Transcript Using Statistical Design and Analysis to Detect

Statistical Design and Analysis
of Microarray Experiments
Peng Liu
6/15/2010
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Microarray Technology
 Microarray technology allows measuring
expression levels (abundance of mRNA
transcripts) of thousands of genes
simultaneously.
 Two types of platforms:
Affymetrix (single-color)
Two-color microarray
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Wild-type vs. Myostatin Knockout Mice
Belgian Blue
cattle have a
mutation in the
myostatin gene.
Design of Affymetrix experiment: one sample  one chip
Designing 2-color microarray (3 layers)
From Churchill, 2002, nature genetics
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Example I: Sawers et al, 2007, BMC Bioinformatics
bundle sheath strands
mesophyll protoplasts
M B
V
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Example I: Sawers et al, 2007, BMC Bioinformatics
 The establishment of C4 photosynthesis in
maize is associated with differential
accumulation of gene transcripts and proteins
between bundle sheath and mesophyll
photosynthetic cell types.
 Goal: To detect genes that are differentially
expressed in Bundle Sheath (B) and Mesophyll
(M) cells.
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Example I: Sawers et al, 2007, BMC Bioinformatics
 A simple method:
Isolate cells and perform a microarray
experiments to compare the gene expression
between the two cells (treatments).
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Example I: Sawers et al, 2007, BMC Bioinformatics
 A little more complication:
The procedure for extracting mRNA for the two
cells are different. The one to extract mRNA
from M cells introduces stress.
 Solution:
Add two more treatment groups: samples with
both M and B cells going through extraction of
mRNA with and without stress.
B, M, Stress and Total (4 treatment groups)
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Direct comparison vs indirect comparison
 Direct: comparison within slide
 Indirect: comparison between slides
 Suppose we want to compare gene expression
levels between treatment 1 and treatment 2.
1
2
1
2
Direct Comparison
2
1
R
Indirect Comparison
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Comments about 2-color Microarray Designs
 A unique and powerful feature of 2-color
microarray is to make direct comparison
between two samples on the same slide.
 For pairing samples, the variation due to slide
can be accounted for.
 When possible, it is more efficient to use direct
comparison.
 However, sometimes, it is not practical to make
direct comparison of all possible pairs.
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Efficiency of comparison
 The efficiency of comparisons between 2
samples is determined by the length and the
number of paths connecting them.
1
2
1
2
Direct Comparison
(Dye-swap)
2
1
R
Indirect Comparison
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Reference vs Loop design
1
2
R
Reference Design
3
2
1
3
Loop Design
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Designing experiment for example I
B
With 6 biological
replicates
Total
Stress
M
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Performing the experiment (Nature cell biol. 2001
3:8)
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After the bench work…
2-color microarray image
Affymetrix Gene Chip image
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The data table looks like
Header
Begin Raw Data
Flag
Row Column Gene ID
Field Meta Row Meta Column
1 MZ00040724
1
1
1
A
2 MZ00040730
1
1
1
A
3 MZ00040748
1
1
1
A
4 MZ00040754
1
1
1
A
5 MZ00040772
1
1
1
A
6 MZ00040778
1
1
1
A
7 MZ00040796
1
1
1
A
8 MZ00040802
1
1
1
A
9 MZ00013020
1
1
1
A
10 MZ00013026
1
1
1
A
11 MZ00013044
1
1
1
A
0
2
0
0
0
2
2
3
3
3
3
Mean Median
Background
Signal MedianSignal
533
1645.5
469
613
462
741.5
473
909
471.5
964
469
574
487
579
614
38051
516.5
4539
491.5
597.5
521.5
16210
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Pre-normalization analysis
 Image processing
obtain the intensity measurement of the signal
 Background correction
get rid of local background that might due to nonspecific binding and obtain the target sample intensity
 Filtration
remove unreliable spots and reduce the dimension of
data
 Transformation
convert data into a format that makes data analysis
valid or easier
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Normalization
 Normalization describes the process of
removing (or minimizing) non-biological variation
in measured signal intensity levels so that
biological differences in gene expression can be
appropriately detected.
 Aim: remove sources of systematic variation
 Example of non-biological variation: dye
difference for 2-color microarray
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Figure from Dudoit et al, 2002, Statistica Sinica
Self-self experiment
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Log Red-Log Green = M
Normalization: M vs. A Plot (45o rotation)
(Log Green+Log Red)/2 = A
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Log Red-Log Green
LOWESS Fit
(Log Green+Log Red)/2
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Normalized M
After normalization
A
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Statistical Inference
 Data notation for normalized signal intensities
(NSI):
Yijk for each gene (g)
i: treatment index
j: dye index
k: slide index
Y114
treatment
Y224
dye slide
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Fitting linear models to microarray data
 After the normalization, we have one observation
(normalized signal intensity) for each gene on each
channel (a combination of dye and array).
 Together, the data is an array with each row for one
gene and each column for one channel or one chip.
 We will fit a statistical model for each gene separately.
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Mean expressions for 4 treatment groups
Treatments
means
μ+v2+
μ+v1
μ+c*v2+ (1-c)*v1
μ+c*v2+ (1-c)* v1+




M (M cell with stress)
B (B cell without stress)
TO (both cells without stress)
ST (both cells with stress)

Note that c is the proportion of M cells in the total leaf
sample with both cells.

We are interested in testing H0: v1 = v2, whether a given
gene is differentially expressed between M and B cells or
not.
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Fixed effects
 The parameters on the previous slide (v1, v2, and )
specify fixed effects.
 Fixed effects are used to specify the mean of the
response variable.
 A factor is fixed if the levels of the factor were selected
by the investigator with the purpose of comparing the
effects of the levels to one another.
 The fixed effects included in the model depend on the
experimental design.
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Random effects
 There are some random
effects that are unknown:
slide effects
other effects introduced in
the experiment (such as
biological replicate effects)
residual random effects
that include any sources of
variation unaccounted for
by other terms
B
Total
Stress
M
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Random effects
 Random factors are used to specify the correlation
structure among the response variable observations.
e.g., observations on the same slide are more correlated than
observations from different slides.
 The random effects included in the model also depend
on the experimental design.
 A model that has both fixed and random effects is called
a mixed model.
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Detecting differentially expressed genes
 Construct statistical test for parameters that we are
interested in, e.g., what are the difference in gene
expression (v1 - v2)?
v1 - v2  0 means differential expression.
 Model the random effects and perform tests or construct
confidence intervals.
 Perform tests for each gene and obtain a p-value.
Empirical Bayes test that borrows information across genes is
often used because of higher power.
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Results from testing
A set
ID
1
3
8
9
11
12
16
18
21
22
33
35
37
38
40
46
48
50
Gene ID
MZ00040724
MZ00040748
MZ00040802
MZ00013020
MZ00013044
MZ00013050
MZ00013098
MZ00000486
MZ00000528
MZ00000534
MZ00032020
MZ00032044
MZ00032068
MZ00032074
MZ00032098
MZ00008134
MZ00008158
MZ00024806
…
v1-v2
-4.69E-01
1.01E-01
-4.10E-01
-4.96E-01
-2.77E-01
-7.81E-02
-7.50E-02
-5.16E-01
3.69E-01
4.98E-01
1.98E-01
-6.73E-01
-5.98E-01
-4.17E-01
-1.88E-01
2.11E-01
8.70E-02
1.01E-01
…
p-value for (v1-v2)q-value
0.33691808
0.61046054
0.18009214
0.12907116
0.26988092
0.77596069
0.73097085
0.005203899
0.25837106
0.041544897
0.52396675
0.000939694
0.016160615
0.27593771
0.28042709
0.77894787
0.79905176
0.73992828
…
0.4012188
0.5306277
0.2881755
0.2438822
0.3566803
0.5895432
0.5752585
0.04976865
0.3488733
0.1337469
0.4961501
0.02472483
0.0844817
0.3610925
0.3641593
0.5905477
0.5954345
0.5788615
…
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2536 p-values below 0.05.
We would expect around 0.05*40000=2000
p-values to be less than 0.05 by chance
if no genes were differentially expressed.
0.05
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Possible Errors in Testing ONE gene
Hypothesis
Accept Null
Reject Null (sig)
True Null
(non-DE)
correct
Type I Error
False Null
(DE)
Type II Error
correct (Power)
 Type I Error: false positives
 Type II Error: false negatives (1-power)
 Power: true positives
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Error Rate in Multiple Testing
Outcomes when testing m genes
(Benjamini and Hochberg, 1995)
Hypothesis
True Null
(Non-DE)
False Null
(DE)
Total
Accept Null
U
Reject Null
V
Total
m0
T
S
m1
W
R
m
Family-wise error rate, FWER= Pr(V >0)
False Discovery Rate,
FDR = E(V/R |R>0) * Pr(R>0)
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Results from testing for example I
A set
ID
1
3
8
9
11
12
16
18
21
22
33
35
37
38
40
46
48
50
Gene ID
MZ00040724
MZ00040748
MZ00040802
MZ00013020
MZ00013044
MZ00013050
MZ00013098
MZ00000486
MZ00000528
MZ00000534
MZ00032020
MZ00032044
MZ00032068
MZ00032074
MZ00032098
MZ00008134
MZ00008158
MZ00024806
…
v1-v2
-4.69E-01
1.01E-01
-4.10E-01
-4.96E-01
-2.77E-01
-7.81E-02
-7.50E-02
-5.16E-01
3.69E-01
4.98E-01
1.98E-01
-6.73E-01
-5.98E-01
-4.17E-01
-1.88E-01
2.11E-01
8.70E-02
1.01E-01
…
p-value for (v1-v2)q-value
0.33691808
0.61046054
0.18009214
0.12907116
0.26988092
0.77596069
0.73097085
0.005203899
0.25837106
0.041544897
0.52396675
0.000939694
0.016160615
0.27593771
0.28042709
0.77894787
0.79905176
0.73992828
…
0.4012188
0.5306277
0.2881755
0.2438822
0.3566803
0.5895432
0.5752585
0.04976865
0.3488733
0.1337469
0.4961501
0.02472483
0.0844817
0.3610925
0.3641593
0.5905477
0.5954345
0.5788615
…
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Clustering
 Grouping genes into
different “clusters”
based on their
expression profile
 Clustering
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Other analyses
 Relating the gene expressions with biological
functional categories  Gene Enrichment Test
 Connecting microarray data with other kinds of
data such as survival data.
 More …
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Assigned References
 Nettleton, D. (2006) A Discussion of statistical methods
for design and analysis of microarray experiments for
plant scientists. The Plant Cell,18, 2112–2121.
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