Evaluation of normalization methods for microarray data

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Open AcceResearch articleEvaluation of normalization methods for microarray dataTaesung Park*1, Sung-Gon Yi1, Sung-Hyun Kang1, SeungYeoun Lee2, Yong-Sung Lee3 and Richard Simon4
Address: 1Department of Statistics, Seoul National University, Seoul, Korea, 2Department of Applied Mathematics, Sejong University, Seoul, Korea, 3Department of Biochemistry, Hanyang University College of Medicine, Seoul, Korea and 4Biometric Research Branch, Division of Cancer Treatment & Diagnosis National Cancer Institute, Bethesda MD, USA

Email: Taesung Park* - [email protected]; Sung-Gon Yi - [email protected]; Sung-Hyun Kang - [email protected]; SeungYeoun Lee - [email protected]; Yong-Sung Lee - [email protected]; Richard Simon - [email protected]

* Corresponding author

AbstractBackground: Microarray technology allows the monitoring of expression levels for thousands ofgenes simultaneously. This novel technique helps us to understand gene regulation as well as geneby gene interactions more systematically. In the microarray experiment, however, manyundesirable systematic variations are observed. Even in replicated experiment, some variations arecommonly observed. Normalization is the process of removing some sources of variation whichaffect the measured gene expression levels. Although a number of normalization methods havebeen proposed, it has been difficult to decide which methods perform best. Normalization plays animportant role in the earlier stage of microarray data analysis. The subsequent analysis results arehighly dependent on normalization.

Results: In this paper, we use the variability among the replicated slides to compare performanceof normalization methods. We also compare normalization methods with regard to bias and meansquare error using simulated data.

Conclusions: Our results show that intensity-dependent normalization often performs betterthan global normalization methods, and that linear and nonlinear normalization methods performsimilarly. These conclusions are based on analysis of 36 cDNA microarrays of 3,840 genes obtainedin an experiment to search for changes in gene expression profiles during neuronal differentiationof cortical stem cells. Simulation studies confirm our findings.

BackgroundBiological processes depend on complex interactionsbetween many genes and gene products. To understandthe role of a single gene or gene product in this network,many different types of information, such as genome-wide knowledge of gene expression, will be needed.Microarray technology is a useful tool to understand generegulation and interactions [1–3]. For example, cDNAmicroarray technology allows the monitoring of expres-

sion levels for thousands of genes simultaneously. cDNAmicroarrays consist of thousands of individual DNAsequences printed in a high density array on a glass slide.After being reverse-transcribed into cDNA and labelledusing red (Cy5) and green (Cy3) fluorescent dyes, two tar-get mRNA samples are hybridized with the arrayed DNAsequences or probes. Then, the relative abundance ofthese spotted DNA sequences can be measured. Afterimage analysis, for each gene the data consist of two

Published: 02 September 2003

BMC Bioinformatics 2003, 4:33

Received: 13 May 2003Accepted: 02 September 2003

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fluorescence intensity measurements, (R, G), showing theexpression level of the gene in the red and green labelledmRNA samples. The ratio of the fluorescence intensity foreach spot represents the relative abundance of the corre-sponding DNA sequence. cDNA microarray technologyhas important applications in pharmaceutical and clinicalresearch. By comparing gene expression in normal andtumor tissues, for example, microarrays may be used toidentify tumor-related genes and targets for therapeuticdrugs [4].

In microarray experiments, there are many sources of sys-tematic variation. Normalization attempts to remove suchvariation which affects the measured gene expression lev-els. Yang et al. [5] and Yang et al. [6] summarized anumber of normalization methods for dual labelledmicroarrays such as global normalization and locallyweighted scatterplot smoothing (LOWESS [7]). Quacken-bush [8] and Bilban et al. [9] provided good reviews onnormalization methods. There have been some exten-sions for global and intensity-dependent normalizations.For example, Kepler et al. [10] considered a local regres-sion to estimate a normalized intensities as well as inten-sity dependent error variance. Wang et al. [11] proposed aiterative normalization of cDNA microarray data for esti-mating a normalized coefficients and identifying controlgenes. Workman et al. [12] proposed a roust non-linearmethod for normalization using array signal distributionanalysis and cubic splines. Chen et al. [13] proposed asubset normalization to adjust for location biases com-bined with global normalization for intensity biases.Edwards [14] considered a non-linear LOWESS normali-zation in one channel cDNA microarrays mainly for cor-recting spatial heterogeneity. The main idea ofnormalization for dual labelled arrays is to adjust for arti-factual differences in intensity of the two labels. Such dif-ferences result from differences in affinity of the twolabels for DNA, differences in amounts of sample andlabel used, differences in photomultiplier tube and laservoltage settings and differences in photon emissionresponse to laser excitation. Although normalizationalone cannot control all systematic variations, normaliza-tion plays an important role in the earlier stage of micro-array data analysis because expression data cansignificantly vary from different normalization proce-dures. Subsequent analyses, such as differential expres-sion testing would be more important such as clustering,and gene networks, though they are quite dependent on achoice of a normalization procedure [1,3].

Several normalization methods have been proposed usingstatistical models (Kerr et al. [15]; Wolfinger et al. [16]).However, these approaches assume additive effects of ran-dom errors, which needs to be validated. Because they areless frequently used, we have not evaluated them here.

Although several normalization methods have been pro-posed, no systematic comparison has been made for theperformance of these methods. In this paper, we use thevariability among the replicated slides to compare per-formance of several normalization methods.

We focus on comparing the normalization methods forcDNA microarrays. A detailed description on normaliza-tion methods considered in our study is given in the nextsection. Complex methods do not necessarily performbetter than simpler methods. Complex methods may addnoise to the normalized adjustment and may even addbias if the assumptions are incorrect. The fact that a non-linear method linearizes a graph of red intensity versusgreen intensity or a plot of log(R/G) versus log(RG) is notin itself evidence that the method is not just fitting noise.Consequently, proposed normalization methods requirevalidation.

We first compare the methods using data from cDNAmicroarrays of 3,840 genes obtained in an experiment tosearch for changes in gene expression profiles during neu-ronal differentiation of cortical stem cells. Then, we per-form simulation studies to compare these normalizationmethods systematically. Bolstad et al. [17] compare nor-malization methods for high density oligonucleotidearray data using variance and bias.

The paper is organized as follows. Section 2 describes nor-malization methods. Section 3 describes the measures forvariability to compare normalization methods. Section 4shows the comparison results for cDNA microarraysobtained from a cortical stem cells experiment along withsome simulation results. Finally, Section 5 summarizesthe concluding remarks.

Normalization methodsAs pointed out by Yang et al. [5], the purpose of normali-zation is to remove systematic variation in a microarrayexperiment which affects the measured gene expressionlevels. They summarized a number of normalizationmethods: (i) within-slide normalization, (ii) paired-slidenormalization for dye-swap experiments, and (iii) multi-ple slide normalization.

As a first step, one needs to decide which set of genes touse for normalization. Yang et al. [5] suggested threeapproaches: all genes on the array, constantly expressedgenes, and controls. Recently, Tseng et al. [18] suggestedusing the rank invariant genes.

Let (logG, logR) be the green and red background-cor-rected intensities. Then, (M, A) are defined by M = log(R/

G) and . Once the genes for normalizationA log RG= 12

( )



are selected, the following normalization approaches areavailable based on (M, A), as described by Yang et al. [5]:

(1) Global normalization (G) using the global median oflog intensity ratios

(2) Intensity dependent linear normalization (L)

(3) Intensity dependent nonlinear normalization (N)using a LOWESS curve.

Under ideal experimental conditions, we expect M = 0 forthe genes used for normalization. However, quite differ-ent patterns may be observed in real microarray experi-ments. Note that all three normalization methodsconsider regression models in the form of

For global normalization α0 is estimated by the median ofM. For intensity dependent normalization (β0, β1) by leastsquares estimation, and c(A) by using the robust scatterplot smoother LOWESS. Thus, all three normalizationmethods are based on regression models of M in terms of

A. Let (A) be the fitted value of c(A). The normalization

process can be described in terms of (A). For gene j, the

normalized ratio is

(Aj) = Mj - (Aj). (1)

Thus, the normalization process transforms (logG, logR) to(M, A), and then we obtain M* using regression models.The statistical analysis can then be performed using thenormalized M*. The above normalization methods aremainly for controlling location shifts of logarithmicallytransformed intensities. They may be applied separately toeach grid on the microarray because each grid is roboti-cally printed by a different print-tip. Yang et al. [5] alsoproposed scale normalization methods. The main pur-pose of scale normalization is to control between slidevariability and it may also be performed separately foreach print-tip. Figure 1 shows a flowchart for these nor-malization methods.

The detailed descriptions for each normalizationapproach considered in this study are given in Tables 1and 2. We denote global normalization, intensity depend-ent linear normalization, and intensity dependent nonlin-ear normalization by G, L, and N, respectively. They all

represent location normalization and can be carried outglobally or separately over print-tips. Similarly, scale nor-malization can be carried out globally or separately overprint-tips. Furthermore, the global scale normalizationcan also be performed after print-tip scale normalization.All possible combinations of location and scale normali-zation are summarized in Tables 1 and 2. For example,GPS.s denotes between-slide scale normalization (.s) afterglobal (G) median location normalization and scale (S)normalization on each print-tip (P).

Measures of variationIn order to derive measures of variation, we now use yinstead of M to represent the logarithm of the ratio of redand green background-corrected intensities. We introducesubscripts i,j,k and I for describing the cDNA microarraydata introduced in the next section. Suppose there are Iexperimental groups denoted by i, J time points denotedby j, and K replications denoted by k.

Also suppose that there are N genes in each slide. For thesimple case when there are I experimental groups but notime sequences, we can simply let J = 1. For the case whenthere are only time sequences, we can let I = 1. Thus, thesesubscripts represent general cases.

Let yijkl be the logarithm of the red to green intensity ratiofrom group i(= 1, ..., I), time j(= 1, ... , J), replication k(=1, ..., K), and gene l. Using the replicated observations, wewant to derive the variability measures of yijkl. It isexpected that the better the normalization method, thesmaller the variation among the replicated observations.Let σl be the variability measure for the lth gene. We intro-

duce two methods for estimating , l = 1, ... , N. Either

density plots or box plots for the variability measures canbe used for visually comparing different normalizationmethods.

Method 1. Pooled variance estimators

For gene l, a simple variance estimator for can be

obtained by pooling variance estimators for each i and j.That is,

where , for i = 1, ..., I; j = 1, ..., J; l = 1,

..., N. Then, we compare the distributions of . The

better the normalization method, the smaller the varianceestimates.

M A= +αβ β

0

0 1

,

,

for global normalization

for linear normalizatioon

for nonlinear normalizationc A( ),

c

c

Mj*

Mj*

c σl2

σl2

ˆ ( ) , ( )σl ijkl ij lkjiIJ Ky y2 21

12=

−( ) − ⋅∑∑∑

yK

yij l ijklkK

⋅ == ∑11

σl2



Flowchart of normalizationFigure 1Flowchart of normalization

O, G, GP, GPS, G.s, GP.s, GPS.s, L, LP, LPS, L.s, LP.s, LPS.s, N, NP, NPS, N.s, NP.s, NPS.s

normalizationIntensity depedentGlobal normalization

(G)

Normalizationm

Log−ratio (M) dependson Intensity (A).

Linear normalization

(L)

Non−linearNormalization

(N)

on each print−tip

(+P)

withscale normalization

(+S)

between−slidenormalization

(+.s)

M and A has a linear dependency.

The dependencies of M and A among print−tips are different.

The variability of M among print−tips are different.

The variablity of M among slides are different.

YES.NO.

NO.

NO.

NO.

NO.

YES.

YES.

YES.

YES.



Method 2. Variance estimator using analysis of variancemodels

Consider the following two-way analysis of vari-ance(ANOVA) model with interactions for each gene.

yijkl = µl + αil + βjl + (αβ)ijl + εijkl, (3)

where i = 1, ..., I, j = 1, ..., J, k = 1, ..., K, and l = 1, ..., N. Thegene effects µl capture the overall mean intensity in fluo-rescent signals for genes across the arrays, groups, andtime points. The αil terms account for gene specific groupeffects representing overall differences between twogroups. The βjl account for time effects that capture differ-ences in the overall concentration of mRNA in the sam-ples from the different time points. The terms (αβ)ijl

Table 1: Abbreviation for Normalization Methods

Abbreviation Description

O Original dataG Global median normalizationL Intensity dependent linear normalizationN Intensity dependent nonlinear normalization (LOWESS)P Print-tip normalizationS Print-tip scale normalization.s Between-slide scale normalization

Table 2: List of Normalization Methods

List of normalization methods including print-tip scale normalization

Method Notation Description

O Original data

Global G Global median normalizationGP Global median normalization on each print-tipGPS Global median normalization on each print-tip with scale normalizationG.s Global median normalization and between-slide scale normalizationGP.s Global median normalization on each print-tip and between-slide scale normalizationGPS.s Global median normalization on print-tip with scale normalization and between-slide scale

normalization

Linear L Intensity dependent linear regression normalizationLP Intensity dependent linear regression normalization on each print-tipLPS Intensity dependent linear regression normalization on each print-tip with scale normalizationL.s Intensity dependent linear regression normalization and between-slide scale normalizationLP.s Intensity dependent linear regression normalization on each print-tip and between-slide scale

normalizationLPS.s Intensity dependent linear regression normalization on each print-tip with scale normalization and

between-slide scale normalization

Nonlinear N Intensity dependent nonlinear regression normalization (LOWESS)NP Intensity dependent nonlinear regression normalization (LOWESS) on each print-tipNPS Intensity dependent nonlinear regression normalization (LOWESS) on each print-tip with scale

normalizationN.s Intensity dependent nonlinear regression normalization (LOWESS) and between-slide scale

normalizationNP.s Intensity dependent nonlinear regression normalization (LOWESS) on each print-tip and between-

slide scale normalizationNPS.s Intensity dependent nonlinear regression normalization (LOWESS) on each print-tip with scale

normalization and between-slide scale normalization



account for the interaction effects between group and timerepresenting the signal contribution due to the combina-tion of group and time.

From this ANOVA model, an unbiased estimate of

can be obtained which is the error sum of squares divided

by an appropriate degrees of freedom. Let be the vari-

ance estimate for the lth gene. Note that for Model (3) the

values of are the same with those of (2), if there are no

missing observations. However, this measure of variabil-ity is more flexible to use in the sense that it can be usedwith any ANOVA model which fits the intensity data well.

ResultsDataThe data studied here are from a study of cortical stem ratcells. The goal of the experiment is to identify genes thatare associated with neuronal differentiation of corticalstem cells. A detailed description of data is given by Parket al. [19]. From a developing fetal rat brain, 3,840 genesincluding novel genes were immobilized on a glass chipand fluorescence-labelled target cDNA were hybridized.After expansion, differentiation to neuronal cells wasinduced by removing bFGF with or without ciliary neuro-trophic factor (CNTF) at six time points (12 hrs, 1 day, 2days, 3 days, 4 days, 5 days). To get more reliable data, allthe hybridization analyses were carried out three timesagainst same RNA, and the scanned images were analyzedusing an edge detection mode [20]. As an illustration ofnormalization methods, we chose one slide among 36slides to see the effect of normalization. In Figure 2, theoriginal slide is the graph of (logG, logR) before normali-zation which shows a nonlinear spatial pattern. In thiscase, three normalization methods yielded quite differentresults. On the other hand, for the slides with a linearpattern three normalization methods yielded similarresults in making the slope 1.

For this dataset, Park et al. [19] presented clustering anal-ysis results after nonlinear LOWESS normalization. Weapplied three normalization methods to all 36 slides andcompared the performance of normalization methodsusing the measures of variation among the replicatedobservations described in Section 3. This data set is a spe-cial case of the one described in Section 3 with two exper-imental groups, I = 2, six time points, J = 6, and threereplications K = 3. For these microarray data, we derivedthe distribution of variance estimates by the methodsgiven in Section 3. Since the two methods provided quitesimilar results, we only present the results from theANOVA model.

Figure 3 shows the dot plots of the mean values of log-

transformed variances, say, log( ), for the original data,

global normalization, intensity dependent linear normal-ization, and intensity dependent nonlinear normaliza-tion, denoted by O, G, L, and N, respectively. Figure 3a is

a dot plot showing the mean values of log( ) from O, G,

L, N as well as those corresponding to the scale normal-ized approaches. Figures 3b to 3d focus on the effect ofscale normalization and print-tip stratification.

As shown in Figure 3a, the three normalization methodsG, L, N reduce the variability greatly. The two intensitydependent normalization methods denoted by L and Nperform equally well and somewhat better than globalnormalization.

Figure 3b shows the results of global normalization withdifferent scale normalization approaches. Great differ-ences are not found among the six approaches. Hence glo-bal normalization does not appear to be improved bynormalizing separately over the grids of spots defined bythe print-tips or by scale adjustments.

Figure 3c focuses on intensity dependent linear normali-zation with different scale normalization approaches. Fig-ure 3d is for intensity dependent non-linear LOWESSnormalization with different scale normalizationapproaches. Neither linear nor non-linear intensitydependent normalization appear to benefit greatly byscale adjustments or by performing normalization byprint-tip grids for this set of data.

Based on these figures, we conclude that intensity depend-ent normalization methods perform better than globalnormalization methods. Small differences are observedbetween the linear and nonlinear normalization meth-ods. In addition, small effects are observed for scale nor-malization methods.

Simulation studiesIn order to compare the normalization methods more sys-tematically, we performed a simulation study by generat-ing typical patterns of microarray data. Using simulateddata we could compare the normalization methods withregard to bias and mean squared error as well as variance.In general, mean square error (MSE) is defined by the sumof variance and bias2. MSE has been used as a criterion tocompare normalization methods for the cases when theycan be computed. Bolstad et al. [17] used variance andbias to compare normalization methods for high densityoligonucleotide array data. Since we do not know the truevalues for real datasets, however, we cannot find outwhether the normalization methods reduce biases or not,while we can get estimates of variance. For the simulated

σl2

σl2

σl2

σl2

σl2



datasets, on the other hand, we know the true values andthus we can compute biases. From biases and variances wecan derive mean square errors. Simulation studies providesome useful information that the public datasets do notprovide. After a careful examination of all 36 slides in ourstudy, we considered four typical types of microarray data.

These four types are shown in Figure 4. Although theywere selected from our study, we think that they representvarious linear and nonlinear types of artifacts commonlyobserved in microarray studies. For simplicity, we gener-ated the replicated microarray data from the same distri-bution, with 5,000 spots in one microarray.

(A) The original slide with a non-linear patternFigure 2(A) The original slide with a non-linear pattern. (B-D) Three normalized slides (global median, intensity dependent linear regression, intensity dependent non-linear regression.

4 6 8 10 12 14 16

46

810

1214

16

(A) (B)

log Glo

g R

(C)

log G

log

R

4 6 8 10 12 14 16

46

810

1214

16

(D)



Type I

Figure 4a shows the plot of (logG, logR) for Type I whichshows a clear linear pattern. Most observations are scat-

tered around the y = x line showing a high correlationbetween the two intensity values.

Type II

Dot Plots of Log-transformed Variance Estimates for Cortical Stem Cells DataFigure 3Dot Plots of Log-transformed Variance Estimates for Cortical Stem Cells Data. The Y-axis represents normalization methods and the X-axis represents the mean values of log-transformed variance estimates. (A) Dot plots for O, G, G.s, L, L.s, N, and N.s, (B) Dot plots for Global Normalization Methods, (C) Dot plots for Intensity-dependent Linear Normalization Methods, (D) Dot plots for Intensity-dependent Nonlinear Normalization Methods.

O

G

G.s

L

L.s

N

N.s

−1.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4

(A)

O

G

G.s

GP

GP.s

GPS

GPS.s

−1.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4

(B)

O

L

L.s

LP

LP.s

LPS

LPS.s

−1.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4

(C)

O

N

N.s

NP

NP.s

NPS

NPS.s

−1.0 −0.9 −0.8 −0.7 −0.6 −0.5 −0.4

(D)



Figure 4b shows the second type. It has a specific non-lin-ear pattern with many spots distant from the y = x line.

Type III

Figure 4c shows the third type which has the same linearpattern as Type I. However, the lower intensity values havehigher variabilities than those of higher intensity values.

Type IV

Four types of (logG, logR) plots for the simulated microarray data: Type I (A), Type II (B), Type III (C), Type IV (D)Figure 4Four types of (logG, logR) plots for the simulated microarray data: Type I (A), Type II (B), Type III (C), Type IV (D).

6 8 10 12 14 16

68

1012

1416

(A) (B)

log Glo

g R

(C)

log G

log

R

6 8 10 12 14 16

68

1012

1416

(D)



Figure 4d shows the fourth type. It is a combination ofType II and Type III. That is, it has a non-linear patternwith higher variability at the lower intensities. In order togenerate (logGI, logRI), we assume that they are observedfrom the bivariate normal distribution with mean vectorβ and covariance matrix Σ, where

For simplicity, let the random vector (YG, YR)T representthe log-transformed intensity values, say (logGI, logRI). Togenerate bivariate normal random variables, it is conven-ient to generate YG first and then generate YR from theconditional distribution of YR| YG = Y. Note that the con-ditional distribution is given by

where µR|G = µR - ρσR/σG(Y - µG) and .

For Type II, we use the same values of YG generated fromType I. For YR, however, we use the transformed mean andvariance to add a pattern like that shown in Figure 4b.

That is, and . We first

tried generating Type II data by directly transforming thedata generated from Type I but could not get a graph withthe desired pattern. The functions f1 and f2 are found bytrial and error. For Type III, we use a similar approach.That is, we use the same values of YG generated from TypeI. For YR, we use the transformed variance to allow largervariability for the lower intensity observations. Thus,

and . For simplicity, we

use the same function f2 used for Type II. Similarly, forType IV we use the same values of YG generated from TypeI. For YR, we use the transformed mean and variance to

add a specific pattern. That is, and

. The functions f3 and f4 are also found

by trial and error. For each type, we generate ten replicatedsamples. For these replicated samples, we apply the nor-malization methods and draw the distributions for thevariation measures. For simplicity, we do not consider theprint-tip variation in this simulation. We compare fourgraphs: original data(O), globally normalized data(G),linear normalized data(L), and non-linear normalizeddata(N) using LOWESS.

In order to compare these normalization methods, wecompute the mean square error(MSE). For each gene, theMSE is computed as the average of the distances betweennormalized data and true expected value. Figure 5 showsthe dot plots for the means of log-transformed MSEs. Fig-ure 5a shows the dot plot for Type I. As expected, the fourdots look exactly the same. These plots imply that thesenormalization approaches are equivalent when normali-zation is unnecessary. On the other hand, Figure 5b showsquite different patterns for Type II. Note that Type II con-tains a specific non-linear pattern on the original data. Theoriginal data have the largest MSEs. Large differences inMSEs are observed between original data and globallynormalized data. Furthermore, there is substantial addi-tional reduction in MSEs for the intensity dependent lin-ear and non-linear normalization approaches, thoughslight differences are observed between them. Figure 5cshows the results for Type III. Surprisingly, no clear differ-ences are observed among four box plots. This impliesthat these normalization methods do not reduce the MSEsof data when no specific patterns are observed but varia-bility differs greatly depending on the intensity levels.Finally, Figure 5d shows the results for Type IV which con-tains a specific non-linear pattern as well as higher varia-bility for lower intensity observations. Only smalldifferences are observed between the original data andglobally normalized data. In addition, the reduction ofMSEs by linear and non-linear normalization approachesare not as large as those of Type II. One possible explana-tion is that Type IV appears to have a more similar patternto Type III than to Type II. Though not reported here, wealso examined variances and squared biases. For Types I,III, and IV, three normalization approaches show similardistributions as the original data with regard to thesemeasures. For Type II, however, quite different patternsare observed for variances and biases. For variances, glo-bally normalized data have similar distributions as theoriginal data, while the intensity dependent linear andnon-linear normalization approaches have much reducedvariances. For biases, similar graphs are obtained. That is,globally normalized data have smaller biases, and inten-sity dependent normalized data have much smaller biasesthan original data. Only slight differences are observedbetween two intensity dependent normalized data. Thegraphs of biases and variances show that the global nor-malization method has the effect of reducing biases, whileintensity dependent normalization methods have effectson reducing both biases and variation.

We summarize our findings from the simulation studies.First, the normalization methods performed similarlywhen the original data has a linear pattern such as Type I,and when there are high variabilities for observations withlower intensities such as Types III. Second, when there is aspecific pattern such as Type II, all normalization methods

µµ ∑∑=

=

µµ

σ ρσ σ

ρσ σ σR

G

G G R

G R R

, .and2

2

Y Y NR G RGI

RGI∼ ( , ),| |µ σ 2

σ σ ρRG R| ( )2 2 21= −

µ µRGII

RGIf| |( )= 1 σ σRG

IIRGIf| |( )2

22=

µ µRGIII

RGI

| |= σ σRGIII

RGIf| |( )2

22=

µ µRGIV

RGIf| |( )= 3

σ σRGIV

RGIf| |( )2

42=



tend to reduce MSEs. Third, in this case, MSEs are domi-nated by biases. Fourth, only small differences areobserved between the intensity-dependent linear andnon-linear normalization methods.

DiscussionIn this article, we compare normalization methods com-monly used to analyze microarray data. The comparisonis based on the variability measures derived from the rep-licated microarray samples. These variability measures canbe easily derived from any replicated microarray experi-

Dot Plots of Log-transformed Variance Estimates for Simulated DataFigure 5Dot Plots of Log-transformed Variance Estimates for Simulated Data. The Y-axis represents normalization methods and the X-axis represents the mean values of log-transformed variance estimates.

O

G

L

N

−1.5 −1.0 −0.5 0.0

(A)

O

G

L

N

−1.5 −1.0 −0.5 0.0

(B)

O

G

L

N

−1.5 −1.0 −0.5 0.0

(C)

O

G

L

N

−1.5 −1.0 −0.5 0.0

(D)



ment. As pointed out by many researchers, manyundesirable systematic variations are observed in themicroarray experiment. Normalization becomes a stand-ard process for removing some of the variation whichaffects the measured gene expression levels. Although anumber of normalization methods have been proposed, ithas been difficult to decide which method performs betterthan the others. Thus, the evaluation of normalizationmethods in microarray data analysis is indeed an impor-tant issue. In this article, we show that the intensitydependent normalization method performs better thanthe simpler global normalization methods in many cases.We have not been sure about whether apparent nonline-arity of an M-A scatter plot or a scatter plot of red vs greenis sufficient basis for feeling confident that a non-linearnormalization is useful. Although we have studied only alimited number of data sets, our findings can providesome guidance on the selection of normalizationmethods. There are clearly cases where intensity depend-ent normalization performs substantially better than glo-bal normalization methods. In most of the cases that weconsidered, the non-linear intensity dependent proce-dures did not perform substantially better than a linearintensity dependent method, although there may be data-sets where this is not the case. For the cases we considered,we did not see large benefits to separate normalization byprint-tip grids or for scale normalization. None of the nor-malization methods effectively addressing the depend-ence of the variance of measurements on intensity level.Recently, some other non-linear normalization methodshave been employed such as B-splines and Gaussian-ker-nel fitting [12,21]. These non-linear normalization meth-ods seem to be comparable to the LOWESSnormalization. We think the basic idea of non-linear nor-malization is the same whether they use LOWESS curve,splines, or kernels. They are quite effective in controllingspecific non-linear variations. Some methods may havemore computational efficiency. We believe that moresophisticated non-linear normalization methods areunder development. We recommend that experimental-ists examine their data carefully and consider applyingintensity-dependent normalization methods routinely.Software for intensity dependent normalization is availa-ble on desktop packages such as BRB-ArrayTools http://linus.nci.nih.gov/BRB-ArrayTools and via the internet inSNOMAD http://pevsnerlab.kennedykrieger.org/snomad.htm tools which provide any DNA array researcherwith the tools to apply a variety of non-linear intensity-dependent normalization methods to their data [22].

AcknowledgementThe authors wish to thank two anonymous referees whose comments were extremely helpful. The work was supported by the IMT2000 contri-bution from Korea Ministry of Health and Welfare, and Ministry of Infor-mation and Communication (01-PJ11-PG9-01BT-00A-0045).

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http://linus.nci.nih.gov/BRB-ArrayTools

http://linus.nci.nih.gov/BRB-ArrayTools

http://pevsnerlab.kennedykrieger.org/snomad.htm

http://pevsnerlab.kennedykrieger.org/snomad.htm













































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22. Colantuoni C, Henry G, Zeger S and Pevsner J: SNOMAD (Stand-ardization and Normalization of MicroArray Data): Web-Accessible Tools for Gene Expression Data Analysis. Bioinfor-matics 2002, 18:1540-1541.






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Evaluation of normalization methods for microarray data