Design Issues in cDNA Microarray Analysis by Yang and Speed

1
Design Issues in cDNA Microarray Analysisby Yang
and Speed

• Jim Booth
• UF Genomics Discussion Group
• Feb. 5, 2003

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cDNA Microarrays

• Relative expression of up to 20,000 genes
  (probes)
• in two mRNA samples.
• Samples (targets) labeled with own fluorophore
• Cy3 (green) or Cy5 (red).
• After competitive hybridization, ratio of
  red/green
• intensities measures relative abundance of DNA
  probes
• Membrane and Affy arrays measure gene expression
  
• in samples separately.

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General Design Issues

• Most efficient use of resources
• Minimize sample size
• Eliminate potential biases
• Answer primary question of interest

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Split Plot Experiment
A
B
A
B
B
A
B
A
1
2
3
4

• Each cDNA array is a split plot.
• Between plot/slide variability greater than
• within.

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Design Issues

• Which mRNA samples (targets) are to be
• labeled with which fluor?
• Which are to be hybridized on the same slide?

Practical Issues

• Type of mRNA samples reference, control,
  treatment
• Amount of mRNA available.
• Number of slides.

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Multi-digraphs
A
B
Box 1a A and B samples hybridized together. 5
replicates. Green-labeled sample at tail.
5
A
Box 1b Direct estimate of AvB abundance more
accurate than indirect.
B
C
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One design choice example 1
Samples Liver tissue from mice treated
with cholesterol-modifying drugs from
untreated (control) mice. Question Which genes
have differential expression in treated and
untreated mice?
T1
T2
T3
Ctr
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One design choice example 2
Samples Tissue from different tumors Question
What are the tumor subtypes?
Ref
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Direct v. Indirect Designs
Fig 1a Direct estimation of Log
Expression Ratio
T
C
LER
Var(LER)
Fig 1b Indirect estimation
C
T
LER
R
Var(LER)
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Designs with Replication
Dye-swap experiments

• Systematic differences in red/green intensities
• Normalization unlikely to remove bias for all
  genes
• simultaneously
• Two hybridizations for each target pair
• Dye assignment reversed in second hybridization

T
Without dye-swap
LER
With dye-swap
LER
C
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Single-factor Designs
Refer to Table 1
Design I A B C R

• 3 slides
• 3 samples (ABC1)
• average variance 2.00

Design II A B C R

• 6 slides
• 6 samples (ABC2)
• average variance 1.00

2
2
2
Design III A C B

• 3 slides
• 6 samples (ABC2)
• average variance 0.67

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Loop designs

• Design III is not feasible for larger numbers of
• samples
• e.g. if n6 there are 15 pairs and each sample
  is
• co-hybridized on 5 arrays.
• Loop designs
• Direct
  AvB comparison
• Indirect
  AvC comparison
• Are some comparisons more important than others?

A
B
D
C
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Time-course experiments
Refer to Table 2
Design I T1 as common reference T1 T2
T3 T4 average variance 1.5
Design II direct sequential T1 T2 T3
T4 average variance 1.67
Design V direct loop T1 T2 T3
T4 average variance 0.83
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Multi-factorial Experiments

• Study differential expression that results from
  joint
• effect of two or more factors
• Interaction joint effect not the sum of
  separate effects
• 2x2 factorial experiment.
• e.g. two ways of treating a cell line A and
  B.
• Let C denote mRNA derived from untreated cells

Factor 2 Factor 1
Untreated Treated Untreated
C B Treated A
AB
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2 x 2 Factorial Experiment 1
Refer to Table 3
Design I Effect
Variance A B AB main A
0.50
main B 0.50 C
interaction 1.50
Interaction
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2 x 2 Factorial Experiment 2
Refer to Table 3
Design III Effect
Variance C A main
A 0.67
main B 0.43 B
AB interaction 0.67
Interaction
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Variability and Replication 1

• Spot replicates replicate cDNA probes on array
• Technical replicates replicate hybridizations
  using
• target mRNA from the same pool
• Biological replicates replicate hybridizations
  using
• mRNA from different extractions
• e.g. different samples of cells from the same
  tissue

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Variability and Replication 2

• Averaging over replicates reduces variability!
• Let denote the log expression ratio from
• replicate i, i1,n. Then

where
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Power Analysis
Power calculation (to determine sample size)
requires

• Variance of individual log ratios,
• Magnitude of effect to be detected.
• Acceptable false-positive rate.
• e.g. How many hybridizations required to have a
  90
• chance of detecting a two-fold change?

• Variance, , varies across genes
• Use median or upper quartile based on previous
• experiments!