Hunting for Genes with Longitudinal
Phenotype Data Using Stata
United Kingdom Stata Conference 2010
September 9, 2010
John Charles “Chuck” Huber Jr, PhD
Assistant Professor of Biostatistics
Department of Epidemiology and Biostatistics
School of Rural Public Health
Texas A&M Health Science Center
jchuber@tamu.edu
Co-Authors
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Michael Hallman, PhD (Principal Investigator)
Ron Harrist, PhD
Victoria Friedel, MA
Melissa Richard, MS
Huandong Sun
All at University of Texas School of Public Health
Motivation – Project Heartbeat!
Reference: Fulton, JE, Dai, S, Grunbaum, JA, Boerwinkle, E, Labarthe, R (1999) Apolipoprotein E affects serial changes
In total and low-density lipoprotein cholesterol in adolescent girls: Project Heartbeat!. Metabolism 48(3): 285-290
Motivation
Reference: Fulton, JE, Dai, S, Grunbaum, JA, Boerwinkle, E, Labarthe, R (1999) Apolipoprotein E affects serial changes
In total and low-density lipoprotein cholesterol in adolescent girls: Project Heartbeat!. Metabolism 48(3): 285-290
Motivation
Reference: Fulton, JE, Dai, S, Grunbaum, JA, Boerwinkle, E, Labarthe, R (1999) Apolipoprotein E affects serial changes
In total and low-density lipoprotein cholesterol in adolescent girls: Project Heartbeat!. Metabolism 48(3): 285-290
Motivation
• Human genetics studies in the 1990s tended
to focus on family data – Project Heartbeat!
was a population-based study (no relatives)
• Genetic studies of unrelated individuals
became popular in the 2000s
• Genetic markers called Single Nucleotide
Polymorphisms (SNPs) became cheap to
ascertain on a very large scale
What is a SNP?
Hartl & Jones (1998) pg 9, Figure 1.5
What is a SNP?
Watson et al. (2004) pg 23, Figure 2.5
What is a SNP?
• A SNP is a single nucleotide polymorphism
(the individual nucleotides are called alleles)
Person 1 – Chromosome 1
Person 1 – Chromosome 2
Person 2 – Chromosome 1
Person 2 – Chromosome 2
ataagtcgatactgatgcatagctagctgactgacgcgat
ataagtccatactgatgcatagctagctgactgaagcgat
ataagtccatactgatgcatagctagctgactgacgcgat
ataagtcgatactgatgcatagctagctgactgaagcgat
SNP1
SNP2
Motivation
Stored Genotype Data
Blood samples and
DNA available for 131
African-American and
505 non-Hispanic
white children
between 8 and 17
years of age.
Motivation
Stored Phenotype Data
Longitudinal measurements of:
Body Mass Index
Total Cholesterol
HDL & LDL Cholesterol
Systolic and Diastolic BP
Much, much more…..
Motivation
Let’s go gene hunting!!!
Challenges
1.
2.
3.
4.
5.
Longitudinal Data – PLINK or HelixTree?
Specialized genetic data analysis
Need to run a very large number of graphs and models
Multiple comparisons and replication
Scaling up to 100,000 SNP Chips
Longitudinal Phenotype Data
No PLINK….
No HelixTree….
No dice?
Longitudinal Phenotype Data
• Stata is well equipped for longitudinal data
– xtreg
– xtgee
– gllamm
– xtmixed
Challenges
1.
2.
3.
4.
5.
Longitudinal Data – PLINK or HelixTree?
Specialized genetic data analysis
Need to run a very large number of graphs and models
Multiple comparisons and replication
Scaling up to 100,000 SNP Chips
Genetic Data Analysis
1.
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5.
6.
Genotype Frequencies
Allele Frequencies
Hardy-Weinberg Equilibrium
Haplotype Reconstruction
Linkage Disequilibrium
TagSNPs
Stata for Genetic Data Analysis
2007 UK Stata Users Group meeting:
http://www.stata.com/meeting/13uk/
A brief introduction to genetic epidemiology using Stata
Neil Shephard, University of Sheffield
An overview of using Stata to perform candidate gene association analysis will be
presented. Areas covered will include data manipulation, Hardy–Weinberg
equilibrium, calculating and plotting linkage disequilibrium, estimating haplotypes,
and interfacing with external programs.
User Written Genetics Commands
Programs written by David Clayton
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ginsheet- Read genotype data from text files.
gloci - Make a list of loci.
greshape - Reshape a file containing genotypes to a file of alleles.
gtab - Tabulate allele frequencies within genotypes and generate indicators (performs Hardy-Weinberg
Equilibrium testing).
gtype - Create a single genotype variable from two allele variables.
htype - Create a haplotype variable from allele variables.
mltdt - Multiple locus TDT for haplotype tagging SNPs (htSNPs).
origin - Analysis of parental origin effect in TDT trios.
pseudocc - Create a pseudo-case-control study from case-parent trios.
pscc - Experimental version of pseudocc in which there may be several groups of linked loci.
pwld - Pairwise linkage disequilibrium measures.
rclogit - Conditional logistic regression with robust standard errors.
snp2hap - Infer haplotypes of 2-locus SNP markers.
tdt - Classical TDT test.
trios - Tabulate genotypes of parent-offspring trios.
User Written Genetics Commands
Programs written by Adrian Mander
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gipf - Graphical representation of log-linear models.
hapipf - Haplotype frequency estimation using an EM algorithm and log-linear modelling.
pedread - Read's pedigree data file (in pre-Makeped LINKAGE format), similar to ginsheet
pedsumm - Summarises a pre-Makeped LINKAGE file that is currently in Stata's memory.
pedraw - Draws one pedigree in the graphics window
plotmatrix - Produces LD heatmaps displaying graphically the strength of LD between markers.
profhap - Calculates profile likelihood confidence intervals for results from hapipf
swblock - A step-wise hapipf routine to identify the parsimonious model to describe the Haplotype block
pattern.
qhapipf - Analysis of quantitative traits using regression and log-linear modelling when phase is unknown.
hapblock - attempts to find the edge of areas containing high LD within a set of loci
User Written Genetics Commands
Programs written by Mario Cleves
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gencc - Genetic case-control tests
genhw - Hardy-Weinberg Equilibrium tests
qtlsnp - A program for testng associations between SNPs an a quantitative trait.
Programs written by Catherine Saunders
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co_power - Power calculations for Case-only study designs.
gei_matching geipower - Power calculations for Gene-Environment interactions.
ggipower - Power calculations for Gene-Gene interactions.
tdt_geipower - Power calculations for Gene-Environment interactions via TDT analysis.
tdt_ggipower - Power calculations for Gene-Gene interactions via TDT analysis.
Programs written by Neil Shephard
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genass- Performs a number of statistical tests on your genotypic data and collates the results into a Stata
formatted data set for browsing.
User Written Genetics Commands
Programs written by Roger Newson
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multproc – multiple comparison procedures and False Discovery Rates
Far too many others to list…….
Programs written by Chuck Huber
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Accepted by the Stata Journal
phaseout – export genotype data to PHASE
phasein – import haplotype data from PHASE
haploviewout – export haplotype data in HaploView format for estimating and visualizing LD and other tasks
Forthcoming (when I have time to clean them up)
snpsumm – summarize allele/genotype frequencies and H-W equilibrium for large numbers of SNPs
manhattanplot – creates “Manhattan” plots from the results of a genome-wide association study (GWAS)
User Written Genetics Commands
Command: haplologit
Y. V. Marchenko, R. J. Carroll, D. Y. Lin, C. I. Amos, and R.
G. Gutierrez (2008) Semiparametric analysis of case-control genetic data in the presence of
environmental factors. The Stata Journal 8 (3): 305333
User Written Genetics Commands
So Stata is well equipped for
genetic data analysis!
Challenges
1.
2.
3.
4.
5.
Longitudinal Data – PLINK or HelixTree?
Specialized genetic data analysis
Need to run a very large number of graphs and models
Multiple comparisons and replication
Scaling up to 100,000 SNP Chips
Looping Over Graphs and Models
Very simplistic structure of a model:
E(Phenotypeit )  0  1ageit  2 SNPi  3 (ageit  SNPi )
(12 Phenotypes) x (1753 SNPs) x (5 Candidate Models Each)
= 105,180 Models!
Looping Over Graphs and Models
• Looping Over Lists
– Code:
* LOOPING THROUGH A SINGLE LIST OF WORDS
local SnpList "rs2239560 rs7524046 rs35610691"
foreach snp of local SnpList {
disp "Currently processing SNP `snp'"
}
– Output:
Currently processing SNP rs2239560
Currently processing SNP rs7524046
Currently processing SNP rs35610691
Looping Over Graphs and Models
– Code:
* LOOPING THROUGH TWO LISTS OF WORDS
local SnpList "rs2239560 rs7524046 rs35610691"
local PhenotypeList "bmi sbp tc"
foreach Phenotype of local PhenotypeList {
foreach snp of local SnpList {
disp "The outcome variable is `Phenotype' and the SNP is `snp'."
}
}
– Output:
The outcome variable is bmi and the SNP is rs2239560.
The outcome variable is bmi and the SNP is rs7524046.
The outcome variable is bmi and the SNP is rs35610691.
The outcome variable is sbp and the SNP is rs2239560.
The outcome variable is sbp and the SNP is rs7524046.
The outcome variable is sbp and the SNP is rs35610691.
The outcome variable is tc and the SNP is rs2239560.
The outcome variable is tc and the SNP is rs7524046.
The outcome variable is tc and the SNP is rs35610691.
Looping Over Graphs and Models
• Lowess Curves for each Phenotype/SNP Combination:
LOOPING THROUGH TWO LISTS OF WORDS
local SnpList "rs2239560 rs7524046 rs35610691“
local PhenotypeList "bmi sbp tc“
foreach Phenotype of local PhenotypeList {
foreach snp of local SnpList {
twoway (lowess mean_`Phenotype' mean_age if `snp'=="AA",
*/ (lowess mean_`Phenotype' mean_age if `snp'=="AG",
*/ (lowess mean_`Phenotype' mean_age if `snp'=="GG",
graph export Graph_`Phenotype'_`snp'.ps, as(ps) logo(off)
}
}
sort lcolor(red)) /*
sort lcolor(green)) /*
sort lcolor(blue)) /*
replace
Note: Postscript files can be easily combined in Adobe Acrobat Professional
Looping Over Graphs and Models
• If we run many models, we need to be able to
save the results to an output file.
• Commands for writing to data files
– postfile: creates an output data file and describes
its structure
– post: writes data to the output data file
– postclose: closes the output data file
Looping Over Graphs and Models
• Longitudinal model for each Phenotype/SNP Combination:
postfile Output str16 phenotype str16 snp chi2 using OutputFile.dta, replace
local SnpList "rs2239560 rs7524046 rs35610691"
local PhenotypeList "bmi sbp tc"
foreach Phenotype of local PhenotypeList {
foreach snp of local SnpList {
xtmixed `Phenotype‘ age i.`snp‘ c.age#i.`snp‘ || Id: age, cov(unstruct)
post Output ("`Phenotype'") ("`snp'") (e(chi2))
}
}
postclose Output
Challenges
1.
2.
3.
4.
5.
Longitudinal Data – PLINK or HelixTree?
Specialized genetic data analysis
Need to run a very large number of graphs and models
Multiple comparisons and replication
Scaling up to 100,000 SNP Chips
Multiple Comparisons
• In our study, we will be computing hundreds
of thousands of p-values. How do we control
for multiple comparisons?
– False Discovery Rates
– Replication in a second dataset
Multiple Comparisons
• False Discovery Rates are a collection of
methods for adjusting for multiple
comparisons commonly used in large scale
genetics studies where the number of pvalues regularly exceeds 500,000.
• Calculate a threshold p-value for determining
overall statistical significance much like a
Bonferroni correction.
False Discovery Rates
Copied from Benjamini & Hochberg (1995) page 291
V

False DiscoveryRate  E  | R  0 P( R  0)
R

Reference: Benjamini, Y. & Hochberg Y. (1995) Controlling the false discovery rate: a practical and powerful
Approach to multiple testing. Journal of the Royal Statistical Society, Series B 57: 289-300
Replication Data
• Bogalusa Heart Study
– Similar longitudinal study
– Included children in the 8-17 age range
– 478 African-American participants
– 1081 non-Hispanic White participants
– Same phenotypes
– Same genotypes (more or less)
Multiple Comparisons
Strategy
1. Identify the SNPs in the Project Hearbeat!
sample that meet the overall threshold for
statistical significance using False Discovery
Rates.
2. Run the significant SNPs with the Bogalusa
data to check for replication of the results.
Challenges
1.
2.
3.
4.
5.
Longitudinal Data – PLINK or HelixTree?
Specialized genetic data analysis
Need to run a very large number of graphs and models
Multiple comparisons and replication
Scaling up to 100,000 SNP Chips
Scaling up to 100,000 SNPs
HELP!
Scaling up to 100,000 SNPs
• Possible Strategies:
– Read data from text files in “chunks” using the
“infix” command.
– Bribe Bill Gould with vast quantities of wine.
– Other suggestions?
Actual Analysis
Disclaimer:
• Since this study is a work in progress, I have
changed the gene and SNP names to protect
the innocent.
Actual Analysis
• Example Data
. list
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id age bmi SNP1 SNP2 SNP3 if id==1, sepby(id)
+--------------------------------------------+
| id
age
bmi
SNP1
SNP2
SNP3 |
|--------------------------------------------|
| 1
14.33812
26.07
AG
GG
GG |
| 1
14.6694
27.06
AG
GG
GG |
| 1
15.00616
28.33
AG
GG
GG |
| 1
15.40041
28.78
AG
GG
GG |
| 1
15.66324
29.76
AG
GG
GG |
| 1
15.97536
29.29
AG
GG
GG |
| 1
16.33128
28.28
AG
GG
GG |
| 1
16.65435
29.85
AG
GG
GG |
| 1
17.01848
28.52
AG
GG
GG |
| 1
17.30595
27.96
AG
GG
GG |
| 1
17.63997
28.28
AG
GG
GG |
+--------------------------------------------+
Actual Analysis
• Variable “Characteristics”
* EXAMPLE OF HOW TO ADD CHARACTERISTICS TO A VARIABLE AND EXTRACT THEM TO A LOCAL MACRO
char SNP1[chromosome] 7
char SNP1[gene] Gene1
char SNP1[position] 142702852
local TempChromosome : char SNP1[chromosome]
local TempGene : char SNP1[gene]
local TempPosition : char SNP1[position]
. disp "SNP1 is on Chromosome `TempChromosome', in `TempGene' at position `TempPosition'"
SNP1 is on Chromosome 7, in Gene1 at position 142702852
Actual Analysis
Lowess curve of BMI over age
Actual Analysis
Data checking with the “snpsumm” command:
. snpsumm SNP*, listgeno
Genotype Information
=================================================================
gen1, gen2 and gen3 are the genotypes
gencou~1, gencou~2, gencou~3 are the counts of each genotype
genfreq1, genfreq2 and genfreq3 are the genotype frequencies
=================================================================
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+----------------------------------------------------------------------------------------------------------+
| Marker
gen1
gencou~1
genfreq1
gen2
gencou~2
genfreq2
gen3
gencou~3
genfreq3
gentotal |
|----------------------------------------------------------------------------------------------------------|
|
SNP1
AA
23
0.0375
AG
177
0.2887
GG
413
0.6737
613 |
|
SNP2
AA
37
0.0605
AG
200
0.3268
GG
375
0.6127
612 |
|
SNP3
AG
1
.
GG
612
.
.
.
. |
|
SNP4
AA
35
0.0571
AG
201
0.3279
GG
377
0.6150
613 |
|
SNP5
AA
203
0.3524
AG
259
0.4497
GG
114
0.1979
576 |
|----------------------------------------------------------------------------------------------------------|
|
SNP6
AA
55
0.0899
AG
251
0.4101
GG
306
0.5000
612 |
|
SNP7
AG
1
.
GG
612
.
.
.
. |
|
SNP8
AA
8
0.0131
AG
124
0.2023
GG
481
0.7847
613 |
|
SNP9
AA
41
0.0669
AG
204
0.3328
GG
368
0.6003
613 |
| SNP10
AA
51
0.0833
AC
247
0.4036
CC
314
0.5131
612 |
|----------------------------------------------------------------------------------------------------------|
| SNP11
AA
30
0.0489
AG
208
0.3393
GG
375
0.6117
613 |
+----------------------------------------------------------------------------------------------------------+
Actual Analysis
Data checking with the “snpsumm” command:
. snpsumm SNP*, listallele
Allele Information
=================================================================
a1 and a2 are the alleles
acount1 and acount2 are the counts of each allele
afreq1 and afreq2 are the counts of each allele
maf is the Minor Allele Frequency
=================================================================
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+--------------------------------------------------------------------------+
| Marker
a1
acount1
afreq1
a2
acount2
afreq2
atotal
maf |
|--------------------------------------------------------------------------|
|
SNP1
A
223
0.1819
G
1003
0.8181
1226
0.1819 |
|
SNP2
A
274
0.2239
G
950
0.7761
1224
0.2239 |
|
SNP3
G
614
.
G
.
.
.
. |
|
SNP4
A
271
0.2210
G
955
0.7790
1226
0.2210 |
|
SNP5
A
665
0.5773
G
487
0.4227
1152
0.4227 |
|--------------------------------------------------------------------------|
|
SNP6
A
361
0.2949
G
863
0.7051
1224
0.2949 |
|
SNP7
G
614
.
G
.
.
.
. |
|
SNP8
A
140
0.1142
G
1086
0.8858
1226
0.1142 |
|
SNP9
A
286
0.2333
G
940
0.7667
1226
0.2333 |
| SNP10
A
349
0.2851
C
875
0.7149
1224
0.2851 |
|--------------------------------------------------------------------------|
| SNP11
A
268
0.2186
G
958
0.7814
1226
0.2186 |
+--------------------------------------------------------------------------+
Actual Analysis
Data checking with the “snpsumm” command:
. snpsumm SNP*, listhw
Hardy-Weinberg Equilibrium Information
=================================================================
maf is the Minor Allele Frequency
hw_c2 is the Pearson Chi-squared
hw_c2p is the Pearson Chi-Squared p-value
hw_lr is the Likelihood Ratio Chi-squared
hw_lrp is the Likelihood Ratio Chi-Squared p-value
hw_ex is the Exact p-value
=================================================================
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+------------------------------------------------------------+
| Marker
maf
hw_c2
hw_c2p
hw_lr
hw_lrp
hw_ex |
|------------------------------------------------------------|
|
SNP1
0.1819
0.54
0.4605
0.53
0.4662
0.4965 |
|
SNP2
0.2239
2.17
0.1407
2.10
0.1470
0.1618 |
|
SNP3
.
.
.
.
.
. |
|
SNP4
0.2210
1.40
0.2363
1.37
0.2425
0.2410 |
|
SNP5
0.4227
3.57
0.0589
3.56
0.0591
0.0605 |
|------------------------------------------------------------|
|
SNP6
0.2949
0.12
0.7316
0.12
0.7321
0.7705 |
|
SNP7
.
.
.
.
.
. |
|
SNP8
0.1142
0.00
0.9979
0.00
0.9979
1.0000 |
|
SNP9
0.2333
2.98
0.0844
2.88
0.0896
0.0901 |
| SNP10
0.2851
0.06
0.8050
0.06
0.8053
0.8427 |
|------------------------------------------------------------|
| SNP11
0.2186
0.03
0.8670
0.03
0.8673
0.9058 |
+------------------------------------------------------------+
Actual Analysis
• Reconstructing haplotypes using PHASE
without leaving Stata!
local PositionList "142702852 142736196 142747932 etc.......”
phaseout SNP*, idvar(id) filename("Gene1.inp") position(`PositionList')
shell PHASE -S1234 Gene1.inp Gene1.out 100 1 100
clear
phasein Gene1.out, markers("MarkerList.txt") positions("PositionList.txt")
What is a Haplotype?
• A haplotype is the combination of one or
more alleles found on the same chromosome
– Person 1 has a “gc” haplotype and a “ca” haplotype
– Person 2 has a “cc” haplotype and a “ga” haplotype
Person 1 – Chromosome 1
Person 1 – Chromosome 2
Person 2 – Chromosome 1
Person 2 – Chromosome 2
ataagtcgatactgatgcatagctagctgactgacgcgat
ataagtccatactgatgcatagctagctgactgaagcgat
ataagtccatactgatgcatagctagctgactgacgcgat
ataagtcgatactgatgcatagctagctgactgaagcgat
SNP1
SNP2
Actual Analysis
The resulting haplotypes are back in Stata:
. list id haplotype SNP1 SNP2 SNP3 in 1/10, sepby(id)
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+---------------------------------------+
| id
haplotype
SNP1
SNP2
SNP3 |
|---------------------------------------|
| 1
AGGGAAGGGCG
A
G
G |
| 1
GGGGAGGGGAG
G
G
G |
|---------------------------------------|
| 2
GGGGAGGGGCG
G
G
G |
| 2
GGGGAGGGGCA
G
G
G |
|---------------------------------------|
| 3
GGGGAGGGGAG
G
G
G |
| 3
GGGAGAGGGCA
G
G
G |
|---------------------------------------|
| 4
AGGGAGGGGAG
A
G
G |
| 4
GGGAGGGAGCG
G
G
G |
|---------------------------------------|
| 5
GGGGAGGGGAG
G
G
G |
| 5
GAGGGGGGACG
G
A
G |
+---------------------------------------+
Actual Analysis
haploviewout SNP*, idvariable(id) filename("Gene1") poslabel
Actual Analysis
Actual Analysis
. multproc, pval(pvalue) meth(simes) rank(FDR_rank) critical(FDR_critical) reject(FDR_reject)
. list Chromosome Position pvalue FDR_rank FDR_critical FDR_reject in 1/22, sepby( FDR_reject)
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+------------------------------------------------------------------+
| Chromo~e
Position
pvalue
FDR_rank
FDR_cri~l
FDR_re~t |
|------------------------------------------------------------------|
|
3
1.60e+08
.0000372
1
.00003266
Yes |
|
8
4.59e+07
.0000465
2
.00006532
Yes |
|
12
9.73e+07
.0000529
3
.00009798
Yes |
|
7
7.08e+07
.0000661
4
.00013063
Yes |
|
3
2.02e+08
.0000701
5
.00016329
Yes |
|
11
3.02e+07
.0001106
6
.00019595
Yes |
|
2
2.15e+07
.0001391
7
.00022861
Yes |
|
5
9.80e+07
.0001418
8
.00026127
Yes |
|
4
9229619
.0002013
9
.00029393
Yes |
|
2
2.02e+08
.0002179
10
.00032658
Yes |
|
5
1.39e+08
.0002698
11
.00035924
Yes |
|
18
5.69e+07
.0003339
12
.0003919
Yes |
|
12
8.07e+07
.0003429
13
.00042456
Yes |
|
16
5.66e+07
.0004299
14
.00045722
Yes |
|
3
9249973
.0004815
15
.00048988
Yes |
|
9
1.43e+08
.0005735
16
.00052253
Yes |
|
19
4.66e+07
.0005778
17
.00055519
Yes |
|
8
2.29e+08
.0006019
18
.00058785
Yes |
|
13
4.65e+07
.0006124
19
.00062051
Yes |
|------------------------------------------------------------------|
|
1
4.39e+07
.0007301
20
.00065317
No |
|
5
1.52e+08
.000731
21
.00068583
No |
|
8
4.88e+07
.0007519
22
.00071848
No |
+------------------------------------------------------------------+
This continues for
all 1753 SNPs
Actual Analysis
manhattanplot pvalue Chromosome Position, critical(`FDR_cutoff')
This is VERY heavily based on code by Stephen Turner and Will Bush of Vanderbilt University
http://gettinggeneticsdone.blogspot.com/2010/01/genome-wide-manhattan-plots-in-stata.html
Summary
Stata is a very useful platform for
doing longitudinal genome-wide
association studies!
Acknowledgements
• Grant 1-R01DK073618-02 from the National Institute of Diabetes and
Digestive and Kidney Diseases
• Michael Hallman, PhD
– Assistant Professor of Epidemiology, UTSPH-Houston
• Ron Harrist, PhD
– Associate Professor of Biostatistics, UTSPH-Austin
• Eric Boerwinkle, PhD
– Professor and Director of the Division of Epidemiology
– Kozmetsky Family Chair in Human Genetics, UTSPH-Houston
• Darwin Labarthe, MD, PhD, MPH
– Director of the Division for Heart Disease and Stroke Prevention, CDCAtlanta
References
• Barrett, J., Fry, B., Maller, J., & Daly, M. (2005). Haploview: analysis and
visualization of LD and haplotype maps. Bioinformatics, 21, 263-265.
• Hartl, D.L., Jones, E.W. (1998) Genetics: Principles and Analysis, 4th Ed.
Jones & Bartlett Publishers
• Stephens, M., & Donnelly, P. (2003). A Comparison of Bayesian Methods
for Haplotype Reconstruction from Population Genotype Data. American
Journal of Human Genetics, 73, 1162–1169.
• Stephens, M., Smith, N. J., & Donnelly, P. (2001). A New Statistical Method
for Haplotype Reconstruction from Population Data. American Journal of
Human Genetics, 68, 978–989.
• Watson, J.D., Baker, T.A., Bell, S.P., Gann, A., Levine, M., Losick, R. (2004)
Molecular Biology of the Gene, 5th Ed. Benjamin Cummings