Feature Selection for Predicting Tumor Metastases in Microarray Experiments using Paired Design

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1 Feature Selecton for Predctng Tumor Metastases n Mcroarray Experments usng Pared Desgn Qhua Tan 1,2, Mads Thomassen 1 and Torben A. Kruse 1 ORIGINAL RESEARCH 1 Department of Bochemstry, Pharmacology and Genetcs, Odense Unversty Hosptal, Odense, Denmark. 2 Department of epdemology, Insttute of Publc Health, Unversty of Southern Denmark, Odense, Denmark. Abstract: Among the major ssues n gene expresson profle classfcaton, feature selecton s an mportant and necessary step n achevng and creatng good classfcaton rules gven the hgh dmensonalty of mcroarray data. Although dfferent feature selecton methods have been reported, there has been no method specfcally proposed for pared mcroarray experments. In ths paper, we ntroduce a smple procedure based on a modfed t-statstc for feature selecton to mcroarray experments usng the popular matched case-control desgn and apply to our recent study on tumor metastass n a lowmalgnant group of breast cancer patents for selectng genes that best predct metastases. Gene or feature selecton s optmzed by thresholdng n a leavng one-par out cross-valdaton. Model comparson through emprcal applcaton has shown that our method manfests mproved effcency wth hgh senstvty and specfcty. Keywords: gene expresson mcroarray, feature selecton, metastass, predcton. Introducton Characterzed by smultaneous proflng for the transcrptonal actvtes of thousands of mrna speces n a human tssue, the DNA mcroarray technology represents an mportant hgh-throughput platform for analyzng and understandng human dseases. The tremendous potental provded by the new technology s servng us not only as a molecular tool for nvestgatng dsease mechansms but also for classfcaton and clncal outcome predcton (Dudda-Subramanya et al. 2003). Applcaton of the technology n clncal oncology s demonstratng t as a powerful tool for refnng dagnoss and mprovng prognostc predcton accuracy of cancer patents (Puszta et al. 2003). Bonformatcs and bostatstcs play mportant roles n such practces n establshng gene expresson sgnatures or prognostc markers and n buldng up effcent classfers (Asyal et al. 2006). Among the major ssues n gene expresson profle classfcaton, feature selecton s an mportant and necessary step n achevng and creatng good classfcaton rules gven the hgh dmensonalty of mcroarray data. There are varous approaches for feature selecton n the lterature among whch one common approach s the unvarate selecton scheme for selectng only genes wth the hghest statstcal sgnfcance. Such an approach can be nadequate because (1) t tends to nclude elements that contrbute hghly redundant nformaton and (2) t gnores the co-regulatory network n gene functon. As a result, the unvarate approach does not necessarly guarantee a best classfer (En-Dor et al. 2005; Baker and Kramer, 2006). Tbshran et al. (2002) proposed a Nearest Shrunken Centrods (NSC) method for both feature selecton and tumor classfcaton. In NSC, weak elements of the class centrods are shrunk or deleted va soft-thresholdng to dentfy genes that best characterze each class. The method mplemented n an R package (PAM, Predcton Analyss of Mcroarrays) performs well n dentfyng subsets of genes that can be used for classfcaton and predcton. Although dfferent feature selecton methods have been reported for tumor classfcaton (Inza et al. 2004), there has been no method specfcally proposed for pared mcroarray experments. In ths paper, we ntroduce a smple feature selecton procedure based on a modfed t-statstc to mcroarray experments usng the popular matched case-control desgn and apply to our recent study on tumor metastass n a low-malgnant group of breast cancer patents for selectng genes that best predct metastases. Gene or feature selecton s optmzed by thresholdng n a leavng one-par out cross-valdaton procedure usng the support vector machnes (SVM) (Brown Correspondence: Dr. Qhua Tan, Department of Bochemstry, Pharmacology and Genetcs, Odense Unversty Hosptal, Sdr. Boulevard 29, DK-5000 Odense C,Denmark. Tel: ; Fax: ; Emal: qhua.tan@ouh.fyns-amt.dk Please note that ths artcle may not be used for commercal purposes. For further nformaton please refer to the copyrght statement at Cancer Informatcs 2007:

2 Tan et al et al. 2000). Such an approach s necessary consderng the advantages n a matched desgn because there are multple factors (nodal status, tumor sze, age, etc.) that convey mportant mplcatons on tumor outcomes. Performance of the feature selecton method s compared wth that from PAM and from the ordnary pared t-test usng recever operatng characterstcs (ROC) analyss (Fawcett, 2006). Methods Suppose n a pared mcroarray experment, we have the gene expresson values (usually n log scale) from n pars of samples j = 1, 2, n. For each gene ( = 1, 2, p), we obtan the dfferental gene expresson n par j, d j, by substractng the expresson value of the control from the case and calculate the mean dfference as d Σ n 1 d / nand = j= j n 2 Σ j= 1 j the standard error of d as s d d n = ( ) /( 1) Now we can calculate the t-test statstc for the pared data as t d = (1) s Smlar to Tusher et al. (2001), we add a postve constant s 0 to the denomnator of (1) so that (1) becomes d t = s + s = t 1 s 1+ s 0 0 (2) From (2) we can see that our modfed t-statstc s a down-scaled t-statstc wth the scalng determned by the rato between s 0 and s. Once s 0 s specfed, the scalng has a large effect on genes wth small standard errors. Followng Tbshran et al. (2002), we set s 0 to the medan value of s ( = 1, 2, p). For the purpose of feature selecton, we specfy a threshold Δ and pck up genes wth t Δ > 0. The optmal subset of genes s obtaned through a leavng one-par out cross-valdaton procedure usng SVM. Smlar to PAM, the optmal threshold Δ s determne through a grd search n whch for each gven Δ, the performance of classfer s judged by leavng one-par out cross-valdaton to ensure that the tranng set and the predcton set are ndependent. The Δ that corresponds to the lowest classfcaton error s taken as the optmal threshold. Once the optmal threshold Δ s determned, the overall optmal sub-set of genes s selected by applyng the optmal Δ to the whole sample. The realzaton of SVM s done usng the svm procedure n the R package e1071 ( at.r-project.org/src/contrb/packages). In order to assess and compare our model performance wth that from PAM and the ordnary pared t-test, we ntroduce the ROC analyss and calculate the area under an ROC curve (AUC). A ROC curve s a two-dmensonal depcton of classfer performance whch plots senstvty on the Y and 1-specfcty on the X axes. As such, a hgh- AUC classfer has better average performance than a low-auc classfer (Fawcett, 2006) wth AUC = 0.5 for a random classfer. ROC analyss s performed usng the free R package catools. Applcaton We apply our method to a mcroarray dataset on tumor metastass from low-malgnant breast cancer patents collected n our lab (Thomassen et al. 2006a). In ths study, 13 low-malgnant T1 (tumor sze n dameter T 20 mm) and 17 low-malgnant T2 (20 mm < T 50 mm) tumors from patents who developed metastases were matched to metastass-free tumors from patents (followed up for about 12 years after dagnoss) of the same tumor type and accordng to year of surgery, tumor sze, and age. Gene expresson analyss was performed on 29K olgonucleotde arrays wth duplcated measurements for each gene (Thomassen et al. 2006b). Data were normalzed usng the varance stablzaton normalzaton method (Huber et al. 2002) mplemented n the free R package vsn n Boconductor ( The study by Thomassen et al. (2006a) dentfed a 32-gene sgnature that classfes the 60 tumor samples wth a mean accuracy of 78% (specfcty 77%; senstvty 80%) usng leavng one-par out cross-valdaton (Fgure 1a). In the analyss, feature selecton was done usng the nearest shrunken centrods methods n the R package pamr (Tbshran et al. 2002) and classfcaton done usng SVM n the R package e1071. Note that the feature selecton procedure usng pamr does not take the pared matchng nto account n dentfyng the subset of genes for tranng and predcton. Usng our method descrbed above, we re-analyze the data by ntroducng the modfed t-statstc for 214 Cancer Informatcs 2007:3

3 Mcroarray Experments usng Pared Desgn CV probablty of metastass CV probablty of metastass CV probablty of metastass a) metastass non-metastass Sample b) metastass non-metastass Sample c) metastass non-metastass Sample Fgure 1. Probablty of metastass calculated by SVM usng leavng one-par out cross-valdaton based on the 32-gene sgnature by PAM (1a), the 5-gene sgnature by our new method (1b) and the 43-gene sgnature by pared t-test (1c) for the 13 pars of low-malgnant T1 (astersk) and 17 pars of low-malgnant T2 (trangle) patents. The best performance s acheved by our 5-gene sgnature wth mproved predcton accuracy and better separaton. pared data n defnng the gene expresson sgnature for predctng metastases. Our analyss acheved an overall accuracy of 83% ( = 0.396) wth a specfcty of 83% and a senstvty of 83% usng a subset of only 5 genes (Fgure 1b). Comparng Fgure 1a wth 1b, one can see that our method has mproved separaton based on predcton probablty and ncreased effcency (medan of correct predcton probablty: 0.88 versus 0.86 for metastass and 0.84 versus 0.81 for non-metastass). Interestngly, all the 5 selected genes are wthn the 32-gene lst dentfed by PAM n Thomassen et al. (2006a). To further compare our analyss, we addtonally ntroduce the ordnary pared t-test for gene selecton. Here the thresholdng s mposed upon the ordnary pared t-statstc,.e. we pck up genes wth t Δ > 0. Lkewse, we agan select the optmal subset of genes through cross-valdaton by leavng one-par out. The classfer based on the expresson sgnature specfed by the ordnary pared t-test yelds an average accuracy of 74% (specfcty 74%; senstvty 74%) when s set to 3.1 (43 genes selected). The cross-valdaton probabltes plotted n Fgure 1c shows that the model based on ordnary pared t-test has the lowest effcency (medan of correct predcton probablty: 0.85 for metastass and 0.83 for non-metastass) even though the method makes use of the pared desgn. We fnally evaluate the overall performances of the 3 methods usng ROC analyss. Based on the cross-valdaton probablty of metastass from SVM and the observed metastass status for each sample, we are able to draw the ROC curves and show t n Fgure 2 wth the dotted curves for the new method n black, for PAM n red and for the pared t-test n green. Vsualzaton of Fgure 2 ndcates that snce the black curve runs on top of the other curves n the upper-left trangle of the fgure, our new method exhbts hgher effcency as compared wth the others. Ths s further confrmed by calculatng the AUC, a standard summary metrc for assessng the overall performance of a classfer. The hgh AUC for our new method (0.86) agan shows that t outperforms PAM (AUC = 0.83) and the ordnary pared t-test (AUC = 0.80). Dscusson We have ntroduced a smple feature selecton method for predctng tumor metastases n pared mcroarray experments. Model comparson through emprcal applcaton has shown that our Cancer Informatcs 2007:3 215

4 Tan et al ROC Curves Senstvty New method PAM Pared t-test 1-Specfcty Fgure 2. ROC analyss for model comparson wth the dotted curves for the new method n black, for PAM n red and for the pared t-test n green. Snce the black curve runs on top of the others n the upper-left trangle of the f gure, our new method exhbts hgher eff cency n ts performance. The hgh AUC for our new method (0.86) ndcates that t outperforms PAM (AUC = 0.83) and the pared t-test (AUC = 0.80). method manfests hgh effcency and outperforms exstng methods. As shown n the results secton, the ordnary pared t-tests has the worst performance as compared wth the other two methods whch use modfed t-statstcs for thresholdng to elmnate genes that do not contrbute towards class predcton. Although both the modfed and the ordnary pared t-statstcs make use of the matched desgn, the better performance of our method s acheved by thresholdng upon a new metrc that s less dependent on gene-specfc varances whch helped to flter statstcally sgnfcant genes due to small standard errors n ther dfferental expressons. It s more nterestng to compare the performances between our method and PAM. Although both methods use the modfed versons of t-statstcs, our method takes the followng advantages of the pared desgn n selectng nformatve features. Frst, as a popular method n cancer research (Breslow and Day, 1990), the pared desgn helps to mnmze the nfluence on tumor metastass from non-transcrptomc factors such as age, clncal stage, treatment, etc (Gonzalez-Angulo et al. 2005). Second, n a transcrptomc study on tumor metastass, these confoundng factors not only affect the metastass phenotype whch s of our prmary nterest but could also nfluence the transcrptonal profles of 216 Cancer Informatcs 2007:3

5 Mcroarray Experments usng Pared Desgn Table 1. Informaton on the 5 selected genes. GenBank Gene symbol accesson Descrpton Gene Ontology Hypothetcal proten FLJ20354 NM_ FLJ20354, mrna. Intracellular sgnalng cascade IMAGE: BC Clone IMAGE: , mrna Unknown Lgase actvty; ubqutn conjugatng Ubqutn-conjugatng enzyme actvty; Ubqutn cycle; UBE2R2 NM_ enzyme E2R 2, mrna. ubqutn-lgase actvty ZNF533 NM_ Znc f nger proten 533 Unknown DTL NM_ Dentcleless homolog Unknown genes. Ignorng these nfluences wll smply ntroduce nose n feature selecton resultng n low accuracy of the classfer. A good classfcaton sgnature should be a mnmal subset of genes that s not only dfferentally expressed but also contans most relevant genes wthout redundancy (Peng et al. 2006; Baker and Kramer, 2006). A comparatve analyss on data across several studes has found that classfcaton rules for 5 genes can acheve comparable performance as that for 20 or 50 genes (Baker and Kramer, 2006). In our analyss, the hgh performance s acheved by basng our classfer concdently on 5 nformatve genes. It s nterestng that all 5 genes overlap wth the 32-gene sgnature dentfed by PAM (Thomassen et al. 2006a) and 2 of the 5 genes overlap wth the 70-gene sgnature from van t Veer et al. (2002) n ther studes on breast cancer metastases. Further nformaton on the 5 selected genes s provded n Table 1. Fnally, t s necessary to pont out that the pared experment desgn n studyng tumor metastass usng two-channel cdna mcroarrays can be further advantaged by the reduced expermental cost when drectly labelng, for example, metastass mrna wth cy5 and non-metastass mrna wth cy3 n each matched par. Snce our method works wth the par-wsed dfference n the log expresson values, the feature selecton algorthm s vald for both one- and two- channel mcroarray platforms. Overall, gven the popularty of the par matched desgn n cancer studes, we hope that our new method for feature selecton can be of use n dentfyng effcent and nformatve gene expresson sgnatures for predctng tumor metastases n clncal cancer research. Acknowledgements Ths work was partally supported by the Human Mcroarray Center project funded by The Dansh Research Agency through the Dansh Botechnology Instrumentaton Center (DABIC). References Asyal, M.H., Colak, D., Demrkaya, O. and Inan, M.S Gene expresson profle classfcaton: A revew. Current Bonformatcs, 1: Baker, S.G., Kramer, B.S Identfyng genes that contrbute most to good classfcaton n mcroarrays. BMC Bonformatcs, 7:407. Breslow, N.E., Day, N.E Statstcal methods n cancer research. Vol. 1. The analyss of case-control studes. Lyon: Internatonal Agency for Research on Cancer (IARC Scentfc Publcatons, No. 32). Brown, M.P., Grundy, W.N., Ln, D., Crstann, N., Sugnet, C.W., Furey, T.S., Ares, M., Jr. and Haussler, D Knowledge-based analyss of mcroarray gene expresson data by usng support vector machnes. Proc. Natl. Acad. Sc. U.S.A., 97: Dudda-Subramanya, R., Lucchese, G., Kanduc, D. and Snha, A.A Clncal applcatons of DNA mcroarray analyss. J. Exp. Ther. Oncol., 3: En-Dor, L., Kela, I., Getz, G., Gvol, D. and Domany, E Outcome sgnature genes n breast cancer: s there a unque set? Bonformatcs, 21: Fawcett, T An ntroducton to ROC analyss. Pattern Recognton Letters, 27: Gonzalez-Angulo, A.M., McGure, S.E., Buchholz, T.A., Tucker, S.L., Kuerer, H.M., Rouzer, R., Kau, S.W., Huang, E.H., Morand, P., Ocana, A., Crstofanll, M., Valero, V., Buzdar, A.U. and Hortobagy, G.N Factors predctve of dstant metastases n patents wth breast cancer who have a pathologc complete response after neoadjuvant chemotherapy. J. Cln. Oncol., 23: Huber, W., von Heydebreck, A., Sultmann, H., Poustka, A. and Vngron, M Varance stablzaton appled to mcroarray data calbraton and to the quantfcaton of dfferental expresson. Bonformatcs, 18 Suppl 1:S Inza, I., Larranaga, P., Blanco, R. and Cerrolaza, A.J Flter versus wrapper gene selecton approaches n DNA mcroarray domans. Artf. Intell. Med., 31: Peng, Y., L, W. and Lu, Y A hybrd approach for bomarker dscovery from mcroarray gene expresson data for cancer classfcaton. Cancer Informatcs, 2: Cancer Informatcs 2007:3 217

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