Background: Validation of a novel gene expression signature in independent data sets is a critical step in the development of a clinically useful test for cancer patient risk-stratification. However, validation is often unconvincing because the size of the test set is typically small. To overcome this problem we used publicly available breast cancer gene expression data sets and a novel approach to data fusion, in order to validate a new breast tumor intrinsic list. Results: A 105-tumor training set containing 26 sample pairs was used to derive a new breast tumor intrinsic gene list. This intrinsic list contained 1300 genes and a proliferation signature that was not present in previous breast intrinsic gene sets. We tested this list as a survival predictor on a data set of 311 tumors compiled from three independent microarray studies that were fused into a single data set using Distance Weighted Discrimination. When the new intrinsic gene set was used to hierarchically cluster this combined test set, tumors were grouped into LumA, LumB, Basal-like, HER2+/ER-, and Normal Breast-like tumor subtypes that we demonstrated in previous datasets. These subtypes were associated with significant differences in Relapse-Free and Overall Survival. Multivariate Cox analysis of the combined test set showed that the intrinsic subtype classifications added significant prognostic information that was independent of standard clinical predictors. From the combined test set, we developed an objective and unchanging classifier based upon five intrinsic subtype mean expression profiles (i.e. centroids), which is designed for single sample predictions (SSP). The SSP approach was applied to two additional independent data sets and consistently predicted survival in both systemically treated and untreated patient groups. Conclusion: This study validates the "breast tumor intrinsic" subtype classification as an objective means of tumor classification that should be translated into a clinical assay for further retrospective and prospective validation. In addition, our method of combining existing data sets can be used to robustly validate the potential clinical value of any new gene expression profile.

Research in several fields now requires the analysis of data sets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introduce Joint and Individual Variation Explained (JIVE), a general decomposition of variation for the integrated analysis of such data sets. The decomposition consists of three terms: a low-rank approximation capturing joint variation across data types, low-rank approximations for structured variation individual to each data type, and residual noise. JIVE quantifies the amount of joint variation between data types, reduces the dimensionality of the data and provides new directions for the visual exploration of joint and individual structures. The proposed method represents an extension of Principal Component Analysis and has clear advantages over popular two-block methods such as Canonical Correlation Analysis and Partial Least Squares. A JIVE analysis of gene expression and miRNA data on Glioblastoma Multiforme tumor samples reveals gene–miRNA associations and provides better characterization of tumor types. Data and software are available at https://genome.unc.edu/jive/.

An exact and easily computable expression for the mean integrated squared error (MISE) for the kernel estimator of a general normal mixture density, is given for Gaussian kernels of arbitrary order. This provides a powerful new way of understanding density estimation which complements the usual tools of simulation and asymptotic analysis. The family of normal mixture densities is very flexible and the formulae derived allow simple exact analysis for a wide variety of density shapes. A number of applications of this method giving important new insights into kernel density estimation are presented. Among these is the discovery that the usual asymptotic approximations to the MISE can be quite inaccurate, especially when the underlying density contains substantial fine structure and also strong evidence that the practical importance of higher order kernels is surprisingly small for moderate sample sizes.

Motivation: Systematic differences due to experimental features of microarray experiments are present in most large microarray data sets. Many different experimental features can cause biases including different sources of RNA, different production lots of microarrays or different microarray platforms. These systematic effects present a substantial hurdle to the analysis of microarray data. Results: We present here a new method for the identification and adjustment of systematic biases that are present within microarray data sets. Our approach is based on modern statistical discrimination methods and is shown to be very effective in removing systematic biases present in a previously published breast tumor cDNA microarray data set. The new method of ‘Distance Weighted Discrimination (DWD)’ is shown to be better than Support Vector Machines and Singular Value Decomposition for the adjustment of systematic microarray effects. In addition, it is shown to be of general use as a tool for the discrimination of systematic problems present in microarray data sets, including the merging of two breast tumor data sets completed on different microarray platforms. Availability: Matlab software to perform DWD can be retrieved from https://genome.unc.edu/pubsup/dwd/ Supplementary information: The complete figures that represent the cluster diagrams in Figure 6 and other figures are available at https://genome.unc.edu/pubsup/dwd/