Steilkurs in praktischer MikroarrayAnalyse

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Steilkurs in praktischer Mikroarray-Analyse
Mainz, 22.6.2006

• Andreas Buneß

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Differential Gene Expression
Setting Two or more types of samples (e.g.
treated cell lines, biopsies) For each sample we
have thousands of gene expresssion
levels Goal Which genes are differentially
expressed ?
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Trade Off or Everything is a Compromise
Sensitivity simply take all ?
Specificity simply take none ?
Here statistical testing framework - ranking of
genes (ordered list wrt up/down regulation) -
cut off, i.e. significant genes
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T-test difference of the means, but takes
variance into account
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Multiple Testing
statistical test for each gene g yields a p-value
for each gene under the null hypothesis of no
differential expression p-value is a uniformly
distributed random number between 0 and 1 under
the null hypothesis of no differential expression

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Multiple Testing The Problem
Multiplicity problem thousands of hypotheses are
tested simultaneously. Increased chance of
false positives. E.g. suppose you have 10,000
genes on a chip and not a single one is
differentially expressed. You would expect
100000.01 100 of them to have a p-value lt
0.01.
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Andreas Buneß
Multiple Testing - Error Control
Null hypothesis no differential expression
between the two types/groups
R all which are called significant
V Type I error, false positives (FP)
T Type II error, miss, false negatives (FN)
power of the test
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What kind of error do we exactly want to control
? error concepts, like FWER, FDR
How to we achieve this error control
? procedures or methods, like Bonferroni, Holm,
Benjamini-Hochberg, ... R packages
multtest, qvalue / limma,
samr
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Family Wise Error Rate (FWER)
FWER Pr(V gt 0) The probability of at least one
Type I error (false positive) among the genes
selected as significant.
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False Discovery Rate (FDR)
FDR E(Q), where QV/R if R gt 0 and Q0 if
R 0
The expected proportion of Type I errors among
the rejected hypotheses. The expected proportion
of false positives among all genes called
significant.
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p-values refer to a single gene FDR and FWER
error control refers to a list of genes (the FDR
corresponding to the ordered list up to the
particular gene is often referred to as its
q-value)
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FDR Horizontal cutoff
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FWER The Bonferroni Correction
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Example
Golub data, 27 ALL vs. 11 AML samples, 3,051
genes.

98 genes with Bonferroni-adjusted p lt 0.05, praw
lt 0.000016
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FDR The Optimal Discovery Procedure
John Storey, software edge
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FWER or FDR ?
Choose FWER control if high confidence in all
selected genes is desired. Choose FDR control
if a certain proportion of false positives is
tolerable - frequently used in practice.
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Statistical Tests

• Standard t-test assumes normally distributed
  data in each class (almost always questionable,
  but may be a good approximation), equal variances
  within classes
• Welch t-test as above, but allows for unequal
  variances
• Wilcoxon test nonparametric, rankbased
• Permutation test estimate the distribution of
  the test statistic (e.g., the t-statistic) under
  the null hypothesis by permutations of the sample
  labelsThe pvalue is given as the fraction of
  permutations yielding a test statistic that is at
  least as extreme as the observed one.

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SAM (significance analysis of microarrays)
permutation test regularized
t-statistics multiple testing correction R
package samr
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T-test difference of the means, but takes
variance into account
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Few replicates regularized/moderated
tstatistics

• With the ttest, we estimate the variance of each
  gene individually. This is fine if we have enough
  replicates, but with few replicates (say 25 per
  group), the variance estimates are unstable.
• In a moderated tstatistic, the estimated
  genespecific variance s2g is augmented with s20,
  a global variance estimator obtained from pooling
  all genes. This gives an interpolation between
  the tstatistic and a foldchange criterion

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Permutation tests
test statistic
true class labels
null distribution of test statistic
2.2
(random) permutations of class labels
1.5 -0.4 2.3 0.7 0.2 -1.2
2.2
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SAM typical plot
Expected random score vs observed scores
Deviations from the main diagonal are evidence
for differentially expressed genes
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What you typically observe

No differential gene expression
A lot of differential gene expression
Global changes in gene expression
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Statistical tests Different settings

• comparison of two classes (e.g. tumor vs. normal)
• paired observations from two classes e.g. the
  ttest for paired samples is based on the
  withinpair differences.
• more than two classes and/or more than one factor
  (categorical or continuous) tests may be based
  on linear models

paired samples
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LIMMA (Linear models for microarray data)
moderated t-statistic multiple testing
correction analysis of complex designs and
factorial experiments
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Linear models

• Linear models are a flexible framework for
  assessing the associations of phenotypic
  variables with gene expression.
• The expression yi of a given gene in sample i is
  modeled as linearly depending on one or several
  factors (e.g. cell type, treatment, encoded in
  xij) of the sample yi
  a1xi1 amxim ei.
• Estimated coefficients aj and their standard
  errors are obtained using least squares, assuming
  normally distributed errors ei (R function lm)
  or with a robust method (R function rlm).

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Linear models

• Contrasts, that is, differences/linear
  combinations of the coefficients, express the
  differences between phenotypes and can be tested
  for significance (ttest).
• Example Consider a study of three different
  types of kidney cancer. For each gene set up a
  linear model yi a1xi1 a2xi2
  a3xi3 ei,where xij 1 if tumor sample i is
  of type j, and 0 otherwise.
• The least squares estimates of the coefficients
  ai are the mean expression levels in the classes.
• The contrast a1 - a2 expresses the mean
  difference between class 1 and 2.

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Linear model analysis with the Bioconductor
package limma

• The phenotype information for the samples is to
  be entered as a design matrix (xij from the above
  formula). The rows of the matrix correspond to
  the samples, and the columns to the coefficients
  of the linear model.
• Contrasts are extracted after fitting the linear
  model.
• The significance of contrasts is assessed with a
  moderated tstatistic.

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Experimental Design Complex Designs
Aim of the experiment Robustness Extensibility Ef
ficiency
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Aim of the experiment
Major focus differential expression treatment
vs. control (multiple treatments) tumor vs.
normal (tumor subtypes) time series of multiple
treatments Well defined goal or competing goals
? several comparisons (different
subgroups) one factor per comparison (skipping
others) statistical modelling (various
factors) exact subdivision of all samples
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Efficiency
statistical efficiency (pooling, direct
indirect) cost efficiency (microarray, mRNA
source)
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Replicates required for statistical
inference independent biological
replicates technical replicates may occur
on different levels in the experimental
hierarchy Pooling limited number of mRNA source
or limited number of microarrays
? amplification ? independent pools to estimate
variance one mRNA source may spoil the whole pool
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Blocking Factors ? technical factors (slide
batches, hybridisation day, labelling days)
should not be (completely) confounded with your
comparison of interest Randomisation control
of unknown covariates Balancing control of all
covariates (all are known) Statistical modelling
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single channel/one color microarrays (e.g.
Affymetrix) experimental design one
independent biological sample per microarray/hyb
ridisation pooling/blocking ? two color
microarrays (e.g. spotted cDNA arrays) experiment
al design may become more complex pooling/blockin
g ?
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Dye effect (two color microarrays) different
(gene-specific) labelling efficiencies
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Two colour microarrays
Typical designs reference design loop
design dye-swaps
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Graphical Representation two colour microarrays

node mRNA sample edge hybridisation direction
dye assignment.
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Dye-Swap/(mini-) Loop design
Reference design
A
R
B
two groups A and B independent biological
replicates of A and B
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Reference Design one independent biological
sample against the reference per
hybridizationmicroarray (possible exception
pooling) extendable (e.g. ongoing study) any
unknown/unpredictable comparisons same
efficiency for any comparisons analysis as for
single channel microarray experiments no dye
effect often used with large sample
size simple, i.e. minimizes experimental
confusion
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Dye Swap Design
often refers to a technical replicate where two
slides are used for two samples each labelled
twice (red/green) sometimes used to control the
dye effect, i.e. the different labelling
efficiencies for each gene, via averaging of the
two slides prefer "biological" replicates
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Dye Swap Design
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Loop Design
well defined experimental setting/comparisons
often relatively small smaple size (due to
manageability) requires statistical modelling in
general dye effect is addressed with the
statistical model
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(Mini-) Loop Design
Design matrix A-B dye
A1
B1
B2
A2
(
)
1 -1 1 -1
1 1 1 1
A3
B3
B4
A4
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C
A
C
B
A
B
R
A-R B-R C-R Contrast A-BA-R-(B-R)
C-A A-B (direct) B-C A-BB-C-(C-A) (indirect)
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Recommendations
Large patient sample collective reference
design Unknown/unpredictable comparisons
reference design Small scale cell-line
experiments direct comparisons
Recall statistical analysis is limited by the
number of independent biological replicates !
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• Thanks to ...
• Anja von Heydebreck,
• Rainer Spang
• Tim Beißbarth
• for some of the slides.

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Links
www.r-project.org/ www.bioconductor.org/ bioinf.w
ehi.edu.au/limma/ www-stat.stanford.edu/tibs/SAM
/ www.biostat.washington.edu/software/jstorey/edg
e/ NGFN course material http//compdiag.molgen.m
pg.de/ngfn/
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References

• Y. Benjamini and Y. Hochberg (1995). Controlling
  the false discovery rate a practical and
  powerful approach to multiple testing. Journal of
  the Royal Statistical Society B, Vol. 57,
  289300.
• S. Dudoit, J.P. Shaffer, J.C. Boldrick (2003).
  Multiple hypothesis testing in microarray
  experiments. Statistical Science, Vol. 18,
  71103.
• J.D. Storey and R. Tibshirani (2003). SAM
  thresholding and false discovery rates for
  detecting differential gene expression in DNA
  microarrays. In The analysis of gene expression
  data methods and software. Edited by G.
  Parmigiani, E.S. Garrett, R.A. Irizarry, S.L.
  Zeger. Springer, New York.
• V.G. Tusher et al. (2001). Significance analysis
  of microarrays applied to the ionizing radiation
  response. PNAS, Vol. 98, 51165121.
• M. Pepe et al. (2003). Selecting differentially
  expressed genes from microarray experiments.
  Biometrics, Vol. 59, 133142.

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References

• T. P. Speed and Y. H Yang (2002). Direct versus
  indirect designs for cDNA microarray experiments.
  Sankhya The Indian Journal of Statistics, Vol.
  64, Series A, Pt. 3, pp 706-720
• Y.H. Yang and T. P. Speed (2003). Design and
  analysis of comparative microarray Experiments In
  T. P Speed (ed) Statistical analysis of gene
  expression microarray data, Chapman Hall.
• R. Simon, M. D. Radmacher and K. Dobbin (2002).
  Design of studies using DNA microarrays. Genetic
  Epidemiology 2321-36.
• F. Bretz, J. Landgrebe and E. Brunner (2003).
  Efficient design and analysis of two color
  factorial microarray experiments. Biostaistics.
• G. Churchill (2003). Fundamentals of experimental
  design for cDNA microarrays. Nature genetics
  review 32490-495.
• G. Smyth, J. Michaud and H. Scott (2003) Use of
  within-array replicate spots for assessing
  differential experssion in microarray
  experiments. Technical Report In WEHI.
• Glonek, G. F. V., and Solomon, P. J. (2002).
  Factorial and time course designs for cDNA
  microarray experiments. Technical Report,
  Department of Applied Mathematics, University of
  Adelaide. 10/2002

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Verschiedene Designs 4 Bedingungen
A.B
B
A
C
A
A.B
B
C
C
A
C
A
A.B
B
A.B
B
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Graphische Representation

• Die Struktur des Graphen legt fest, welche
  Effekte geschätzt werden können und wie präzise
  die Schätzungen sind.
• Zwei mRNA Samples können nur verglichen werden,
  wenn es einen Pfad gibt, welcher die zugehörigen
  Knoten verbindet.
• Die Präzision der geschätzten Kontraste hängt
  direkt von der Anzahl der Pfade, welche die
  Knoten verbinden und zur Länge dieser Pfade.
• Direkte Vergleiche auf demselben Slide geben
  präzisere Messungen als indirekte Vergleiche.

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Strong control any combination of true and
false hypotheses
Weak control complete null hypotheses, all
null hypotheses in the family are true