Gene Expression Analysis and Statistics: A Case Study in Bioinformatics - Prof. Nicholas S, Lab Reports of Computer Science

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Gene Expression Analysisand Statistics: A Case Study

Bioinformatics: Problems and SolutionsDr. John R. StevensUtah State UniversityCS 5890/68909 July 2007

Outline

Background – ALL data

Differential Expression

Multiple Comparisons

Report File

Visual Summaries

Annotation Test

Reference: Bioinformatics and Computational BiologySolutions Using R and Bioconductor (2005), edited byGentleman et al.

Here, focus on the main ideas

Microarray Technology: General Idea

Use mRNA transcript

abundance level as a measure

of the level of “expression” for the correspondinggene

Represent thousands of genes on an array 

each spot on array corresponds to a specific gene(a set of probes on the array represent a gene)



“apply” a prepared sample to chip (array)



mRNA in sample hybridizes to array



fluoresces



look at spot intensities



intensity assumed proportional to mRNA transcriptabundance level

Background: ALL data

A

cute L

ymphoblastic L

eukemia (Ritz lab)

12,625 genes



128 samples (arrays)



phenotypic data on all 128 patients, including:

95 B-cell cancer patients

33 T-cell cancer patients

Reference: Chiaretti et al., Blood (2004)103(7)

Array images and “quality”

(code chunk 1)

residual images from 2 of the 128 arrays

Boxplots and “Preprocessing”

(code chunk 2)

boxplots of log2intensities from 20 ofthe 128 arrays

Common preprocessing methods– each has strengths and weaknesses

MAS5 

Affymetrix’s algorithm

dChip 

Li & Wong’s model (probe-level model)

vsn 

“Variance Stabilization”

RMA 

fits probe-level model to all arrays(assume probes have same “effect” on each array)

GCRMA 

RMA-based, with additional adjustment for position of G & Cnucleotides in probe sequence

(more proposed all the time – active area of research)

Each point represents asingle gene’sexpression level on onearray afterpreprocessing all thearrays togetherNotice similarities anddifferences

(code chunk 3)

13

Simple / Naïve test of DE

“Observe” gene expression levels under twoconditions (after preprocessing)

Calculate: average log fold change

Make a cut-off: R

i

treatment" "

of j

replicate

in k

gene

of

level

expr.

log

ijk Y

k

gene

for

change

fold

log

ave.

i

treatment

in k

gene

for

expr.

log

ave.

1

2

=

−

= =

⋅

⋅

⋅

k

k

k k i

Y

Y

LFC

Y

R

LFC

k

>

if

t"

significan "

is k

Gene

What’s wrong with the naïve test?

Summary interpretation okay:

LFC > 0 for “up-regulated” genesLFC < 0 for “down-regulated” genes

Ignores variability of estimate 

cannot really test for “significance”



what if larger LFC have large variability?

• then not necessarily significant

How to use this to “test” for DE?

What is being tested?

Null: No change for gene k

Under null, t

k

~ t dist. with n

k

d.f.

(expected distribution under repeat sampling)

But what is needed to do this? 

“Large” sample size



Estimate

σ

k

= “pop. SD” for gene k

“parametric” assumption

(code chunk 3.5)

What if we don’t have a large enoughsample size? (note: probably don’t)

Two main problems: 

1. Estimate

σ

k

(especially for small sample size)

1. Appropriate sampling distribution of test stat.

Basic solutions: 

1. To estimate

σ

k

: Pool information across genes

1. For comparison:
   

use parametric assumption on “improved” test stat.

use non-parametric methods

Assumptions in linear model (Smyth)

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For

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Obtain

,

,

k not necessary here

This is a traditional statisticallinear regression model.

Hierarchical model to borrow informationacross genes (Smyth): eBayes

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Assume

,

,

0

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(^20) 0

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0

(^20)

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(^20) 0

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&

σ

β

σ

σ

σ

σ

χ

σ

represents added information from usingall genes

(using all of the genes)