Supplementary Material
for
Testing the Key Assumption of Heritability Estimates Based on Genome-wide Genetic
Relatedness
Dalton Conley* [1], Mark L. Siegal [1], Benjamin W. Domingue [2], Kathleen Mullan Harris
[3], Matthew B. McQueen [2] & Jason D. Boardman [2]
*Corresponding Author
[1] Center for Genomics and Systems Biology, New York University
[2] Institute for Behavioral Sciences, University of Colorado, Boulder
[3] Department of Sociology, University of North Carolina, Chapel Hill
1
Data: We chose three datasets—the Framingham Heart Study (FHS), the Health and
Retirement Study (HRS) and the National Longitudinal Survey of Adolescent Health (Add
Health)—to conduct this test. We examined the relationship between subject genetic relatedness
and parental education in the FHS and for childhood urbanicity in the HRS. We then reran these
analyses also with the Add Health data. The FHS is intergenerational in nature and thus has
responses on questions from the parents of the proband respondents. This attenuates any
concerns about mean-regressive recall bias—where more genetically similar individuals tend to
report their parents’ educations more similarly than they actually are. The drawback of the FHS
is that it is a geographically limited sample. Though by the third generation respondents have
fanned out across North America, given their common origins in generation one in Framingham,
Massachusetts, they are not representative of the population. By contrast, the HRS is a
nationally representative sample of older adults (ages 50 and older); but the question about where
respondents mostly grew up was asked of them directly, not their parents. There could be recall
bias; however, such bias is less likely to emerge for a question about childhood residence than it
is about parental education. Second, the HRS is externally valid only to the population of those
who reach age 50. If early mortality is non-randomly distributed with respect to the joint
distribution of genetic relatedness and childhood urbanicity, then results could be affected. Add
Health has the strength of picking up childhood urbanicity directly from the address of the
respondent and maternal education directly from the parent interview itself. It is considered a
nationally representative sample of U.S. adolescents (grades 7 to 12) in Wave I. Final,
completed education is taken in Wave IV, when respondents are 24 to 32 years old and thus have
plausibly completed their ultimate schooling level.
2
A generalized relatedness matrix (GRM) was calculated using GCTA12 (though results do
not vary if we use KING 27 or PLINK 28) on data that was pruned using PLINK with a standard
window of 50 SNPs, a frame shift of five SNPs per iteration and a variance inflation factor (VIF)
threshold of five to capture linkage disequilibrium. Once this GRM was obtained on this pruned
set of independently assorting SNPs, we then subsampled respondent pairs who showed
relatedness scores of less than 0.025 and 0.01, respectively. (See Figures S3-S6 for density plots
of the GRM scores for the various datasets under different cut-offs.) We then used GCTA
software to perform GREML analysis. We also performed analysis using traditional, ordinary
least squares (OLS) regression models and linear probability models (LPM)—see below.
Finally, we ran sensitivity analysis using another phenotype (maternal education) as well as
using other datasets (the Framingham Heart Study and the National Longitudinal Survey of
Adolescent Health). These datasets, however, are underpowered for the analysis, so results are
only shown in the supplementary materials.
HRS: Data for the analysis of childhood urbanicity come from the Health and Retirement
Survey (HRS). Data about childhood urbanicity is obtained from the question, “URBRUR08,”
asked in the 2008 survey wave
(http://hrsonline.isr.umich.edu/modules/meta/xyear/region/codebookx/hrsxregion10.txt).
Responses are collapsed (to preserve respondent confidentiality) based on the 2003 Beale RuralUrban Continuum Code to: “Urban” (Beale Rural-Urban Continuum code 1); Suburban (Beale
Rural-Urban Continuum code 2); or Ex-urban (Beale Rural-Urban Continuum codes
3,4,5,6,7,8,9). We compared urban versus non-urban childhoods by collapsing codes 2 through 9
into one category of an urbanicity variable. Valid responses were obtained for 18,597
3
respondents. (See Figure S1 for a histogram of categories and S2 for the pairwise shared urban
status variable; Figures S7-S9 show histograms for other variables, height, BMI and respondent
education, respectively.) Genotypic data were obtained for 12,507 study subjects by the Illumina
HumanOmni2.5-4v1 array. According to HRS documentation: “The median call rate was 99.7%
and the error rate estimated from 336 pairs of study sample duplicates is 6x10-5.” We removed
samples with an overall missing call rate > 2%. After data cleaning 1,707,214 markers were
included in the analysis. For additional details on quality control of HRS genetic data, please see:
http://hrsonline.isr.umich.edu/sitedocs/genetics/HRS_QC_REPORT_MAR2012.pdf. The Health
and Retirement Study (HRS; accession number 0925-0670) is sponsored by the National Institute
on Aging (grant numbers NIA U01AG009740, RC2AG036495, and RC4AG039029) and is
conducted by the University of Michigan. Additional funding support for genotyping and
analysis were provided by NIH/NICHD R01 HD060726.
FHS: Data for analysis of parental education come from the Framingham Heart Study
(FHS), second (parental) and third (sibling) generation respondents. Education of the parents
was taken from self-report in Wave II and coded as highest grade completed (i.e. years of
schooling), with a score of 12 for completion of high school, 16 for a bachelor degree, and a
maximum of 21 for post-graduate work. (See Figure S10 for a histogram.) Genotypes were
assayed using the Affymetrix GeneChip Human Mapping 500K Array and the 50K Human Gene
Focused Panel. Genotypes were determined using the BRLMM algorithm. Of the original
500,568 SNPs, 214,011 were left after quality control conducted by the present research team
(HWE screens with a p-value cut-off of .001, call rate of 95 percent and a MAF cut-off of 0.05).
The screens were conducted using all available individuals with genetic data, not only those that
4
were included in this analysis. After picking one respondent per pedigree, 366 individuals were
included in the analysis. The Framingham Heart Study (FHS; accession #7909-7) was supported
by the National Heart Lung and Blood Institute of the National Institutes of Health and Boston
University School of Medicine, and the National Heart, Lung and Blood Institute’s Framingham
Heart Study.
Add Health: Genetic data for Add Health come from the Wave IV pairs sample. Samples
from 1,946 individuals were genotyped on the Illumina HumanOmni1-Quad v1 platform, which
contained probes for 1,004,256 SNPs, 120,107 CNVs and 314 INDELs. After QC, including
validation against 1000 genomes, 959,952 markers remained. A 95 percent call rate threshold
was implemented as was a HWE cut off of p<.001 and a MAF threshold of one percent. The
result was 884,556 autosomal markers and 20,946 X-chromosome markers for 1886 individuals
who did not exceed a marker missingness rate of five percent. When we restricted our analysis
to whites and randomly selected one individual per pedigree, we obtained an N of 483
respondents. Maternal education is coded as years of schooling, top-coded at 18, which indicates
graduate school attendance regardless of type of degree. (See Figure S11.) Urbanicity is
indicated by a score of one on the urban classification variable for Add Health (see Figure S12
for a histogram of this variable, and S13 for the pairwise variable of shared urban status).
The National Longitudinal Study of Adolescent Health (Add Health) is a program project
directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and
Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant
P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human
Development, with cooperative funding from 23 other federal agencies and foundations.
5
Information on how to obtain the Add Health data files is available on the Add Health website
(http://www.cpc.unc.edu/addhealth).
OLS Results
At the two upper-bounds of genetic relatedness to estimate GREML models—0.025 and
0.01—we find that those with greater genetic similarity across the set of markers (see Online
Methods) tend to have more similar childhood conditions in terms of urbanicity but not in terms
of their maternal education (a far more important factor). These effects were estimated by
regression of the squared difference of maternal education, or of an indicator variable for shared
childhood urbanicity, on genetic relatedness, controlling for population stratification (see Table
S2). According to the regression analysis using data from pairs of respondents with genetic
relatedness less than 0.025, pairs who are related at one-half of one percent have mothers who
are, on average, 3.1552 years different in schooling in the Framingham Heart Study sample. But,
according to the same analysis, a pair of individuals who are one percent related will have a
smaller average difference in their mothers’ schooling levels: 3.1524 years. This 0.0028 year
difference is in the direction predicted by confounding of genetic relatedness and environmental
similarity. However, the difference is not statistically significant and even if it were, it may not
be enough to bias models of heritability for phenotypes where maternal schooling matters. (If
we use the 0.01 kinship cut-off for the regression analysis, results are similar.) To better
understand the magnitude of these effects (if they were indeed statistically significant) it helps to
examine the standardized coefficients, which are the nominal regression coefficients adjusted by
the ratio of the standard deviations of genetic relatedness (0.00589) and maternal education
6
(16.8). When we do this, we find that a one standard deviation change in relatedness results in a
point estimate change of a 0.001 standard deviation difference in maternal education. Thus, the
effect of genetic relatedness on maternal-education difference is hardly a substantial source of
bias even if it were discernible from zero. We replicated this analysis using data from the
National Longitudinal Survey of Adolescent Health (Add Health). The point estimates in the
replication sample are larger, but they are also statistically indiscernible from zero (Table S2).
We performed an analogous analysis on childhood urbanicity using data from the Health
and Retirement Study. We find that among the pool of HRS respondents where pairs are no more
than 0.025 related, if we compare an individual with another individual who is one-half of one
percent related, we find that the probability they both lived (or both did not live) in a city during
their childhood (as opposed to suburban or rural environment) is 51.68 percent. But if we
compare two individuals who are one percent related, then we find that their probability of both
living in either a city or both in a non-city is 52.35 percent. When we eliminate all pairs over
one percent related, we still find an effect of relatedness. Within this subsample, two individuals
who are one-half percent related have a probability of 51.64 percent of both having lived as
children in an urban (or non-urban) setting. But two people who are one percent (twice as)
related have a probability of 52.28 percent of both having lived in the same childhood
environment with respect to urbanicity. All these differences with respect to urbanicity are
statistically significant (p<0.0001). Qualitative results do not change if we define urbanicity to
include categories one and two together (i.e. contrast rural to urban/suburban see Materials and
Methods). Again, to make the magnitude of this understandable, we can express it in standard
deviation changes of genetic relatedness (0.00396) and urbanicity (0.5). In this case, a one
standard deviation change in relatedness yields a 0.01 standard deviation change in probability of
7
both having lived as children in a city or a non-city. Although statistically significant (driven by
the huge number of pairs in the analysis), this appears to be a trivially small effect. Moreover, we
replicated the analysis using data from Add Health, and the difference (whether estimated using
the 2.5-percent relatedness cutoff or the 1-percent relatedness cutoff) is not statistically
significant (p=0.2891 and p=.2824, respectively).
8
9
Figure S1: Distribution of HRS white, non-Hispanic respondents by urbanicity Category.
(Category 1, N = 8713; Category 2, N=4014; Category 3, N=5870; N/A, N=24). Responses are
collapsed (to preserve respondent confidentiality) based on the 2003 Beale Rural-Urban
Continuum Code to: “Urban” (Beale Rural-Urban Continuum code 1); Suburban (Beale RuralUrban Continuum code 2) or; Ex-urban (Beale Rural-Urban Continuum codes 3,4,5,6,7,8,9). In
the analysis, we compared urban versus non-urban childhoods by collapsing codes 2 through 9
into one category of an urbanicity variable, though combining codes 1 and 2 into a more
comprehensive urban category does not change results.
10
Figure S2: Distribution of HRS white, non-Hispanic respondent pairs related less than .025, by
shared status on urbanicity variable. In the analysis, we compared urban versus non-urban
childhoods by collapsing codes 2 and 3 into one category of an urbanicity variable, though
combining codes 1 and 2 into a more comprehensive urban category does not change results.
Pairs with same urbanicity status: 12,269,572; those with unshared status: 11,781,008.
11
Figure S3: Distribution of genetic relatedness among HRS respondents, white, non-Hispanics
only, by relatedness cut-off.
12
Figure S4: Distribution of genetic relatedness among FHS respondents (whites), all respondents
included, by relatedness cut-off.
13
Figure S5: Distribution of genetic relatedness among FHS respondents (white, non-Hispanics),
one-randomly respondent per pedigree, by relatedness cut-off.
14
Figure S6: Distribution of genetic relatedness among Add Health respondents (white, nonHispanics), by relatedness cut-off and pedigree status.
15
Figure S7: Distribution of HRS white, non-Hispanic respondents by education level.
Years of Completed Schooling
16
Figure S8: Distribution of HRS white, non-Hispanic respondents by height.
Height in Meters
17
Figure S9: Distribution of HRS white, non-Hispanic respondents by BMI level.
18
Figure S10: Distribution of maternal education in white, non-Hispanic FHS respondents—one
respondent per pedigree.
19
Figure S11: Distribution of maternal education in white, non-Hispanic respondents of the
National Longitudinal Survey of Adolescent Health—one respondent per pedigree.
Years of Completed Schooling
20
Figure S12: Distribution of Add Health white, non-Hispanic respondents by urbanicity Category
(one per pedigree). (Category 1, N = 83; Category 2, N=195; Category 3, N=160). In the
analysis, we compared urban versus non-urban childhoods by collapsing codes 2 and 3 into one
category of an urbanicity variable, though combining codes 1 and 2 into a more comprehensive
urban category does not change results.
21
Figure S13: Distribution of Add Health white, non-Hispanic respondent pairs related less than
.025, by shared status on urbanicity variable. In the analysis, we compared urban versus nonurban childhoods by collapsing codes 2 and 3 into one category of an urbanicity variable, though
combining codes 1 and 2 into a more comprehensive urban category does not change results.
Pairs with same urbanicity status: 66,198; those with unshared status: 29,446.
22
Table S1.GREML heritability estimates for shared childhood urbanicity, height, body mass index
(BMI) and education among white, non-Hispanic respondents in the Health and Retirement
Study (HRS) for cryptic relatedness cut-off of 0.01.*
Urban
Child.
N=789
Height
N=789
h2
No
controls
(2 PCs)
A
.000001
h2
Urban
Control
(2 PCs)
B
n/a
h2
No
controls
(10 PCs)
C
.000001
[.53973]
h2
Urban
Control
(10 PCs)
D
n/a
h2
No
controls
(25 PCs)
E
0.000001
[.552652]
h2
Urban
Control
(25 PCs)
F
n/a
[.53632]
.785364
[.52213]
.801276
[.52176]
.867399
[.52885]
.893727
[.52831]
0.61156
[.540092]
0.632902
[.540197
BMI
N=787
.999999
[.51576]
.999999
[.51612]
.999999
[.51905]
.999999
[.51939]
0.999999
[.52824]
0.999999
[.528677]
Educ.
N=782
.115819
[.51378]
.256257
[.51505]
.000001
[.52668]
.095754
[.09575]
0.000001
[.54731]
0.000001
[.547955]
Two principal components control for population stratification in first set of analyses (A,B), ten
PCs in second set of analyses (C,D) and 25 PCs in third set (E,F). Standard errors in brackets.
*
23
Table S2. Effect of genetic relatedness on differences in childhood environment.*
A
Intercept
Brelatedness
Npairs
R2
(Δ Maternal Education)2
(FHS, Relatedness.025)
9.972
[0.079]
-3.462
[11.683]
66,718
2.77e-05
Residual
Error
16.8
(Δ Maternal Education)2
(FHS, Relatedness<.01)
9.968
[0.081]
-3.956
[12.479]
65,634
2.72e-05
16.9
(Δ Maternal Education)2
(Add Health, Relatedness<.025)
11.191
[0.087]
-13.476
[11.584]
70,082
6.46e-05
14.0
(Δ Maternal Education)2
(Add Health, Relatedness <.01)
10.120
[0.088]
-21.120
[12.100]
69,533
9.52e-05
14.0
B
Intercept
Brelatedness
Npairs
R2
Shared Childhood Urbanicity –
HRS Relatedness <.025
.510
[1.03e-04]
1.35
[.0003]
24,030,580
0.0001
Residual
Error
0.50
Shared Childhood Urbanicity –
HRS Relatedness <.01
.510
[1.03e-04]
1.28
[.0003]
23,865,229
9.39e-05
0.50
Shared Childhood Urbanicity –
Add Health Relatedness <.025
.707
[0.002]
.336
[.317]
95,645
0.099
0.46
Shared Childhood Urbanicity –
Add Health Relatedness <.01
.708
[0.002]
.356
[.331]
94,922
.0097
0.46
Squared difference in parental education among white, non-Hispanic second and third
generation respondents of the Framingham Heart Study (FHS) and the National Longitudinal
Survey of Adolescent Health (Add Health) where one respondent per pedigree was randomly
chosen and included (panel A); and, (B), on shared childhood urbanicity status among white,
non-Hispanic respondents in the Health and Retirement Study (HRS) and the National
Longitudinal Survey of Adolescent Health (one respondent per pedigree), respectively, by cryptic
relatedness cut-off. Two principal components control for population stratification in all
analyses. Standard errors in brackets.
*
24
25