Outline

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• Outline
• Experimental design of cDNA array
• Calibration and replicate
• Choice of reference sample
• Design of two-color array
• Filtering (in all platforms)
• Missing value imputation (in all platforms)

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1.1. Calibration and replicate

• Calibration
• Use the same sample on both dyes for
  hybridization.
• Calibration experiments help to validate
  experiment quality and gene-specific variability.

Comparative Tumor vs Ref
Calibration Ref vs Ref
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1.1. Calibration and replicate

• Replicates (replicate spots, slides)
• Multiple-spotting helps to identify local
  contaminated spots but will reduce number of
  genes in the study.
• Multi-stage strategy Use single-spotting to
  include as many genes as possible for pilot
  study. Identify a subset of interesting genes and
  then use multiple-spotting.
• Replicate spots and slides help to verify
  reproducibility on the spot and slide level.

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1.1. Calibration and replicate
Biological replicate
From Yang, UCSF
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1.1. Calibration and replicate
Technical replicate
From Yang, UCSF
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1.1. Calibration and replicate

• (iii) Reverse labelling
• Advantage
• Cancel out linear normalization scaling and
  simplifies the analysis. However, the linear
  assumption is often not true.
• Help to cancel out gene-label interactions if it
  exists.

Sample A
Sample B
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1.2. Choice of reference sample

• Different choices of reference sample
• Normal patient or time 0 sample in time course
  study
• Pool all samples or all normal samples
• Embryonic cells
• Commercial kit

Ideally we want all genes expressed at a
constant moderate level in reference sample.
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1.3. Design issue
From Yang, UCSF
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1.3. Design issue

• Design issues
• Reference design
• Loop design
• Balance design

Reference sample is redundantly measured many
times.
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(c)
v samples with v2 experiments
v samples with 2v experiments
See Kerr et al. 2001
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2. Filtering

• Filter out genes with bad quality
• Outputs from imaging analysis usually have a
  quality index or flag to identify genes with bad
  quality image.
• Three common sources of bad quality probes
• Problematic probes probes with non-uniform
  intensities.
• Low-intensity probes genes with low intensities
  are known to have bad reproducibility and hard to
  verify by RT-PCR. Normally genes with intensities
  less than 100 or 200 are filtered.
• Saturated probes genes with intensities reaching
  scanner limit (saturation) should also be
  filtered.

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2. Filtering
Filtering by quality index different array
platform and image analysis have different format
low intensity
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2. Filtering
Filtering by quality index
Array 1
Array 2
? ? ?
Array S
NA not applicable Missing values due to bad
quality, low or saturated intensities
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2. Filtering

• Filter genes with low information content
• Small standard deviation (stdev)
• Small coefficient of variation (CV stdev/mean)

130
125
115
stdev6.45 CV0.29
120
stdev6.45 CV0.053
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25
15
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Note CV is more reasonable for original
intensities. But for log-transformed intensities,
stdev is enough Why?
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2. Filtering
Gene filtering

• A simple gene filtering routine (I usually use)
  before down-stream analyses
• Take log (base 2) transformation.
• Delete genes with more than 20 missing values
  among all samples.
• Delete genes with average expression level less
  than, say a7 (27128).
• Delete genes with standard deviation smaller
  than, say ß0.4 (20.41.32, i.e. 32 fold
  change).
• Adjust a and ß so that the number of remaining
  genes are computationally manageable in
  downstream analysis. (e.g. around 3000 genes)

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2. Filtering
Sample filtering (detecting problematic slides)
Compute correlation matrix of the samples

• Arrays of replicates should have high
  correlation. (m,n,o,p are replicates and q,r,s,t
  are another set of replicates)
• A problematic array is often found to have low
  correlation with all the other arrays.
• Heatmap is usually plotted for better
  visualization.

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2. Filtering
Diagnostic plot by correlation matrix
White high correlation Dark gray low
correlation
m,n,o,p
q,r,s,t
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3. Missing Value Imputation

• Reasons of missing values in microarray
• spotting problems (cDNA)
• dust
• finger prints
• poor hybridization
• inadequate resolution
• fabrication errors (e.g. scratches)
• image corruption
• Many down-stream analysis require a complete
  data.
• Imputation is usually helpful.

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3. Missing Value Imputation
It is common to have 5 MVs in a
study. 5000(genes)?50(arrays) ?512,500
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3. Missing Value Imputation
Existing methods

• Naïve approaches
• Missing values 0 or 1 (arbitrary signal)
• missing values row (gene) average
• Smarter approaches have been proposed
• K-nearest neighbors (KNN)
• Regression-based methods (OLS)
• Singular value decomposition (SVD)
• Local SVD (LSVD)
• Partial least square (PLS)
• More (Bayesian Principal Component Analysis,
  Least Square Adaptive, Local Lease Square)
• Assumption behind Genes work cooperatively in
  groups. Genes with similar pattern will provide
  information in MV imputation.

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3. Missing Value Imputation
KNN.e KNN.c

• choose k genes that are most similar to the
  gene with the missing value (MV)
• estimate MV as the weighted mean of the neighbors
• considerations
• number of neighbors (k)
• distance metric
• normalization step

randomly missing datum
?
Expression
Arrays
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3. Missing Value Imputation
KNN.e KNN.c

• parameter k
• 10 usually works (5-15)
• distance metric
• euclidean distance (KNN.e)
• correlation-based distance (KNN.c)
• normalization?
• not necessary for euclidean neighbors
• required for correlation neighbors

?
Expression
Arrays
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3. Missing Value Imputation
OLS.e OLS.c

• regression-based approach
• KNNOLS
• algorithm
• choose k neighbors (euclidean or correlation
  normalize or not)
• the gene with the MV is regressed over the
  neighbor genes (one at a time, i.e. simple
  regression)
• for each neighbor, MV is predicted from the
  regression model
• MV is imputed as the weighed average of the k
  predictions

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3. Missing Value Imputation
OLS.e OLS.c
randomly missing datum
y1 a1 b1 x1
y2 a2 b2 x2
?
Expression
y w1 y1 w2 y2
Arrays
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3. Missing Value Imputation
SVD

• Algorithm
• set MVs to row average (need a starting point)
• decompose expression matrix in orthogonal
  components, eigengenes.
• use the proportion, p, of eigengenes
  corresponding to largest eigenvalues to
  reconstruct the MVs from the original matrix
  (i.e. improve your estimate)
• use EM approach to iteratively imporove estimates
  of MVs until convergence
• Assumption
• The complete expression matrix can be
  well-decomposed by a smaller number of principle
  components.

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3. Missing Value Imputation
LSVD.e LSVD.c

• KNNSVD
• choose k neighbors (euclidean or correlation
  normalize or not)
• Perform SVD on the k nearest neighbors and get a
  prediction of the missing value.

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3. Missing Value Imputation
PLS

• PLS Select linear combinations of genes (PLS
  components) exhibiting high covariance with the
  gene having the MV.
• The first linear combination of genes has the
  highest correlation with the target gene.
• The second linear combination of genes had the
  greatest correlation with the target gene in the
  orthogonal space of the first linear combination.
  
• MVs are then imputed by regressing the target
  gene onto the PLS components

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3. Missing Value Imputation

• Types of missing mechanism
• Missing completely at random (MCAR)
• Missingness is independent of the observed values
  and their own unobserved values.
• Spot missing due to mis-printing or dust
  particle.
• Spot missing due to scratches.
• Missing at random (MAR)
• Missingness is independent of the unobserved data
  but depend on the observed data.
• Missing not at random (MNAR)
• MIssingness is dependent on the unobserved data
• 1. Spots missing due to saturation or low
  expression.

Currently imputation methods only work for MCAR,
not MNAR.
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Which missing value imputation method to use in
expression profiles a comparative study and two
selection schemes Guy N. Brock1, John R.
Shaffer2, Richard E. Blakesley3, Meredith J.
Lotz3, George C. Tseng2,3,4 BMC Bioinformatics,
2008
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Comparative study
9 data sets multiple exposure, time series or
both 7 methods were compared KNN, OLS, LSA, LLS,
PLS, SVD, BPCA
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Comparative study
Global-based methods PLS, SVD,
BPCA Neighbor-based methods KNN, OLS, LSA,
LLS Intuitively global-based methods require
that dimension reduction of the data can be
effectively performed. We define an entropy
measure for a given data D to determine how well
the dimension reduction of the data can be done
(?i are the eigenvalues)
.
Entropy low the first few eigenvalues dominate
and the data can be reduced to low-dimension
effectively.
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Comparative study
LRMSE is the performance measure, the lower the
better. KNN, OLS, LSA, LLS are neighbor-based
methods and work better in low-entropy data
sets. PLS and SVD are global-based methods and
work better in high-entropy data sets.
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Comparative study
Three methods (LSA, LLS, BPCA) performed best
but none dominated. Performed two selection
schemes (entropy-based scheme and self-training
scheme) to select the best imputation method.