Significant probelets and corresponding tumor and normal arraylets uncovered by GSVD of the patient-matched GBM and normal aCGH profiles.

<p>(<i>a</i>) Plot of the second tumor arraylet describes a global pattern of tumor-exclusive co-occurring CNAs across the tumor probes. The probes are ordered, and their copy numbers are colored, according to each probe's chromosomal location. Segments (black lines) identified by circular binary segmentation (CBS) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Olshen1" target="_blank">[20]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Venkatraman1" target="_blank">[21]</a> include most known GBM-associated focal CNAs (black), e.g., <i>EGFR</i> amplification. CNAs previously unrecognized in GBM (red) include an amplification of a segment containing the biochemically putative drug target-encoding <i>TLK2</i>. (<i>b</i>) Plot of the second most tumor-exclusive probelet, which is also the most significant probelet in the tumor dataset (Figure S1<i>a</i> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), describes the corresponding variation across the patients. The patients are ordered and classified according to each patient's relative copy number in this probelet. There are 227 patients (blue) with high (0.02) and 23 patients (red) with low, approximately zero, numbers in the second probelet. One patient (gray) remains unclassified with a large negative (−0.02) number. This classification significantly correlates with GBM survival times (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g003" target="_blank">Figure 3<i>a</i></a> and Table S1 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>). (<i>c</i>) Raster display of the tumor dataset, with relative gain (red), no change (black) and loss (green) of DNA copy numbers, shows the correspondence between the GBM profiles and the second probelet and tumor arraylet. Chromosome 7 gain and losses of chromosomes 9p and 10, which are dominant in the second tumor arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>a</i></a>), are negligible in the patients with low copy numbers in the second probelet, but distinct in the remaining patients (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>b</i></a>). This illustrates that the copy numbers listed in the second probelet correspond to the weights of the second tumor arraylet in the GBM profiles of the patients. (<i>d</i>) Plot of the 246th normal arraylet describes an X chromosome-exclusive amplification across the normal probes. (<i>e</i>) Plot of the 246th probelet, which is approximately common to both the normal and tumor datasets, and is the second most significant in the normal dataset (Figure S1<i>b</i> in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), describes the corresponding copy-number amplification in the female (red) relative to the male (blue) patients. Classification of the patients by the 246th probelet agrees with the copy-number gender assignments (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-t001" target="_blank">Table 1</a> and Figure S9 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098.s001" target="_blank">Appendix S1</a>), also for three patients with missing TCGA gender annotations and three additional patients with conflicting TCGA annotations and copy-number gender assignments. (<i>f</i>) Raster display of the normal dataset shows the correspondence between the normal profiles and the 246th probelet and normal arraylet. X chromosome amplification, which is dominant in the 246th normal arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>d</i></a>), is distinct in the female but nonexisting in the male patients (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>e</i></a>). Note also that although the tumor samples exhibit female-specific X chromosome amplification (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>c</i></a>), the second tumor arraylet (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone-0030098-g002" target="_blank">Figure 2<i>a</i></a>) exhibits an unsegmented X chromosome copy-number distribution, that is approximately centered at zero with a relatively small width.</p

Survival analyses of the three sets of patients classified by GSVD, age at diagnosis or both.

<p>(<i>a</i>) Kaplan-Meier (KM) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Kaplan1" target="_blank">[36]</a> curves for the 247 patients with TCGA annotations in the initial set of 251 patients, classified by copy numbers in the second probelet, which is computed by GSVD for the 251 patients, show a median survival time difference of 16 months, with the corresponding log-rank test <i>P</i>-value . The univariate Cox <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Cox1" target="_blank">[37]</a> proportional hazard ratio is 2.3, with a <i>P</i>-value (Table S1), meaning that high relative copy numbers in the second probelet confer more than twice the hazard of low numbers. The <i>P</i>-values are calculated without adjusting for multiple comparisons <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Rothman1" target="_blank">[38]</a>. (<i>b</i>) Survival analyses of the 247 patients classified by age, i.e., 50 or 50 years old at diagnosis, show that the prognostic contribution of age, with a KM median survival time difference of 11 months and a univariate Cox hazard ratio of 2, is comparable to that of GSVD. (<i>c</i>) Survival analyses of the 247 patients classified by both GSVD and age, show similar multivariate Cox hazard ratios, of 1.8 and 1.7, that do not differ significantly from the corresponding univariate hazard ratios, of 2.3 and 2, respectively. This means that GSVD and age are independent prognostic predictors. With a KM median survival time difference of 22 months, GSVD and age combined make a better predictor than age alone. (<i>d</i>) Survival analyses of the 334 patients with TCGA annotations and a GSVD classification in the inclusive confirmation set of 344 patients, classified by copy numbers in the second probelet, which is computed by GSVD for the 344 patients, show a KM median survival time difference of 16 months and a univariate hazard ratio of 2.4, and confirm the survival analyses of the initial set of 251 patients. (<i>e</i>) Survival analyses of the 334 patients classified by age confirm that the prognostic contribution of age, with a KM median survival time difference of 10 months and a univariate hazard ratio of 2, is comparable to that of GSVD. (<i>f</i>) Survival analyses of the 334 patients classified by both GSVD and age, show similar multivariate Cox hazard ratios, of 1.9 and 1.8, that do not differ significantly from the corresponding univariate hazard ratios, and a KM median survival time difference of 22 months, with the corresponding log-rank test <i>P</i>-value . This confirms that the prognostic contribution of GSVD is independent of age, and that combined with age, GSVD makes a better predictor than age alone. (<i>g</i>) Survival analyses of the 183 patients with a GSVD classification in the independent validation set of 184 patients, classified by correlations of each patient's GBM profile with the second tumor arraylet, which is computed by GSVD for the 251 patients, show a KM median survival time difference of 12 months and a univariate hazard ratio of 2.9, and validate the survival analyses of the initial set of 251 patients. (<i>h</i>) Survival analyses of the 183 patients classified by age validate that the prognostic contribution of age is comparable to that of GSVD. (<i>i</i>) Survival analyses of the 183 patients classified by both GSVD and age, show similar multivariate Cox hazard ratios, of 2 and 2.2, and a KM median survival time difference of 41 months, with the corresponding log-rank test <i>P</i>-value . This validates that the prognostic contribution of GSVD is independent of age, and that combined with age, GSVD makes a better predictor than age alone, also for patients with measured GBM aCGH profiles in the absence of matched normal profiles.</p

Enrichment of the significant probelets in TCGA annotations.

<p>Enrichment of the significant probelets in TCGA annotations.</p

Generalized singular value decomposition (GSVD) of the TCGA patient-matched tumor and normal aCGH profiles.

<p>The structure of the patient-matched but probe-independent tumor and normal datasets and , of the initial set of  = 251 patients, i.e., -arrays  = 212,696-tumor probes and  = 211,227-normal probes, is of an order higher than that of a single matrix. The patients, the tumor and normal probes as well as the tissue types, each represent a degree of freedom. Unfolded into a single matrix, some of the degrees of freedom are lost and much of the information in the datasets might also be lost. The GSVD simultaneously separates the paired datasets into paired weighted sums of outer products of two patterns each: One pattern of copy-number variation across the patients, i.e., a “probelet” , which is identical for both the tumor and normal datasets, combined with either the corresponding tumor-specific pattern of copy-number variation across the tumor probes, i.e., the “tumor arraylet” , or the corresponding normal-specific pattern across the normal probes, i.e., the “normal arraylet” (Equation 1). This is depicted in a raster display, with relative copy-number gain (red), no change (black) and loss (green), explicitly showing only the first though the 10th and the 242nd through the 251st probelets and corresponding tumor and normal arraylets, which capture 52% and 71% of the information in the tumor and normal dataset, respectively. The significance of the probelet in the tumor dataset relative to its significance in the normal dataset is defined in terms of an “angular distance” that is proportional to the ratio of these weights (Equation 4). This is depicted in a bar chart display, showing that the first and second probelets are almost exclusive to the tumor dataset with angular distances 2/9, the 247th to 251st probelets are approximately exclusive to the normal dataset with angular distances , and the 246th probelet is relatively common to the normal and tumor datasets with an angular distance . We find and confirm that the second most tumor-exclusive probelet, which is also the most significant probelet in the tumor dataset, significantly correlates with GBM prognosis. The corresponding tumor arraylet describes a global pattern of tumor-exclusive co-occurring CNAs, including most known GBM-associated changes in chromosome numbers and focal CNAs, as well as several previously unreported CNAs, including the biochemically putative drug target-encoding <i>TLK2</i> <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Heidenblad1" target="_blank">[22]</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Sillj1" target="_blank">[25]</a>. We find and validate that a negligible weight of the global pattern in a patient's GBM aCGH profile is indicative of a significantly longer GBM survival time. It was shown that the GSVD provides a mathematical framework for comparative modeling of DNA microarray data from two organisms <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Alter1" target="_blank">[12]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Alter2" target="_blank">[39]</a>. Recent experimental results <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Omberg1" target="_blank">[40]</a> verify a computationally predicted genome-wide mode of regulation <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Alter3" target="_blank">[41]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030098#pone.0030098-Omberg2" target="_blank">[42]</a>, and demonstrate that GSVD modeling of DNA microarray data can be used to correctly predict previously unknown cellular mechanisms. This GSVD comparative modeling of aCGH data from patient-matched tumor and normal samples, therefore, draws a mathematical analogy between the prediction of cellular modes of regulation and the prognosis of cancers.</p