Interpreting Patterns and Analysis of Acute Leukemia Gene Expression Data by Multivariate Statistical Analysis

Transcription

1 Interpretng Patterns and Analyss of Acute Leukema Gene Expresson Data by Multvarate Statstcal Analyss ChangKyoo Yoo * and Peter A. Vanrolleghem BIOMATH, Department of Appled Mathematcs, Bometrcs and Process Control, Ghent Unversty, Coupure Lnks 3, B-9 Gent, Belgum ( * ChangKyoo.Yoo@bomath.UGent.be Abstract DNA mcroarray technologes are leadng to an exploson n avalable gene expresson data whch smultaneously montor the expresson pattern of thousands of genes. Gene expresson data are characterzed by a very hgh dmensonalty (genes, a relatvely small number of samples (observatons, rrelevant features, and t leads to a collnearty and multvarate problem. In ths paper, we propose a systematc approach to gene selecton based on dscrmnant partal least squares (DPLS and fuzzy clusterng methods. The proposed method was appled to mcroarray data from leukema patents; specfcally, t was used to nterpret the gene expresson pattern and analyze the leukema subtype whose expresson profles correlated wth four cases of acute leukema gene expresson. Keywords: Bonformatcs, classfcaton and clusterng, dscrmnant partal least squares, DNA mcroarray, gene expresson data analyss. Introducton The use of relatvely new DNA mcroarray technologes, whch smultaneously montor the expresson pattern of thousands of genes, has led to an exploson of readly avalable gene expresson data. Correspondngly, there now s a great need for methods capable of nterpretng, vsualzng and analyzng the patterns and nformaton contaned wthn these large data sets. However, gene expresson data are characterzed by a hgh dmensonalty (genes, a relatvely small numbers of samples (observatons, rrelevant features, and leads to a collnearty and multvarate problems. Thus, comprehensble nterpretaton and analyss s dffcult and the complexty of the orgnal data entals a hgh computatonal cost. To solve the above mentoned problems, the frst step n creatng such a new method s to extract the fundamental features (or genes of the gene expresson data set (.e. a dmensonal reducton, and the second step s to compare the expresson data wth the desred level of data analyss (.e. clusterng smlar genes or samples, and/or dentfyng the tumor class. Several studes have used mcroarray technology to analyze gene expresson n colon, breast, leukema and other cancers (Alzadeh et al., 2; Cho et al., 22; Dudot et al., 22; Nguyen and Rocke, 22; Stephanopoulos et al., 22. In ths paper, we propose a systematc approach to gene selecton that uses the dscrmnant partal least squares (DPLS and fuzzy clusterng methods to nterpret the

2 gene expresson patterns of acute leukema, to dentfy obscure leukema subtypes n mcroarray data, and to establsh the relatonshp between an expresson-based leukema subclass and a clncal outcome. 2. Theory 2. Dscrmnant partal least squares (DPLS DPLS s a dmensonalty reducton technque for maxmzng the covarance between the predctor (ndependent block X and the predcted (dependent block Y for each component. DPLS models the relatonshp between X and Y usng a seres of local leastsquares fts. PLS components are obtaned n such a way that the sample covarance between the response varables (leukema classes and a lnear combnaton of the predctors (genes, are maxmzed. In other words, the PLS fnds a weght vector w whch satsfes (Yeung and Ruzzo, 2; Cho et al., 22; Nguyen and Rocke, 22, w k = arg max Cov( Xw, y ( subject to the unt weght and orthogonalty constrant w 'Sw j = for all j k (2 where S'= X' X. The -th PLS component s a lnear combnaton of the orgnal predctors ( Xw. The varable mportance n the projecton (VIP s a good measure of the nfluence of all varables n the PLS model on the response varables. The VIP can be calculated from the weght vector of the DPLS model and the percentage that s explaned by the dmenson of the model, whch s defned as follows: VIP = a ( w ak 2 Note that after the PLS weght vectors are computed, genes are selected va the VIP. For a gven PLS dmenson, (VIP ak 2 s equal to the squared PLS weght (w ak 2. The VIP can be consdered as a measure of how much a certan gene corresponds to the samples. Thus, we can select mportant genes based on the VIP value. It s reasonable to assume that the weghts of the features are proportonal to ther mportance n the determnaton of the class labels; that s, the hgher the weght, the better the dstncton power of the feature wth respect to the class label. Therefore, gven a traned PLS classfer, a set of K hgh-rankng genes are obtaned by selectng the genes wth the top K VIP weghts. 2.2 Fuzzy c-means (FCM clusterng In the FCM clusterng method, an object can smultaneously be a member of multple classes (Duda et al., 2, Yoo et al., 23. The objectve functon, whch s mnmzed teratvely, s a weghted wthn-groups sum of dstances d k,. The weghtng s performed by multplyng the squared dstances by membershp values u k,. C N m 2 J ( C, m = ( u d (4 m = k = k, k, where C s the total number of clusters, N s the total number of objects n the calbraton data, d k, s the dstance between an object k and a prototype (cluster, and u k, s the membershp functon. After computng the membershp values for all calbraton objects, the cluster centers (v are descrbed by prototypes, whch are fuzzy weghted means, accordng to the followng equaton: (3

3 N m ( u x k = v k, k (5, N m ( u k = k, In the predcton of a new test sample, a new value s computed usng Eq. (6 (Yoo et al., 23. u = 2 C 2 + ( m d = k, N, 2 j = dk, j For mcroarray data, we apply the FCM algorthm to the reduced PCA feature space, that s, to the score vector of the PCA. Ths fuzzy clusterng method allows ntermedate logcal assgnments whereby genes or patents are placed nto multple groups by assgnng a membershp value for each group that s compared between (not n group and (completely n group. The use of membershp values has the advantage of allowng a gene or sample to belong to multple clusters, whch may better reflect the underlyng bology. 3. Result and Dscusson The gene selecton method proposed n ths paper s appled to the acute leukema data set publshed by Golub et al. (999. The data set of 729 genes was derved from 72 patents, 47 of whom were affected wth acute lymphoblastc leukema (ALL; 38 B-cell and 9 T-cell and 25 of whom were affected wth acute myelod leukema (AML. The tranng data set conssted of 38 bone marrow samples, 27 of whch were taken from ALL patents (9 B-ALL and 8 T-ALL and of whch were taken from AML patents; the ndependent (test data set conssted of 34 patents, 2 of whch were taken from ALL patents and 4 of whch were taken from AML patents. To remove systematc sources of varaton n the mcroarray, we log transformed the gene expressons, dvded the maxmum value of each gene and standardzed them to have a mean of zero and a standard devaton of one across samples (Yang et al., Interpretng patterns of ALL and AML usng FCM To determne the specfc genes that dscrmnate between ALL and AML, we used the DPLS method for gene selecton, where the response varable Y s (AML or (ALL. Among the 729 genes, 5 were selected on the bass of the VIP value of DPLS. Thus, on the bass of the correlaton coeffcents, we chose the 5 genes that were most correlated wth the classfcaton of leukema. In contrast to the 5 genes of Golub et al. (999, the proposed gene selecton method assgns hgh rankngs to Zyxn, Leukotrene (C4 synthase gene, Leptn, CD33 antgen, FAH, and Myeloperoxdase (MPO as well as Cystatns and Cathepsns. These genes are known to play mportant roles n acute leukema (Golub et al, 999; Cho et al., 22. PCA was appled to nterpret the patterns of ALL and AML n the leukema data set because the presence of too many features degrades the clusterng performance. The four PCs capture about 77.3% of the varaton n the 5 genes by projectng the 5 genes nto four dmensons. We appled the FCM clusterng method (wth four PCs and analyzed the results of the correspondng clusterng and classfcaton. In FCM, the fuzzfer m was set to.2 on the bass of the results of many smulatons under varous condtons. We ntalzed the (6

4 parameters of the cluster prototype center usng k-means clusterng. Fg. show the FCM membershp values for the 38 tranng samples (left and the predcton results for the 34 test samples (rght. In the tranng dataset, patents -27 have hgh membershp values n class (AML and low membershp values n class 2 (ALL, whereas patents show the opposte behavor. Thus, the ALL and AML patents are well clustered wthout any clusterng error. All but two of the 34 test samples were correctly classfed. The two msclassfed samples were ALL(#42, whch showed hgh gene expresson levels n comparson to other ALL patents, and ALL(#66, whch showed low expresson levels n comparson to other AML patents. Ths result s superor to that of Golub et al. (999, who obtaned a strong predcton for 8 out of the 2 ALL test samples and out of the 4 AML samples (.e., a total of sx msclassfcatons. MF of Cluster (AML MF of Cluster (AML MF of Cluster2 (ALL MF of Cluster2 (ALL Fgure. Predcton result of membershp values of FCM for tranng (left and test samples (rght wth cluster (AML, upper and cluster 2 (ALL, lower. 3.2 Analyss of ALL subclass (B-cell and T-cell ALL can be further classfed nto the T-cell and B-cell lneages. In clncal practce, the B-cell lneage responds better to treatment than the T-cell lneage. Therefore, t s mportant dstngush between these lneages. To determne the 25 genes that dscrmnate between T-cell ALL (T-ALL and B-cell ALL (B-ALL, we used the DPLS method to select the top 25 gene selecton, where the response varable Y s (T- ALL or (B-ALL. After selectng the top 25 genes that are dfferentally expressed between the B-cell and T-cell lneages of ALL patents, PCA was used to reduce the data dmenson. Four PCs were determned, and captured about 83% of the varaton n the 25 genes. The result shows that all of the B-cell and T-cell lneage ALL samples are well clustered except for one msclustered sample (# Analyss of AML subclass: M, M2, M4, M5 Among the 25 AML patents, we used 2 patents as a tranng data set, where 4 patents (samples 32, 35, 38, 6 were M, patents (samples 28, 29, 33, 34, 37, 5, 53, 57, 58, and 6 were M2, 4 patents (samples 3, 5, 52, and 54 were M4, and 2 patents (samples 3 and 36 were M5. The remanng 5 patents (samples 62-66, whch could not be classfed by Golub et al. (999, were used as a test data set. To determne the genes that dscrmnate between the AML subclasses ncluded n the tranng data set (.e., M, M2, M4, and M5, we used the DPLS method to select the top 25 gene selecton, where the response matrces (Y were [ ] T for M, [ ] T for M2, [

5 ] T for M4 and [ ] T for M5. After selectng the top 25 genes, PCA was used to reduce the data dmenson. Four PCs were determned, and captured about 82% of the varaton n the 25 genes. Based on the results of the tranng data, we used the FCM clusterng method to predct the subtype of the fve AML samples that could not be predcted by the method of Golub et al. (999. The predcton results ndcate that three AML patents (samples #63, 64, and are of subtype M, and two patents (samples #62 and 66 are of subtype M Predcton of clncal outcome of AML patents (Falure and Success To search for addtonal sets of genes useful for predctng the clncal outcome of leukema patents, we performed addtonal gene selecton for the predcton of clncal output of AML treatment. Among the 25 AML patents, we used 5 patents as a tranng data set, of whom 7 patents (#34-38 and survved and 8 patents (#28-33, 5, and 5 ded durng treatment, and we used the remanng patents (samples # 54, 57, 58, and 6-66, who dd not respond to treatment, as a test data set. We used the DPLS method for selectng the top 25 genes, where the response varable Y s (success and (falure. After selectng the top 25 genes dfferentally expressed between AML patents who lved or ded durng treatment, four PCs usng PCA were determned, and captured about 76% of the varaton n the 25 genes. In the loadng plot (not shown n ths paper, genes that correlate wth successful treatment appear on the rght sde and genes that correlate wth treatment falure appear on the left sde. Almost all of the genes n each gene group have common expresson patterns, that s, group-specfc regulaton patterns known as coregulaton patterns (Stephanopoulos et al., 22. It means that the expresson of each group s hghly elevated only n the sample class and down-regulated n the other classes. Ths result s notable n that these genes may be consdered marker genes related to the clncal outcome of AML patents. MF of Cluster (Success MF of Cluster2 (Falure Fgure 2. Predcton result of membershp values of FCM for test samples (54, 57, 58, 6-66 wth AML patents who lved and ded after treatment. Fg. 2 depcts the predcton results based on the membershp values from FCM clusterng for the AML patents (54, 57, 58, 6-66 whose clncal outcome was not specfed by Golub et al. (999. The results ndcate that eght AML patents (#54, 57, 58, 62, 63, 64,, and 66 are predcted to survve after treatment, and two AML patents (#6 and 62 are predcted to de after treatment. Thus, the proposed method

6 makes t possble to predct the clncal outcome of AML patents. Moreover, based on the present fndngs n regard to the lnk between certan genes and clncal outcome, we can determne the specfc genes and relapse n leukema patents. Although the clncal outcome s also affected by many other factors, such as patent age, treatment regme, and tme of dagnoss, the results presented here hghlght the potental of the proposed method for uncoverng prognostc ndcators for leukema. 4. Concluson The DNA mcroarray technology s useful for dscrmnatng between varous subtypes of leukema, whch s necessary for the accurate dagnoss and treatment of patents. Here, we present a novel class-orented gene selecton method and fuzzy clusterng method. The proposed method allows the dentfcaton of mportant genes and the classfcaton of leukema subtype solely on the bass of molecular-level montorng. Further, the proposed method was used to establsh a relatonshp between expressonbased subclasses of leukema tumors and patent outcome. 5. Acknowledgments Ths work was fnancally supported by the Vstng Postdoctoral Fellowshp of the Scentfc Research-Flanders (FWO. 6. References Alzadeh, A., Esen, and Staudt., L. M. 2. Dfferent types of dffuse large b-cell lymphoma dentfed by gene expresson proflng, Nature, 43, Cho, J.-H., Lee, D. K., Park, J. H., Km, K. W. and Lee, I.-B. 22. Optmal approaches for classfcaton of acute leukema subtypes based on gene expresson data, Botech. Prog., 8(4, Dudot, S., Frdlyand, J. and Speed, T. 22. Comparson of dscrmnaton methods for the classfcaton of tumor usng gene expresson data, J. Am. Stat. Assoc. 97, Golub T. R., Slonm, D. K., Tamayo, P. and Lander, E. S Molecular classfcaton of cancer: Class dscovery and class predcton by gene expresson montorng, Scence, 286, Nguyen, D. V. and Rocke, D. M. 22. Tumor classfcaton by partal least squares usng mcroarray gene expresson, Bonformatcs, 8(, Stephanopoulos G., Hwang, D. H., Schmt, W. A., Msra, J. and Stephanopoulos, G. 22. Mappng physologcal states from mcroarray expresson measurements, Bonformatcs, 8(8, Yang, Y. H., Dudot, S., Luu, P., Ln, D. M., Peng, V., Nga, J. and Speed, T. P., 22. Normalzaton for cdna mcroarray data: A robust composte method addressng sngle and multple slde systematc varaton, Nuclec Acds Res. 3, Yeung, K. Y. and Ruzzo, W. L. 2. Prncpal component analyss for clusterng gene expresson, Bonformatcs, 7, Yoo, C. K., Vanrolleghem, P. A. and Lee, I. 23. Nonlnear modelng and adaptve montorng wth fuzzy and multvarate statstcal method n bologcal wastewater treatment plant. Journal of Botechnology, 5(-2,