Introduction to the design of cDNA microarray experiments

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Introduction to the design of cDNA microarray
experiments

• Statistics 246, Spring 2002
• Week 9, Lecture 1
• Yee Hwa Yang

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Some aspects of design

• Layout of the array
• Which cDNA sequence to print?
• Library
• Controls
• Spatial position
• Allocation of samples to the slides
• Different design layout
• A vs B Treatment vs control
• Multiple treatments
• Time series
• Factorial
• Replication
• number of hybridizations
• use of dye swap in replication
• Different types replicates (e.g pooled vs
  unpooled material (samples))
• Other considerations
• Physical limitations the number of slides and
  the amount of material
• Extensibility - linking

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Issues that affect design of array experiments

• Scientific
• Aim of the experiment
• Specific questions and priorities between them.
• How will the experiments answer the questions
  posed?
• Practical (Logistic)
• Types of mRNA samples
• reference, control, treatment 1, etc.
• Amount of material.
• Count the amount of mRNA involved in one channel
  of a hybridization as one unit.
• Number of slides available for experiment.
• Other Information
• The experimental process prior to hybridization
• sample isolation, mRNA extraction,
  amplification , labelling.
• Controls planned
• positive, negative, ratio, etc.
• Verification method
• Northern, RT-PCR, in situ hybridization, etc.

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Graphical representation
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Natural design choice
C

• Case 1 Meaningful biological control (C)
• Samples Liver tissue from four mice treated by
  cholesterol modifying drugs.
• Question 1 Genes that respond differently
  between the T and the C.
• Question 2 Genes that responded similarly across
  two or more treatments relative to control.
• Case 2 Use of universal reference.
• Samples Different tumor samples.
• Question To discover tumor subtypes.

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Direct vs Indirect

• Two samples
• e.g. KO vs. WT or mutant vs. WT

Indirect
Direct
T
Ref
T
C
C
average (log (T/C))
log (T / Ref) log (C / Ref )
?2 /2
2?2
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One-way layout one factor, k levels
I) Common Reference II) Common reference III ) Direct comparison

Number of Slides N 3 N6 N3
Ave. variance 2 0.67
Units of material A B C 1 A B C 2 A B C 2
Ave. variance 1 0.67
All pair-wise comparisons are of equal importance
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Dye-swap
A
A
C
B
C
B
Design B2
Design B1

• - Design B1 and B2 have the same average variance
• - The direction of arrows potentially affects the
  bias
• of the estimate but not the variance
• For k 3, efficiency ratio (Design A1 / Design
  B) 3
• In general, efficiency ratio (2k) / (k-1)

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Design how we sliced up the bulb
A
D
P
L
V
M
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Multiple direct comparisons between different
samples (no common reference) Different ways of
estimating the same contrast e.g. A compared to
P Direct log(A/P) Indirect log(A/M)
log((M/P) or log(A/D)
log(D/P) or log(A/L)
log((P/L)
D
A
M
L
P
V
How do we combine these?
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Linear model analysis
Define a matrix X so that E(Y)Xb a log(A),
plog(P), dlog(D), vlog(V), mlog(M), llog(L)
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Time Series
T2
T4
T5
T6
T7
T3
T1
Ref

• Possible designs
• All sample vs common pooled reference
• All sample vs time 0
• Direct hybridization between times.

Pooled reference
Compare to T1
t vs t1
t vs t2
t vs t3
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Design choices in time series Design choices in time series t vs t1 t vs t1 t vs t1 t vs t2 t vs t2
Design choices in time series Design choices in time series T1T2 T2T3 T3T4 T1T3 T2T4 T1T4 Ave
N3 A) T1 as common reference 1 2 2 1 2 1 1.5
N3 B) Direct Hybridization 1 1 1 2 2 3 1.67
N4 C) Common reference 2 2 2 2 2 2 2
N4 D) T1 as common ref more .67 .67 1.67 .67 1.67 1 1.06
N4 E) Direct hybridization choice 1 .75 .75 .75 1 1 .75 .83
N4 F) Direct Hybridization choice 2 1 .75 1 .75 .75 .75 .83
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2 by 2 factorial two factors, each with two
levels

• Example 1 Suppose we wish to study the joint
  effect of two drugs, A and B.
• 4 possible treatment combinations
• C No treatment
• A drug A only.
• B drug B only.
• A.B both drug A and B.
• Example 2 Our interest in comparing two strain
  of mice (mutant and wild-type) at two different
  times, postnatal and adult.
• 4 possible samples
• C WT at postnatal
• A WT at adult (effect of time only)
• B MT at postnatal (effect of the mutation only)
• A.B MT at adult (effect of both time and the
  mutation).

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Factorial design
m
ma
Different ways of estimating parameters. e.g. B
effect. 1 (m b) - (m) b 2 - 5 ((m
a) - (m)) -((m a)-(m b)) (a) - (a b)
b
2
A
C
4
1
3
5
6
B
AB
mb
mabab
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Factorial design
m
ma
mabab
mb
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2 x 2 factorial
Indirect A balance of direct and indirect A balance of direct and indirect A balance of direct and indirect
I) II) III) IV)
Slides N 6 N 6 N 6 N 6
Main effect A 0.5 0.67 0.5 NA
Main effect B 0.5 0.43 0.5 0.3
Interaction A.B 1.5 0.67 1 0.67
Table entry variance
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Linear model analysis
Define a matrix X so that E(Y)Xb Use least
squares estimate for a, b, ab
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y1 log (A / C) a
y2 log (B / C) b
y3 log (AB / C) a b ab

• Common reference approach
• Estimate (ab) with y3 - y2 - y1

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2 x 2 factorial
Indirect A balance of direct and indirect A balance of direct and indirect A balance of direct and indirect
I) II) III) IV)
Slides N 6 N 6 N 6 N 6
Main effect A 0.5 0.67 0.5 NA
Main effect B 0.5 0.43 0.5 0.3
Interaction A.B 1.5 0.67 1 0.67
Table entry variance
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More general n by m factorial experiment

• 2 factors, one with n levels and the other with m
  levels
• OE experiment (2 by 2)
• interested in difference between zones, age
  and also zone.age interaction.
• Further experiment (2 by 3)
• only interested in genes where difference
  between treatment and controls changes with
  time.

treatment
control
control
treatment
0 12 24
0 12 24
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WT.P21 ? a1 a2
WT.P11 ? a1
WT P1 ?
2
5
7
4
1
MT.P21 ? (a1 a2) b (a1 a2)b
MT.P1 ? b
MT.P11 ? a1ba1.b
3
6
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Replication

• Why replicate slides
• Provides a better estimate of the log-ratios
• Essential to estimate the variance of log-ratios
• Different types of replicates
• Technical replicates
• Within slide vs between slides
• Biological replicates

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Sample size
Apo A1 Data Set
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Technical replication - labelling

• 3 sets of self self hybridization (cerebellum
  vs cerebellum)
• Data 1 and Data 2 were labeled together and
  hybridized on two slides separately.
• Data 3 were labeled separately.

Data 3
Data 2
Data 1
Data 1
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(No Transcript)
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• Technical replication - amplification
• Olfactory bulb experiment
• 3 sets of Anterior vs Dorsal performed on
  different days
• 10 and 12 were from the same RNA isolation and
  amplification
• 12 and 18 were from different dissections and
  amplifications
• All 3 data sets were labeled separately before
  hybridization

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T1
T2
Replicate Design 1
amplification
1 2 3 4
T1
amplification
Replicate Design 2
amplification
T2
1 2 3 4
amplification
Amplified samples
Original samples
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M1 Lc.MT.P1 ?
M2 Lc.WT.P11 ? ?1
M3 Lc.WT.P21 ? (?1 ?2)
M4 Lc.MT.P1 ? ?
M5 Lc.MT.P11 ? ?1 ? ?1 ?
M6 Lc.MT.P21 ? (?1 ?2) ? (?1 ?2)?

• Common reference approach
• Estimate (?1.?) with M5 M4 - M2 M1
• Estimate (?1 ?2).? with M6 M4 M3 M1