Predicting phenotypes from microarrays using amplified, initially marginal, eigenvector regression

Abstract

MotivationThe discovery of relationships between gene expression measurements and phenotypic responses is hampered by both computational and statistical impediments. Conventional statistical methods are less than ideal because they either fail to select relevant genes, predict poorly, ignore the unknown interaction structure between genes, or are computationally intractable. Thus, the creation of new methods which can handle many expression measurements on relatively small numbers of patients while also uncovering gene–gene relationships and predicting well is desirable.ResultsWe develop a new technique for using the marginal relationship between gene expression measurements and patient survival outcomes to identify a small subset of genes which appear highly relevant for predicting survival, produce a low-dimensional embedding based on this small subset, and amplify this embedding with information from the remaining genes. We motivate our methodology by using gene expression measurements to predict survival time for patients with diffuse large B-cell lymphoma, illustrate the behavior of our methodology on carefully constructed synthetic examples, and test it on a number of other gene expression datasets. Our technique is computationally tractable, generally outperforms other methods, is extensible to other phenotypes, and also identifies different genes (relative to existing methods) for possible future study.Availability and ImplementationAll of the code and data are available at http://mypage.iu.edu/∼dajmcdon/research/.Supplementary information Supplementary material is available at Bioinformatics online.

Sufficient principal component regression for pattern discovery in transcriptomic data

“…More recent work has attempted to avoid this assumption. Ding and McDonald (2017) uses the initially selected set of features to approximate the information lost in the screening step via techniques from numerical linear algebra. An alternative discussed in Piironen and Vehtari (2018) iterates the screening step with the prediction step, adding back features which correlate with the residual.…”

“…The Oracle estimator uses OLS on the true features and serves as a natural baseline: it uses information unavailable to the analyst (the true genes) but represents the best method were that information available. We also present results for Lasso ( Tibshirani, 1996 ), Ridge ( Hoerl and Kennard, 1970 ), Elastic Net ( Zou and Hastie, 2005 ), SPC ( Bair et al , 2006 ), AIMER ( Ding and McDonald, 2017 ), ISPCA ( Piironen and Vehtari, 2018 ) and PCR using FPS directly without feature screening (using Algorithm 1 without Steps 9–11). For ISPCA, we use the R package to estimate the principal components before performing regression.…”

Sufficient principal component regression for pattern discovery in transcriptomic data

“…The Oracle estimator uses ordinary least squares (OLS) on the true features and serves as a natural baseline: it uses information unavailable to the analyst (the true genes) but represents the best method were that information available. We also present results for Lasso [46], Ridge [26], Elastic Net [56], SPC [6], AIMER [15], ISPCA [43], and PCR using FPS directly without feature screening (using Algorithm 1 without step 9, 10 and 11). For ISPCA, we use the dimreduce R package to estimate the principal components before performing regression.…”

“…The first setting is designed to show the advantages of SuffPCR relative to alternative methods, especially SPC. We note that other methods that employ screening by the marginal correlation [15,43] will have similar deficiencies. Because SPC works well if Equation (1) holds, we design Σ to violate this condition.…”

SMSSVD: SubMatrix Selection Singular Value Decomposition

“…There exist different methods aimed at signal reconstruction and deconvolution of the resulting high dimensional and complex datasets, but these methods almost always contain parameters that need to be estimated or present other types of ad hoc features. Developed specifically for Omics data and more particularly gene expression data such methods include the gene shaving method (Hastie et al , 2000), tree harvesting (Hastie et al , 2001), supervised principal components (Bair and Tibshirani, 2004) and amplified marginal eigenvector regression (Ding and McDonald, 2017). They employ widely different strategies to deal with the ubiquitous P ≫ N (many more variables than samples) problem in omics data.…”