ECS 289A PresentationJimin Ding

• Problem & Motivation• Two-component Model• Estimation for Parameters in above model• Define low and high level gene expression• Comparing expression levels• Limitations of the model and method• Other possible solutions• References

A Model for Measurement Error for Gene Expression Arrays

David Rocke & Blythe DurbinJournal of Computational Biology Nov.2001

Problem & Motivation • Statistical inference for data need assumption of normality

with constant variance

--- So hypothesis testing for the difference between control and treatment need equal variance (not depending on the mean of the data);

• Measurement error for gene expression rises proportionately to the expression level

--- So linear regression fails and log transformation has been tried;

• However, for genes whose expression level is low or entirely unexpressed, the measurement error doesn’t go down proportionately Example

--- So log transformation fails by inflating the variance of observations near background, and two component model is introduced.

Example: MiceFrom: Barosiewics etatl, 2000

From Durbin et.al 2002back

Two-Component Model

ey

• Y is the intensity measurement• is the expression level in arbitrary units• is the mean intensity of unexpressed genes• Error term:

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),0(~

N

N

Estimation for background ( )

• Estimation of background using negative controls

• Estimation of background with replicate measurements Detail

• Estimation of background without replicate

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Estimation of with replicate measurements

• Begin with a small subset of genes with low intensity (10%)

• Define a new subset consisting of genes whose intensity values are in

• Repeat the first and second steps until the set of genes does not change.

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Estimation of the High-level RSD• The variance of intensity in two-component model:

, where

• At high expression level, only multiple error term is noticeable, so the ratio of the variation to the mean is a constant, i.e. RSD=

• For each replicated gene that is at high level, compute the mean of the and the standard deviation of

• Then use the pooled standard deviation to estimate :

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i y

Define “high” and “low”

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• Low expression level:Most of the variance is due to the additive error component. 95% CI:

• High expression level:Most of the variance is due to the multiplicative error component. 95% CI:

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))ˆ(96.1ˆ,)ˆ(96.1ˆ( VarVar

Comparing Expression Levels

• Common method: standard t-test on ratio of expression for treatment and control (low level), or its logarithm (high level).

• Problem:

Less effective when gene is expressed at a low level in one condition and high in the other:

Solution consider treatment and control are correlated

• Model:

• Variation:

Background: High-level RSD:

Hypothesis testing (Comparison)

• Assume the data have been adjusted:

• Testing: (Gene has same expression level at

Control and treatment)

• Then using the following approximate variance to do standard t-test for log ratio of raw data:

Limitations

• No theoretical result for above estimations. (Consistency and asymptotical distribution)

• Cutoff point of high level and low level is fairly artificial

• The convergence of estimation of background information is heavily dependent on data and initial selection

Literature & Other Possible Solutions for Measurement Error

• Chen et al. (1997): measurement error is normally distributed with constant coefficient of variation (CV)—in accord with experience

• Ideker et al.(2000) introduce a multiplicative error component (normal)

• Newton et al. (2001) propose a gamma model for measurement error.

• Durbin et al.(2002) suggest transformation, where

• Huber et al.(2002) introduce transformation ])(ln[)( 2 cyyyg

)sinh()( bxaarxh

22 / sc

References

• Blythe Durbin, Johanna Hardin, Douglas Hawkins, and David Rocke. “A variancestabilizing transformation from gene-expression microarray data”, Bioinformatics, ISMB, 2002.

• Chen. Y., Dougherty, E.R. and Bittner, M.L.(1997) “Ratio-based decisions and the quantitative analysis of cDNA microarray images”, J.Biomed. Opt.,2,364-374

• Wolfgang Huber, Anja von Heydebreck,Martin Vingron (Dec.2002) “Analysis of microarray gene expression data”, Preprint

• Wolfgang Huber, Anja von Heydebreck, Holger S¨ultmann, Annemarie Poustka, and Martin Vingron. “Variance stablization applied to microarray data calibration and to the quantification of differential expression”, Bioinformatics, 18 Suppl. 1:S96–S104, 2002. ISMB 2002.