make use of family or trio information.
precision in variant calls can in turn lead to increased
power to detect associations.
BEAGLE was used to phase the simulated and autism trio
data. Other programs could have been used to accurately
phase trio data including PHASE (v2.1)
We demonstrate that phasing is quite accurate for trio
data even when ‘‘admixed’’ data were generated. It has
also been demonstrated by others that phasing of haplo-
types is considerably more accurate for trio data than pop-
For example, when PHASE (v2.1) was
used, the percentages of genotypes whose phase was
correctly inferred was 99.8% for simulated trio data and
99.95% for the HapMap Centre d’Etude du Polymor-
phisme Humain (CEPH) trio data, whereas for unrelated
individuals, haplotype phasing was correctly inferred
94.8% for the simulated data and 94.1% for CEPH data.
Therefore, for trio data it is possible to obtain highly accu-
rate haplotype information.
When p values are analytically obtained for TDT-BRV, it
is not necessary to phase the data and additionally for
genotype permutation, phasing of the haplotypes is not
necessary. We demonstrate that although these methods
adequately control type I error when there is no inter-
marker LD, there can be serious inﬂation of type I error
in the presence of LD. For those methods, which require
empirical p values, e.g., TDT-WSS and TDT-VT, haplotypes
must be permuted because permuting genotypes leads to
an increase in type I errors. When population-based data
are analyzed with the BRV method, analytical p values
have well-controlled type I errors. Conversely for trio
data analyzed with the TDT-BRV, analytical p values
have inﬂated type I errors; however, for empirical p values
obtained via haplotype permutation, type I errors are
For rare variants it is usually assumed that there are only
low levels of LD, because it is unlikely that rare variants fall
on the same haplotype background. However, for the
initial analysis of the autism trio data, we detected associa-
tions with several genes with TDT-BRV and genotype
permutation for which no signiﬁcant association was dis-
cerned by using the TDT-CMC or haplotype permutation.
Figure 3. QQ plot of p Values Obtained from the Analysis of African and European Admixed Populations
Genetic variant data for African and European populations were generated under the Boyko model. A total of 1,500 trios were analyzed
using 20,000 replicates. Type I error rates were evaluated for the TDT-BRV, TDT-CMC, TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS. For the
TDT-CMC and TDT-BRV, variants with a MAF % 1% were analyzed while for the TDT-VT-BRV, TDT-VT-CMC, and TDT-WSS, variants with
MAF % 5% were analyzed. All p values were obtained empirically by performing 10,000 haplotype permutations for each replicate,
except for the TDT-CMC analytical. The data were generated with different proportions of African and European admixture: in (A)
75% African and 25% European, (B) 50% African and 50% European, and (C) 25% African and 75% European.
40 The American Journal of Human Genetics 94, 33–46, January 2, 2014
Upon closer inspection we observed that these associations
were driven by multiple rare variants that all lay upon the
same haplotype. When analytical or empirical p values via
genotype permutation are obtained, each variant is treated
as an independent event, but in the presence of LD, this is
not the case. This led to an additional investigation on the
effects of intermarker LD on type I error and the demon-
stration that analytical p values for the TDT-BRV, and
empirical p values obtain through genotype permutation,
which breaks down the LD structure, are not robust to
intermarker LD and therefore should not be used. Only
haplotype permutation retains the LD structure when
used to obtain empirical p values and therefore properly
controls type I errors.
We demonstrate that the rare-variant case-control
design with an equal number of cases and controls is
generally slightly more powerful than the trio design if
an equal number of individuals are analyzed, e.g., 1,000
trios versus 1,500 cases and 1,500 controls. However, if
an equivalent sample size of cases is analyzed, the power
for the RV-TDT methods is slightly higher than the popu-
lation-based design, e.g., 1,000 trios versus 1,000 cases
and 1,000 controls. Additionally, for trio design, only
the proband must be phenotyped, which is equivalent
to one-third of the study participants, whereas for a
case-control design, all study participants should be
A disadvantage of the trio design is that it is not usually
suitable for late-onset diseases, because parents will often
be deceased and no longer available for study. Additionally,
nonpaternity can reduce the power to detect associations,
because genotype data for the biological fathers will not be
available. Its distinct advantages include: control of type I
error in the presence of population substructure and
admixture and the ability to investigate parent-of-origin
effects. These beneﬁts make the family-based design an
excellent choice for sequence-based genetic studies, in
particular for early-onset diseases. An additional advantage
of using the family-based design is that both inherited and
de novo events can be studied and tested simultaneously
using the RV-TDT methods.
If it is of interest to detect an association with either
protective or detrimental variants, although less powerful
than a one-sided test, a two-sided test should be per-
formed. If protective variants are involved in disease
etiology, there is an undertransmission of minor alleles
to the affected proband. In the traditional implementa-
tion of the TDT, parents are not phenotyped and some
of the parents might manifest the phenotype of interest,
thus reducing the power to detect an association with
protective variants. If trios have been ascertained to detect
de novo events where the parents have been screened
to ensure they are unaffected, it could be the case
that they harbor protective variants that prevent them
from being diseased or they might not have the correct
combination of causal variants and\or environmental
exposures to induce the phenotype. Another scenario is
that both protective and detrimental variants within the
same gene are involved in disease etiology. It has been
previously shown that in these situations, variance
component tests such as SKAT can be more powerful
than aggregate rare-variant methods. However, variance-
component methods are less powerful when the vast
majority of variants within a region are either detrimental
Figure 4. Comparison of Power for the
RV-TDT Methods and FB-SKAT
Power was evaluated for an a level of
0.05 for 1,500 trios by generating 2,000
replicates. Analysis was performed with
TDT-BRV, TDT-CMC, TDT-VT-BRV, TDT-
VT-CMC, TDT-WSS, and FB-SKAT. For
the TDT-CMC, TDT-BRV, and FB-SKAT, var-
iants with a MAF % 1% were analyzed
while for the TDT-VT-BRV, TDT-VT-CMC,
and TDT-WSS, variants with MAF % 5%
were analyzed. For the TDT-BRV, TDT-
CMC, TDT-VT-BRV, TDT-VT-CMC, and
TDT-WSS, p values were obtained empiri-
cally by performing 2,000 haplotype
permutations for each replicate. For the
TDT-CMC, p values were also obtained
analytically. For the FB-SKAT, p values
were obtained with a moment matching
approach by using 10,000 Monte Carlo
simulations. Genetic variant data were
generated under the Kryukov model and
the proband’s affection status was ob-
tained with two different penetrance
models: variable-effects model (A, B, C)
and equal-effect model (D, E, F). Different
proportions of the variant sites were
deemed to be causal: (A and D) 50%,
(B and E) 75%, and (C and F) 100%.
The American Journal of Human Genetics 94, 33–46, January 2, 2014 41
We also demonstrate here that FB-SKAT
is considerably less powerful than the other RV-TDT
methods when causal variants within a gene region
have an effect that is unidirectional. Additionally, the
FB-SKAT did not detect an association between autism
and ABCA7 (p ¼ 0.11).
Although the emphasis of this study is performing
complex disease association analysis with the proposed
RV-TDT methods, the RV-TDT is also suitable for analyzing
Mendelian traits. For Mendelian traits, the RV-TDT is
particularly beneﬁcial to use when although a family
history of disease has been recorded, only the proband
and his parents are available for study. The power of the
RV-TDT will be dependent on the underlying Mendelian
model. Assuming that there is no locus heterogeneity for
the disease under study, it is possible to analytically obtain
estimates of the necessary sample sizes to detect an associ-
ation for various Mendelian modes of inheritance. For
80% power, to detect an association for an autosomal
recessive trait when a ¼ 0.05, four trios are needed, and
if an exome-wide signiﬁcance criterion of a ¼ 2.5 3 10
(a Bonferroni correction for testing 20,000 genes) is used,
then 15 trios are necessary to detect an association with
80% power. For autosomal-dominant traits for a ¼ 0.05
and a ¼ 2.5 3 10
, 13 trios and 59 trios, respectively,
are required to detect an association with 80% power. It
is also possible to use the TDT-RV methods to analyze
X-linked traits, although only the mother will provide
informative meioses. To detect an association for an
X-linked recessive trait with a power of 80% for a ¼ 0.05,
seven trios are necessary, but for a ¼ 5 3 10
correction for testing ~1,000 genes on the X chromosome)
23 trios are necessary.
By using the RV-TDT methods, we identiﬁed variants in
ABCA7 (19p13.3) as potentially the underlying cause of
autism by analyzing 199 families from the Simons Simplex
collection. Previously, an ASD locus was mapped to the
19p13.12 region with a maximum nonparametric LOD
(NPL) score of >2.0 in 115 multiplex U.S. families.
Additionally, by using an extended ASD pedigree consist-
ing of 20 nuclear families from Finland, we obtained an
NPL score of 3.57 within chromosome 19p13.3 at marker
which is 1.9 Mb away from ABCA7.
The association between rare variants in ABCA7 and
autism is consistent with the ﬁnding that autistic children
display abnormal rates of in vivo lipid metabolism
compared with healthy controls.
ABCA7 is an integral
transmembrane ATP–binding cassette transporter that in-
volves the translocation of cellular lipid across membrane,
such as cholesterol.
Current studies suggest that lipid
signaling plays an important role in neuronal pro-
cesses, such as synaptogenesis and neurotransmitter
There is increasing evidence suggesting
abnormalities of lipid metabolic pathways might affect
the nervous system and contribute to autism.
Common variants in ABCA7 have been associated with
Alzheimer disease (AD) through brain expression and
genome-wide associationstudieswith samples from patients
of both African and European descent.
It has been
shown that, like in AD, plasma levels of b-amyloid or a-pre-
cursor protein (APP) are signiﬁcantly elevated in ASD pa-
While the occurrence of b-amyloid plaques in the
brain is well-knownas a pathologic hallmarkof AD, the accu-
mulation of b-amyloid in the brains of both pediatric and
adult ASD patients was demonstrated only recently.
mice, phagocytotic cells have reduced ability to
clear amyloid from the brain, which results in decreased
memory and capacity to learn new tasks.
tion of ABCA7 as a gene that is possibly involved in autism
etiology suggests the existence of a common pathway for
neurodevelopmental and neurodegenerative diseases that
might be targeted for prevention and treatment.
The RV-TDT methods were developed to provide a robust
and powerful way to identify rare-variant complex disease
associations by using trio sequence data. Given the problem
of adequately controlling for population substructure and
admixture in rare-variant association studies and the
growing number of sequence-based trio studies, the RV-
TDT is extremely beneﬁcial in elucidating the involvement
of rare variants in the etiology of complex traits. The RV-
TDT methods can be used to analyze exome and genome
sequence data. Additionally, these methods can be applied
Figure 5. Comparison of Power to Detect
Rare-Variant Associations with Population-
Based and Trio Data
The BRV was used to analyze samples of size
1,000 cases and 1,000 controls and 1,500
cases and 1,500 controls, and the TDT-BRV
was used to analyze 1,000 trios. Power was
evaluated for an a level of 0.05 for both case-
control and trio data by generating 2,000 rep-
licates. P values were obtained empirically by
performing 2,000 haplotype permutations
for each replicate. Genetic variant data were
generated with Kryukov model. Affection
status was determined with an equal-effect
penetrance model with ORs varying between
1.8 and 2.5. Different proportions of causal
variants were used in the analysis with 50%
(A), 75% (B), and 100% (C).
42 The American Journal of Human Genetics 94, 33–46, January 2, 2014
Table 2. Bioinformatic Evaluation and Frequencies of Rare Missense Variants within ABCA7
Substitution PolyPhen-2 SIFT MutationTaster
Events dbSNP rsID
c.995G>A 2.90 4.33 p.Gly332Glu Probably
Damaging Polymorphism Functional,
1/0 NA NA NA
1,045,109 c.1324G>A 0.28 2.54 p.Gly442Arg Possibly
Tolerated Polymorphism Nonfunctional,
1/0 NA NA NA
1,046,317 c.1534C>G 0.04 1.11 p.Arg512Gly Benign Tolerated Polymorphism Neutral 1/0 NA 0.0001 0
1.18 2.59 p.Ala877Thr Benign Tolerated Polymorphism Nonfunctional,
5/1 rs74176364 0.006 0.003
1,051,481 c.2858C>A 4.96 4.43 p.Ala953Asp Probably
Damaging Disease-causing Functional,
1/0 NA NA NA
1.58 3.65 p.Val1599Met Probably
Damaging Polymorphism Functional,
2/0 rs117187003 0.004 0.0009
1,058,883 c.5344C>T 1.58 3.14 p.Arg1782Trp Probably
Damaging Disease-causing Functional,
1/0 NA 0.0003 0
1.28 0.81 p.Arg1812His Benign Damaging Polymorphism Neutral 3/1 rs114782266 0.005 0.07
1,062,248 c.5648C>T 4.87 3.61 p.Thr1883Met Probably
Damaging Disease-causing Functional,
1/0 NA 0 0.0002
2.08 3.73 p.Glu2108Lys Benign Tolerated Polymorphism Functional,
1/0 rs139706726 0.0002 0
cDNA position is based on reference sequence NM_019112.3.
PhyloP scores indicate nucleotide conservation under a null hypothesis of neutral evolution.
GERP provides position-speciﬁc estimates of evolutionary constraint.
Minor allele frequencies (MAF) for European-Americans (EA) and African-Americans(AA) from the NHLBI GO – Exome Sequencing Project (ESP) Exome Variant Server. NA, not available.
Conserved nucleotides (both PhyloP and GERP with scores > 1) and damaging variants (deemed damaging by at least three of four bioinformatics tools) are highlighted in bold font.
Included on the Illumina Human Exome BeadChip.
The American Journal of Human Genetics 94, 33–46, January 2, 2014 43
to analyze rare variants obtained from genotyping arrays
including the ‘‘exome’’ chip. To analyze the autism trio
data with all ﬁve RV-TDT methods, TDT-BRV, TDT-CMC,
TDT-WSS, TDT-VT-CMC, and TDT-VT-BRV, obtaining
empirical p values based on haplotype permutation took
a total of 3.1 hr. To analyze the same data set imple-
menting the TDT-CMC, obtaining analytical p values took
4.5 min. The analysis was performed with a single CPU,
however, by using multiple processors for the analysis can
greatly decrease the computational time. The RV-TDT
software package and documentation are publicly available
Supplemental Data includes three ﬁgures and can be found with
this article online at http://www.cell.com/AJHG.
We are grateful to all of the families at the participating Simons
Simplex Collection (SSC) sites, as well as the principal in-
vestigators (A. Beaudet, R. Bernier, J. Constantino, E. Cook,
E. Fombonne, D. Geschwind, E. Hanson, D. Grice, A. Klin,
R. Kochel, D. Ledbetter, C. Lord, C. Martin, D. Martin, R. Maxim,
J. Miles, O. Ousley, K. Pelphrey, B. Peterson, J. Piggot, C. Saulnier,
M. State, W. Stone, J. Sutcliffe, C. Walsh, Z. Warren, and
E. Wijsman). We appreciate obtaining access to phenotypic
data on SFARI Base. This work was supported by the Simons
Foundation Autism Research Initiative (SFARI 137578 and
191889 to E.E.E. and J.S.). E.E.E. is an Investigator of the Howard
Hughes Medical Institute. This study was also funded by the
National Institutes of Health grants HD065285, HL102926,
MD005964, and HG006493.
Received: October 8, 2013
Accepted: November 26, 2013
Published: December 19, 2013
The URLs for data presented herein are as follows:
1000 Genomes, http://browser.1000genomes.org
Exome Variant Server (EVS), http://evs.gs.washington.edu/EVS/
Genome Analysis Toolkit (GATK), http://www.broadinstitute.
Online Mendelian Inheritance in Man (OMIM), http://www.
Simons Foundation Autism Research Initiative (SFARI), http://
Variant Association Tools (VAT), http://varianttools.sourceforge.
The dbGaP accession number for the exome sequences reported in
this paper is phs000482.v1.p.
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