Supplemental material for P. Sankaranarayanan,* T. E. Schomay,* K. A. Aiello and O. Alter, "Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival," Public Library of Science (PLoS) One 10 (4), article e0121396 (April 2015); doi: 10.1371/journal.pone.0121396.
Press Release: J. Kiefer, "New Method Increases Accuracy of Ovarian Cancer Prognosis and Diagnosis," American Association for the Advancement of Science (AAAS) EurekAlert! (April 15, 2015).
Feature: R. Atkins "Calculating Cancer Cures," National Academy of Engineering (NAE) Innovation Podcast and Radio Series (April 19, 2015).¹
Feature: F. Pavlou, "Big Data, Hidden Knowledge," The Pathologist (June 15, 2015).²

Abstract:
The number of large-scale high-dimensional datasets recording different aspects of a single disease is growing, accompanied by a need for frameworks that can create one coherent model from multiple tensors of matched columns, e.g., patients and platforms, but independent rows, e.g., probes. We define and prove the mathematical properties of a novel tensor generalized singular value decomposition (GSVD), which can simultaneously find the similarities and dissimilarities, i.e., patterns of varying relative significance, between any two such tensors. We demonstrate the tensor GSVD in comparative modeling of patient- and platform-matched but probe-independent ovarian serous cystadenocarcinoma (OV) tumor, mostly high-grade, and normal DNA copy-number profiles, across each chromosome arm, and combination of two arms, separately. The modeling uncovers previously unrecognized patterns of tumor-exclusive platform-consistent co-occurring copy-number alterations (CNAs). We find, first, and validate that each of the patterns across only 7p and Xq, and the combination of 6p+12p, is correlated with a patient's prognosis, is independent of the tumor's stage, the best predictor of OV survival to date, and together with stage makes a better predictor than stage alone. Second, these patterns include most known OV-associated CNAs that map to these chromosome arms, as well as several previously unreported, yet frequent focal CNAs. Third, differential mRNA, microRNA, and protein expression consistently map to the DNA CNAs. A coherent picture emerges for each pattern, suggesting roles for the CNAs in OV pathogenesis and personalized therapy. In 6p+12p, deletion of the p21-encoding CDKN1A and p38-encoding MAPK14 and amplification of RAD51AP1 and KRAS encode for human cell transformation, and are correlated with a cell's immortality, and a patient's shorter survival time. In 7p, RPA3 deletion and POLD2 amplification are correlated with DNA stability, and a longer survival. In Xq, PABPC5 deletion and BCAP31 amplification are correlated with a cellular immune response, and a longer survival.

A PDF format file, readable by Adobe Acrobat Reader.

Sankaranarayanan_Schomay_et_al_PLoS_One_2015.pdf

A PDF format file, readable by Adobe Acrobat Reader.

Sankaranarayanan_Schomay_et_al_PLoS_One_2015_Figures.pdf

A PDF format file, readable by Adobe Acrobat Reader.

Sankaranarayanan_Schomay_et_al_PLoS_One_2015_Appendix.pdf

• S1 Dataset: Discovery_Patients.txt

Discovery set of patients.
A tab-delimited text format file, readable by both Mathematica and Microsoft Excel, reproducing TCGA annotations of the discovery set of 249 patients, from the TCGA Research Network. The tumor and normal profiles of the discovery set of patients measured by each of the two DNA microarray platforms, tabulating relative copy-number variation across the 6p+12p, 7p, and Xq tumor and normal probes, are:

• D_Tumor_1_6p+12p.txt

• D_Tumor_2_6p+12p.txt

• D_Normal_1_6p+12p.txt

• D_Normal_2_6p+12p.txt

• D_Tumor_1_7p.txt

• D_Tumor_2_7p.txt

• D_Normal_1_7p.txt

• D_Normal_2_7p.txt

• D_Tumor_1_Xq.txt

• D_Tumor_2_Xq.txt

• D_Normal_1_Xq.txt

• D_Normal_2_Xq.txt

• S2 Dataset: Validation_Patients.txt

Validation set of patients.
A tab-delimited text format file reproducing TCGA annotations of the validation set of 148 patients. The tumor profiles of the validation set of patients, tabulating relative copy-number variation across the 6p+12p, 7p, and Xq tumor probes, are:

• V_Tumor_6p+12p.txt

• V_Tumor_7p.txt

• V_Tumor_Xq.txt

• S3 Dataset: Tumor_Arraylets_1.txt

First, most tumor-exclusive tumor arraylets.
A tab-delimited text format file tabulating the segments of the first, most tumor-exclusive tumor arraylets computed by tensor GSVD of the discovery set of patients across 6p+12p, 7p, or Xq.

• S4 Dataset: mRNA_Differential_Expression.txt

Differential mRNA expression.
A tab-delimited text format file tabulating differential expression of 11,457 autosomal and X chromosome mRNAs in the 6p+12p, 7p, and Xq tensor GSVD classes. The mRNA expression profiles of 394 of the 397 patients in the discovery and validation sets are:

• mRNA_Expression.txt

• S5 Dataset: microRNA_Differential_Expression.txt

Differential microRNA expression.
A tab-delimited text format file tabulating differential expression of 639 autosomal and X chromosome microRNAs in the 6p+12p, 7p, and Xq tensor GSVD classes. The microRNA expression profiles of 395 patients are:

• microRNA_Expression.txt

• S6 Dataset: Protein_Differential_Expression.txt

Differential protein expression.
A tab-delimited text format file tabulating differential expression of 175 antibodies that probe for 136 autosomal and X chromosome proteins in the 6p+12p, 7p, and Xq tensor GSVD classes. The protein expression profiles of 282 patients are:

• Protein_Expression.txt