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Exploratory data analysis
Karl Broman
Biostatistics & Medical Informatics, UW–Madison
kbroman.orggithub.com/kbroman
@kwbromanSlides: kbroman.org/BMI773/eda.pdf
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What is exploratory data analysis?
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What is exploratory data analysis?
Tukey: Looking at data to see what it seems to say.
It is important to understand what you can dobefore you learn to measure how well you seem to have done it.
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What is exploratory data analysis?
Tukey: Looking at data to see what it seems to say.
It is important to understand what you can dobefore you learn to measure how well you seem to have done it.
3
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Uses of EDA
▶ Get a sense of things▶ Data diagnostics (quality control)▶ Hoping for an “a-ha” moment▶ Following up “huh” moments
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Data diagnostics: principles▶ What might have gone wrong?▶ How could it be revealed?▶ Make lots of plots
– scatterplots– plots against time– consider taking logs
▶ Check consistency between files▶ Re-calculate derived variables and check that they match▶ Outliers
– Real or error?– Are the results affected?
▶ Don’t trust anyone, including yourself
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Data diagnostics: principles▶ What might have gone wrong?▶ How could it be revealed?▶ Make lots of plots
– scatterplots– plots against time– consider taking logs
▶ Check consistency between files▶ Re-calculate derived variables and check that they match▶ Outliers
– Real or error?– Are the results affected?
▶ Don’t trust anyone, including yourself5
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Outliers
6 wk body weight (g)
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Weird stuff I’ve seen▶ 500 worksheet excel file where the middle 100 worksheets have the
variables arranged in a different order▶ Weird rounding patterns▶ Missing values that shouldn’t be, because derived values are not
missing▶ Categorical data with inconsistent categories▶ Missing value codes that weren’t mentioned and that could be real
values (e.g., 999)▶ OMG dates
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Weird rounding
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Identifiers
▶ Are the subject IDs unique?▶ Are there subject or gene IDs that don’t fit the typical pattern?
– 1e5 vs 100000– hyphens turned into periods– IDs that became dates
▶ Subjects in one file but not in another and vice versa– Real, or messed up IDs?
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Missing values
▶ As intended?▶ Below detection limit?▶ Telling you something about sample quality?▶ Introducing bias?
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Fitting a model can be useful
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Fitting a model can be useful
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Fitting a model can be useful
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Biggest change vs 2nd difference
Max absolute change
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14
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Fit a smooth curve
Week
Bod
y w
eigh
t (g)
1 5 10 150
5
10
15
20
25
30
35
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15
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Residuals
Index
Abs
olut
e va
lue
of r
elat
ive
resi
dual
(%
)
0 200 400 600 800 1000 1200
5
10
15
20
25
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16
![Page 23: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/23.jpg)
Follow up artifacts
They might be the most interesting results
17
![Page 24: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/24.jpg)
Attie project∼500 B6 × BTBR intercross mice, all ob/ob
▶ Genotypes at 2057 SNPs (Affymetrix arrays)
▶ Gene expression in six tissues (Agilent arrays)– adipose– gastrocnemius muscle– hypothalamus– pancreatic islets– kidney– liver
▶ Numerous clinical phenotypes(e.g., body weight, insulin and glucose levels)
18
![Page 25: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/25.jpg)
Intercross
P1 P2
F1 F1
F2
19
![Page 26: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/26.jpg)
Sex and the X chr
BTBR B6
F1
F2
Female Male
20
![Page 27: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/27.jpg)
Strong eQTL
0
50
100
150
Chromosome
LOD
sco
re
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 X
probe 499541 (on chr 1)
21
![Page 28: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/28.jpg)
Strong eQTL
0
50
100
150
Chromosome
LOD
sco
re
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 X
probe 499541 (on chr 1)
probe 10002916257 (on chr 13)
21
![Page 29: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/29.jpg)
E vs G
−1.0
−0.5
0.0
expr
essi
on o
f 49
9541
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BB BR RR
Genotype at rs13476158
22
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E vs G
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BB BR RR
Genotype at rs13476158
22
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kNN classifier
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BB BR RR
Genotype at rs13476158
23
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E vs G
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−1.0 −0.5 0.0
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−0.2
0.0
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0.4
expression of 518187
expr
essi
on o
f 10
0040
3548
8
BB
BR
RRGenotype at rs6244221
24
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E vs G
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−1.0 −0.5 0.0
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expression of 518187
expr
essi
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f 10
0040
3548
8●
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BB
BR
RRGenotype at rs6244221
24
![Page 34: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/34.jpg)
Basic schemeexpression traits
transcripts
mic
e
observed eQTL genotypes
eQTL
mic
e
25
![Page 35: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/35.jpg)
Basic schemeexpression traits
transcripts
mic
e
observed eQTL genotypes
eQTL
mic
einferred eQTL genotypes
eQTL
mic
e
25
![Page 36: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/36.jpg)
Basic schemeexpression traits
transcripts
mic
e
observed eQTL genotypes
eQTL
mic
einferred eQTL genotypes
eQTL
mic
e
25
![Page 37: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/37.jpg)
Basic schemeexpression traits
transcripts
mic
e
observed eQTL genotypes
eQTL
mic
einferred eQTL genotypes
eQTL
mic
e
25
![Page 38: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/38.jpg)
Prop’n mismatches
26
![Page 39: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/39.jpg)
Prop’n mismatches
20 40 60 80 100
20
40
60
80
100
DNA sample
mR
NA
sam
ple
1
1
0.0
0.2
0.4
0.6
0.8
1.0
27
![Page 40: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/40.jpg)
Prop’n mismatches
220 240 260 280 300
220
240
260
280
300
DNA sample
mR
NA
sam
ple
201
201
0.0
0.2
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0.6
0.8
1.0
28
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Genotype mix-ups
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B6
B6
B6
BTBR
BTBR
F1
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BTBR
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F1
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1628
1629
1630
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1633
1634
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
ABCDEFGH
1 2 3 4 5 6 7 8 9 10 11 12
29
![Page 42: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/42.jpg)
Plate 1631
30
![Page 43: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/43.jpg)
Plates 1632 and 1630
31
![Page 44: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/44.jpg)
E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
e
32
![Page 45: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/45.jpg)
E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
e
32
![Page 46: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/46.jpg)
E vs E
32
![Page 47: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/47.jpg)
E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
e
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−2 −1 0 1 2
−4
−3
−2
−1
0
1
2
islet expression
liver
exp
ress
ion
transcript 497973
32
![Page 48: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/48.jpg)
E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
e
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−1.0 −0.5 0.0 0.5 1.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
islet expression
liver
exp
ress
ion
transcript 512831
32
![Page 49: Exploratory data analysisWhat is exploratory data analysis? Tukey: Looking at data to see what it seems to say. It is important to understand what you can do before you learn to measure](https://reader036.vdocuments.site/reader036/viewer/2022071108/5fe27dffdda1064607453e83/html5/thumbnails/49.jpg)
E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
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islet expression
liver
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transcript 507042
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E vs Eexpression in islet
transcripts
mic
e
expression in liver
transcripts
mic
e
32
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E vs Eexpression in islet
transcripts
mic
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expression in liver
transcripts
mic
e
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islet expression
liver
exp
ress
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Mouse3280
32
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E vs Eexpression in islet
transcripts
mic
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transcripts
mic
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islet expression
liver
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Mouse3598
32
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E vs Eexpression in islet
transcripts
mic
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transcripts
mic
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Mouse3598 islet expr
Mou
se35
99 li
ver
expr
Mouse3599 liver vs Mouse3598 islet
32
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E vs Eexpression in islet
transcripts
mic
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expression in liver
transcripts
mic
e
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Mouse3599 islet expr
Mou
se35
98 li
ver
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Mouse3598 liver vs Mouse3599 islet
32
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Expression mix-upsadipose
● ●3583 3584
●
●●
3187
31883200
gastroc
● ●3655 3659
hypo
● ●3179 3188
● ●3208 3210
● ●3347 3348
● ●3367 3369
● ●3381 3382
● ●3449 3451
● ●3452 3454
● ●3589 3590
● ●3592 3594
islet
● ●●3295 3296
● ●3598 3599
kidney
● ●● ●3484 3503?
● ●3510 3523
liver
● ●●3136 3141
● ●3142 3143
33
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Another example
kbroman.org/blog/2012/04/25/microarrays-suck 34
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What the heck?
kbroman.org/blog/2012/04/25/microarrays-suck 34
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Dense box plots
35
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Follow up artifacts
They might be the most interesting results
36
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37
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Eucalypt genetic map1 2 3 4 5 6
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Byrne et al., Theor Appl Genet 91:869–875, 199538
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Meiosis
39
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CEPH pedigrees1331 1332 1347
1362 1413 1416
884 102
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15 14 13 12
2 1
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40
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Crossover locations
Broman and Weber, Am J Hum Genet 66:1911–1926, 200041
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42
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Crossover interference
Broman and Weber, Am J Hum Genet 66:1911–1926, 2000 43
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Maternal chr 8
44
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Apparent triple XOs
Broman et al., In: Science and Statistics: A Festschrift for Terry Speed, 2003 45
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Chr 8p inversion
Broman et al., In: Science and Statistics: A Festschrift for Terry Speed, 2003 46
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Capturing EDA
▶ what were you trying to do?▶ what you’re thinking about?▶ what did you observe?▶ what did you conclude, and why?
47
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Avoid
▶ “How did I create this plot?”▶ “Why did I decide to omit those six samples?”▶ “Where (on the web) did I find these data?”▶ “What was that interesting gene?”
48
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Basic principles
Step 1: slow down and document.Step 2: have sympathy for your future self.Step 3: have a system.
49
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Capturing EDA
▶ copy-and-paste from a script▶ grab code from the log (e.g., .Rhistory)▶ Write an informal report (R Markdown or Jupyter)▶ Write code for use with the KnitR function spin()
Comments like #' This will become textChunk options like so: #+ chunk_label, echo=FALSE
50
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If you torture the data long enough,it will confess to anything.
– Tukey
51