Reconstruction of genetic association networks from microarray data: a partial least squares approach

MOTIVATION: Gene association/interaction networks provide vast amounts of information about essential processes inside the cell. A complete picture of gene-gene associations/interactions would open new horizons for biologists, ranging from pure appreciation to successful manipulation of biological pathways for therapeutic purposes. Therefore, identification of important biological complexes whose members (genes and their products proteins) interact with each other is of prime importance. Numerous experimental methods exist but, for the most part, they are costly and labor intensive. Computational techniques, such as the one proposed in this work, provide a quick 'budget' solution that can be used as a screening tool before more expensive techniques are attempted. Here, we introduce a novel computational method based on the partial least squares (PLS) regression technique for reconstruction of genetic networks from microarray data. RESULTS: The proposed PLS method is shown to be an effective screening procedure for the detection of gene-gene interactions from microarray data. Both simulated and real microarray experiments show that the PLS-based approach is superior to its competitors both in terms of performance and applicability. AVAILABILITY: R code is available from the supplementary web-site whose URL is given below.     

Tumor classification by partial least squares using microarray gene expression data

MOTIVATION: One important application of gene expression microarray data is classification of samples into categories, such as the type of tumor. The use of microarrays allows simultaneous monitoring of thousands of genes expressions per sample. This ability to measure gene expression en masse has resulted in data with the number of variables p(genes) far exceeding the number of samples N. Standard statistical methodologies in classification and prediction do not work well or even at all when N < p. Modification of existing statistical methodologies or development of new methodologies is needed for the analysis of microarray data. RESULTS: We propose a novel analysis procedure for classifying (predicting) human tumor samples based on microarray gene expressions. This procedure involves dimension reduction using Partial Least Squares (PLS) and classification using Logistic Discrimination (LD) and Quadratic Discriminant Analysis (QDA). We compare PLS to the well known dimension reduction method of Principal Components Analysis (PCA). Under many circumstances PLS proves superior; we illustrate a condition when PCA particularly fails to predict well relative to PLS. The proposed methods were applied to five different microarray data sets involving various human tumor samples: (1) normal versus ovarian tumor; (2) Acute Myeloid Leukemia (AML) versus Acute Lymphoblastic Leukemia (ALL); (3) Diffuse Large B-cell Lymphoma (DLBCLL) versus B-cell Chronic Lymphocytic Leukemia (BCLL); (4) normal versus colon tumor; and (5) Non-Small-Cell-Lung-Carcinoma (NSCLC) versus renal samples. Stability of classification results and methods were further assessed by re-randomization studies.     

Iterative partial least squares with right-censored data analysis: a comparison to other dimension reduction techniques

In the linear model with right-censored responses and many potential explanatory variables, regression parameter estimates may be unstable or, when the covariates outnumber the uncensored observations, not estimable. We propose an iterative algorithm for partial least squares, based on the Buckley-James estimating equation, to estimate the covariate effect and predict the response for a future subject with a given set of covariates. We use a leave-two-out cross-validation method for empirically selecting the number of components in the partial least-squares fit that approximately minimizes the error in estimating the covariate effect of a future observation. Simulation studies compare the methods discussed here with other dimension reduction techniques. Data from the AIDS Clinical Trials Group protocol 333 are used to motivate the methodology.     

Application of partial least squares discriminant analysis to two-dimensional difference gel studies in expression proteomics

Two-dimensional difference gel electrophoresis (DIGE) is a tool for measuring changes in protein expression between samples involving pre-electrophoretic labeling ith cyanine dyes. In multi-gel experiments, univariate statistical tests have been used to identify differential expression between sample types by looking for significant changes in spot volume. Multivariate statistical tests, which look for correlated changes between sample types, provide an alternate approach for identifying spots with differential expression. Partial least squares-discriminant analysis (PLS-DA), a multivariate statistical approach, was combined with an iterative threshold process to identify which protein spots had the greatest contribution to the model, and compared to univariate test for three datasets. This included one dataset where no biological difference was expected. The novel multivariate approach, detailed here, represents a method to complement the univariate approach in identification of differentially expressed protein spots. This new approach has the advantages of reduced risk of false-positives and the identification of spots that are significantly altered in terms of correlated expression rather than absolute expression values.     

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis

MOTIVATION: Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. RESULTS: In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. AVAILABILITY: The software is available as supplementary material.     

LSimpute: accurate estimation of missing values in microarray data with least squares methods

Microarray experiments generate data sets with information on the expression levels of thousands of genes in a set of biological samples. Unfortunately, such experiments often produce multiple missing expression values, normally due to various experimental problems. As many algorithms for gene expression analysis require a complete data matrix as input, the missing values have to be estimated in order to analyze the available data. Alternatively, genes and arrays can be removed until no missing values remain. However, for genes or arrays with only a small number of missing values, it is desirable to impute those values. For the subsequent analysis to be as informative as possible, it is essential that the estimates for the missing gene expression values are accurate. A small amount of badly estimated missing values in the data might be enough for clustering methods, such as hierachical clustering or K-means clustering, to produce misleading results. Thus, accurate methods for missing value estimation are needed. We present novel methods for estimation of missing values in microarray data sets that are based on the least squares principle, and that utilize correlations between both genes and arrays. For this set of methods, we use the common reference name LSimpute. We compare the estimation accuracy of our methods with the widely used KNNimpute on three complete data matrices from public data sets by randomly knocking out data (labeling as missing). From these tests, we conclude that our LSimpute methods produce estimates that consistently are more accurate than those obtained using KNNimpute. Additionally, we examine a more classic approach to missing value estimation based on expectation maximization (EM). We refer to our EM implementations as EMimpute, and the estimate errors using the EMimpute methods are compared with those our novel methods produce. The results indicate that on average, the estimates from our best performing LSimpute method are at least as accurate as those from the best EMimpute algorithm.     

Predicting patient survival from microarray data by accelerated failure time modeling using partial least squares and LASSO

We consider the problem of predicting survival times of cancer patients from the gene expression profiles of their tumor samples via linear regression modeling of log-transformed failure times. The partial least squares (PLS) and least absolute shrinkage and selection operator (LASSO) methodologies are used for this purpose where we first modify the data to account for censoring. Three approaches of handling right censored data-reweighting, mean imputation, and multiple imputation-are considered. Their performances are examined in a detailed simulation study and compared with that of full data PLS and LASSO had there been no censoring. A major objective of this article is to investigate the performances of PLS and LASSO in the context of microarray data where the number of covariates is very large and there are extremely few samples. We demonstrate that LASSO outperforms PLS in terms of prediction error when the list of covariates includes a moderate to large percentage of useless or noise variables; otherwise, PLS may outperform LASSO. For a moderate sample size (100 with 10,000 covariates), LASSO performed better than a no covariate model (or noise-based prediction). The mean imputation method appears to best track the performance of the full data PLS or LASSO. The mean imputation scheme is used on an existing data set on lung cancer. This reanalysis using the mean imputed PLS and LASSO identifies a number of genes that were known to be related to cancer or tumor activities from previous studies.     

Surrogate variable analysis using partial least squares (SVA-PLS) in gene expression studies

MOTIVATION: In a typical gene expression profiling study, our prime objective is to identify the genes that are differentially expressed between the samples from two different tissue types. Commonly, standard analysis of variance (ANOVA)/regression is implemented to identify the relative effects of these genes over the two types of samples from their respective arrays of expression levels. But, this technique becomes fundamentally flawed when there are unaccounted sources of variability in these arrays (latent variables attributable to different biological, environmental or other factors relevant in the context). These factors distort the true picture of differential gene expression between the two tissue types and introduce spurious signals of expression heterogeneity. As a result, many genes which are actually differentially expressed are not detected, whereas many others are falsely identified as positives. Moreover, these distortions can be different for different genes. Thus, it is also not possible to get rid of these variations by simple array normalizations. This both-way error can lead to a serious loss in sensitivity and specificity, thereby causing a severe inefficiency in the underlying multiple testing problem. In this work, we attempt to identify the hidden effects of the underlying latent factors in a gene expression profiling study by partial least squares (PLS) and apply ANCOVA technique with the PLS-identified signatures of these hidden effects as covariates, in order to identify the genes that are truly differentially expressed between the two concerned tissue types. RESULTS: We compare the performance of our method SVA-PLS with standard ANOVA and a relatively recent technique of surrogate variable analysis (SVA), on a wide variety of simulation settings (incorporating different effects of the hidden variable, under situations with varying signal intensities and gene groupings). In all settings, our method yields the highest sensitivity while maintaining relatively reasonable values for the specificity, false discovery rate and false non-discovery rate. Application of our method to gene expression profiling for acute megakaryoblastic leukemia shows that our method detects an additional six genes, that are missed by both the standard ANOVA method as well as SVA, but may be relevant to this disease, as can be seen from mining the existing literature.     

Linking gene expression data with patient survival times using partial least squares

There is an increasing need to link the large amount of genotypic data, gathered using microarrays for example, with various phenotypic data from patients. The classification problem in which gene expression data serve as predictors and a class label phenotype as the binary outcome variable has been examined extensively, but there has been less emphasis in dealing with other types of phenotypic data. In particular, patient survival times with censoring are often not used directly as a response variable due to the complications that arise from censoring. We show that the issues involving censored data can be circumvented by reformulating the problem as a standard Poisson regression problem. The procedure for solving the transformed problem is a combination of two approaches: partial least squares, a regression technique that is especially effective when there is severe collinearity due to a large number of predictors, and generalized linear regression, which extends standard linear regression to deal with various types of response variables. The linear combinations of the original variables identified by the method are highly correlated with the patient survival times and at the same time account for the variability in the covariates. The algorithm is fast, as it does not involve any matrix decompositions in the iterations. We apply our method to data sets from lung carcinoma and diffuse large B-cell lymphoma studies to verify its effectiveness.     

Missing value estimation for DNA microarray gene expression data: local least squares imputation

MOTIVATION: Gene expression data often contain missing expression values. Effective missing value estimation methods are needed since many algorithms for gene expression data analysis require a complete matrix of gene array values. In this paper, imputation methods based on the least squares formulation are proposed to estimate missing values in the gene expression data, which exploit local similarity structures in the data as well as least squares optimization process. RESULTS: The proposed local least squares imputation method (LLSimpute) represents a target gene that has missing values as a linear combination of similar genes. The similar genes are chosen by k-nearest neighbors or k coherent genes that have large absolute values of Pearson correlation coefficients. Non-parametric missing values estimation method of LLSimpute are designed by introducing an automatic k-value estimator. In our experiments, the proposed LLSimpute method shows competitive results when compared with other imputation methods for missing value estimation on various datasets and percentages of missing values in the data. AVAILABILITY: The software is available at http://www.cs.umn.edu/~hskim/tools.html CONTACT: hpark@cs.umn.edu     

Missing value estimation for DNA microarray gene expression data: local least squares imputation

In our article, only a set of random positions of missing valueswas used for each dataset. However, imputation methods may     

Statistical analysis of microarray data: a Bayesian approach

The potential of microarray data is enormous. It allows us to monitor the expression of thousands of genes simultaneously. A common task with microarray is to determine which genes are differentially expressed between two samples obtained under two different conditions. Recently, several statistical methods have been proposed to perform such a task when there are replicate samples under each condition. Two major problems arise with microarray data. The first one is that the number of replicates is very small (usually 2-10), leading to noisy point estimates. As a consequence, traditional statistics that are based on the means and standard deviations, e.g. t-statistic, are not suitable. The second problem is that the number of genes is usually very large (approximately 10,000), and one is faced with an extreme multiple testing problem. Most multiple testing adjustments are relatively conservative, especially when the number of replicates is small. In this paper we present an empirical Bayes analysis that handles both problems very well. Using different parametrizations, we develop four statistics that can be used to test hypotheses about the means and/or variances of the gene expression levels in both one- and two-sample problems. The methods are illustrated using experimental data with prior knowledge. In addition, we present the result of a simulation comparing our methods to well-known statistics and multiple testing adjustments.     

Cue-signal-response analysis of TNF-induced apoptosis by partial least squares regression of dynamic multivariate data.

Biological signaling networks process extracellular cues to control important cell decisions such as death-survival, growth-quiescence, and proliferation-differentiation. After receptor activation, intracellular signaling proteins change in abundance, modification state, and enzymatic activity. Many of the proteins in signaling networks have been identified, but it is not known how signaling molecules work together to control cell decisions. To begin to address this issue, we report the use of partial least squares regression as an analytical method to glean signal-response relationships from heterogeneous multivariate signaling data collected from HT-29 human colon carcinoma cells stimulated to undergo programmed cell death. By partial least squares modeling, we relate dynamic and quantitative measurements of 20-30 intracellular signals to cell survival after treatment with tumor necrosis factor alpha (a death factor) and insulin (a survival factor). We find that partial least squares models can distinguish highly informative signals from redundant uninformative signals to generate a reduced model that retains key signaling features and signal-response relationships. In these models, measurements of biochemical characteristics, based on very different techniques (Western blots, kinase assays, etc.), are grouped together as covariates, showing that heterogenous data have been effectively fused. Importantly, informative protein predictors of cell responses are always multivariate, demonstrating the multicomponent nature of the decision process.     

Reproducibility of microarray data: a further analysis of microarray quality control (MAQC) data

Background  

Many researchers are concerned with the comparability and reliability of microarray gene expression data. Recent completion of the MicroArray Quality Control (MAQC) project provides a unique opportunity to assess reproducibility across multiple sites and the comparability across multiple platforms. The MAQC analysis presented for the conclusion of inter- and intra-platform comparability/reproducibility of microarray gene expression measurements is inadequate. We evaluate the reproducibility/comparability of the MAQC data for 12901 common genes in four titration samples generated from five high-density one-color microarray platforms and the TaqMan technology. We discuss some of the problems with the use of correlation coefficient as metric to evaluate the inter- and intra-platform reproducibility and the percent of overlapping genes (POG) as a measure for evaluation of a gene selection procedure by MAQC.     

样条变换偏最小二乘在肝癌数据分类中的应用

肝癌是中国最常见的恶性肿瘤之一。基于肿瘤基因表达谱数据的分析与研究是当今研究的热点,对于癌症的早期诊断、治疗具有十分重要的意义。针对高维小样本基因表达谱数据所显现的变量间严重共线性、类别变量与预测变量的非线性关系,采用了基于样条变换的偏最小二乘回归新技术。首先通过筛选法去除基因表达谱数据中的冗余信息,然后以3次B基样条变换实现非线性基因表达谱数据的线性化重构,随后将重构的矩阵交由偏最小二乘法构建类别变量与预测变量间的关系模型。最后,通过对肝癌肿瘤基因表达谱数据的分析,结果显示此分类模型对数据重构稳健,有效的解决了高维小样本基因表达谱数据间的过拟合和变量间的共线性,具有较高的拟合和分类正确率。     

Analysis of genetic marker-phenotype relationships by jack-knifed partial least squares regression (PLSR)

The utility of a relatively new multivariate method, bi-linear modelling by cross-validated partial least squares regression (PLSR), was investigated in the analysis of QTL. The distinguishing feature of PLSR is to reveal reliable covariance structures in data of different types with regard to the same set objects. Two matrices X (here: genetic markers) and Y (here: phenotypes) are interactively decomposed into latent variables (PLS components, or PCs) in a way which facilitates statistically reliable and graphically interpretable model building. Natural collinearities between input variables are utilized actively to stabilise the modelling, instead of being treated as a statistical problem. The importance of cross-validation/jack-knifing as an intuitively appealing way to avoid overfitting, is emphasized. Two datasets from chromosomal mapping studies of different complexity were chosen for illustration (QTL for tomato yield and for oat heading date). Results from PLSR analysis were compared to published results and to results using the package PLABQTL in these data sets. In all cases PLSR gave at least similar explained validation variances as the reported studies. An attractive feature is that PLSR allows the analysis of several traits/replicates in one analysis, and the direct visual identification of individuals with desirable marker genotypes. It is suggested that PLSR may be useful in structural and functional genomics and in marker assisted selection, particularly in cases with limited number of objects.