High-dimensional Array Data Research Articles

Good practice guidelines for biomarker discovery from array data: a case study for breast cancer prognosis

BackgroundBiomarker discovery holds the promise for advancing personalized medicine as the biomarkers can help match patients to optimal treatment to improve patient outcomes. However, serious concerns have been raised because very few molecular biomarkers or signatures discovered from high dimensional array data can be successfully validated and applied to clinical use. We propose good practice guidelines as well as a novel tool for biomarker discovery and use breast cancer prognosis as a case study to illustrate the proposed approach.ResultsWe applied the proposed approach to a publicly available breast cancer prognosis dataset and identified small numbers of predictive markers for patient subpopulations stratified by clinical variables. Results from an independent cross-platform validation set show that our model compares favorably to other gene signature and clinical variable based prognostic tools. About half of the discovered candidate markers can individually achieve very good performance, which further demonstrate the high quality of feature selection. These candidate markers perform extremely well for young patient with estrogen receptor-positive, lymph node-negative early stage breast cancers, suggesting a distinct subset of these patients identified by these markers is actually at high risk of recurrence and may benefit from more aggressive treatment than cur-rent practice.ConclusionThe results show that by following good practice guidelines, we can identify highly predictive genes in high dimensional breast cancer array data. These predictive genes have been successfully validated using an independent cross-platform dataset.

Penalized logistic regression for high-dimensional DNA methylation data with case-control studies

DNA methylation is a molecular modification of DNA that plays crucial roles in regulation of gene expression. Particularly, CpG rich regions are frequently hypermethylated in cancer tissues, but not methylated in normal tissues. However, there are not many methodological literatures of case-control association studies for high-dimensional DNA methylation data, compared with those of microarray gene expression. One key feature of DNA methylation data is a grouped structure among CpG sites from a gene that are possibly highly correlated. In this article, we proposed a penalized logistic regression model for correlated DNA methylation CpG sites within genes from high-dimensional array data. Our regularization procedure is based on a combination of the l(1) penalty and squared l(2) penalty on degree-scaled differences of coefficients of CpG sites within one gene, so it induces both sparsity and smoothness with respect to the correlated regression coefficients. We combined the penalized procedure with a stability selection procedure such that a selection probability of each regression coefficient was provided which helps us make a stable and confident selection of methylation CpG sites that are possibly truly associated with the outcome. Using simulation studies we demonstrated that the proposed procedure outperforms existing main-stream regularization methods such as lasso and elastic-net when data is correlated within a group. We also applied our method to identify important CpG sites and corresponding genes for ovarian cancer from over 20 000 CpGs generated from Illumina Infinium HumanMethylation27K Beadchip. Some genes identified are potentially associated with cancers.

About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.