Improving missing value estimation in microarray data with gene ontology

MOTIVATION: Gene expression microarray experiments produce datasets with frequent missing expression values. Accurate estimation of missing values is an important prerequisite for efficient data analysis as many statistical and machine learning techniques either require a complete dataset or their results are significantly dependent on the quality of such estimates. A limitation of the existing estimation methods for microarray data is that they use no external information but the estimation is based solely on the expression data. We hypothesized that utilizing a priori information on functional similarities available from public databases facilitates the missing value estimation. RESULTS: We investigated whether semantic similarity originating from gene ontology (GO) annotations could improve the selection of relevant genes for missing value estimation. The relative contribution of each information source was automatically estimated from the data using an adaptive weight selection procedure. Our experimental results in yeast cDNA microarray datasets indicated that by considering GO information in the k-nearest neighbor algorithm we can enhance its performance considerably, especially when the number of experimental conditions is small and the percentage of missing values is high. The increase of performance was less evident with a more sophisticated estimation method. We conclude that even a small proportion of annotated genes can provide improvements in data quality significant for the eventual interpretation of the microarray experiments. AVAILABILITY: Java and Matlab codes are available on request from the authors. SUPPLEMENTARY MATERIAL: Available online at http://users.utu.fi/jotatu/GOImpute.html.     

Integrative missing value estimation for microarray data

Background  

Missing value estimation is an important preprocessing step in microarray analysis. Although several methods have been developed to solve this problem, their performance is unsatisfactory for datasets with high rates of missing data, high measurement noise, or limited numbers of samples. In fact, more than 80% of the time-series datasets in Stanford Microarray Database contain less than eight samples.     

Collateral missing value imputation: a new robust missing value estimation algorithm for microarray data

MOTIVATION: Microarray data are used in a range of application areas in biology, although often it contains considerable numbers of missing values. These missing values can significantly affect subsequent statistical analysis and machine learning algorithms so there is a strong motivation to estimate these values as accurately as possible before using these algorithms. While many imputation algorithms have been proposed, more robust techniques need to be developed so that further analysis of biological data can be accurately undertaken. In this paper, an innovative missing value imputation algorithm called collateral missing value estimation (CMVE) is presented which uses multiple covariance-based imputation matrices for the final prediction of missing values. The matrices are computed and optimized using least square regression and linear programming methods. RESULTS: The new CMVE algorithm has been compared with existing estimation techniques including Bayesian principal component analysis imputation (BPCA), least square impute (LSImpute) and K-nearest neighbour (KNN). All these methods were rigorously tested to estimate missing values in three separate non-time series (ovarian cancer based) and one time series (yeast sporulation) dataset. Each method was quantitatively analyzed using the normalized root mean square (NRMS) error measure, covering a wide range of randomly introduced missing value probabilities from 0.01 to 0.2. Experiments were also undertaken on the yeast dataset, which comprised 1.7% actual missing values, to test the hypothesis that CMVE performed better not only for randomly occurring but also for a real distribution of missing values. The results confirmed that CMVE consistently demonstrated superior and robust estimation capability of missing values compared with other methods for both series types of data, for the same order of computational complexity. A concise theoretical framework has also been formulated to validate the improved performance of the CMVE algorithm. AVAILABILITY: The CMVE software is available upon request from the authors.     

Improving missing value imputation of microarray data by using spot quality weights

Background  

Microarray technology has become popular for gene expression profiling, and many analysis tools have been developed for data interpretation. Most of these tools require complete data, but measurement values are often missing A way to overcome the problem of incomplete data is to impute the missing data before analysis. Many imputation methods have been suggested, some na?ve and other more sophisticated taking into account correlation in data. However, these methods are binary in the sense that each spot is considered either missing or present. Hence, they are depending on a cutoff separating poor spots from good spots. We suggest a different approach in which a continuous spot quality weight is built into the imputation methods, allowing for smooth imputations of all spots to larger or lesser degree.     

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     

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.     

A Bayesian missing value estimation method for gene expression profile data

MOTIVATION: Gene expression profile analyses have been used in numerous studies covering a broad range of areas in biology. When unreliable measurements are excluded, missing values are introduced in gene expression profiles. Although existing multivariate analysis methods have difficulty with the treatment of missing values, this problem has received little attention. There are many options for dealing with missing values, each of which reaches drastically different results. Ignoring missing values is the simplest method and is frequently applied. This approach, however, has its flaws. In this article, we propose an estimation method for missing values, which is based on Bayesian principal component analysis (BPCA). Although the methodology that a probabilistic model and latent variables are estimated simultaneously within the framework of Bayes inference is not new in principle, actual BPCA implementation that makes it possible to estimate arbitrary missing variables is new in terms of statistical methodology. RESULTS: When applied to DNA microarray data from various experimental conditions, the BPCA method exhibited markedly better estimation ability than other recently proposed methods, such as singular value decomposition and K-nearest neighbors. While the estimation performance of existing methods depends on model parameters whose determination is difficult, our BPCA method is free from this difficulty. Accordingly, the BPCA method provides accurate and convenient estimation for missing values. AVAILABILITY: The software is available at http://hawaii.aist-nara.ac.jp/~shige-o/tools/.     

Iterated local least squares microarray missing value imputation

Microarray gene expression data often contains multiple missing values due to various reasons. However, most of gene expression data analysis algorithms require complete expression data. Therefore, accurate estimation of the missing values is critical to further data analysis. In this paper, an Iterated Local Least Squares Imputation (ILLSimpute) method is proposed for estimating missing values. Two unique features of ILLSimpute method are: ILLSimpute method does not fix a common number of coherent genes for target genes for estimation purpose, but defines coherent genes as those within a distance threshold to the target genes. Secondly, in ILLSimpute method, estimated values in one iteration are used for missing value estimation in the next iteration and the method terminates after certain iterations or the imputed values converge. Experimental results on six real microarray datasets showed that ILLSimpute method performed at least as well as, and most of the time much better than, five most recent imputation methods.     

The influence of missing value imputation on detection of differentially expressed genes from microarray data

MOTIVATION: Missing values are problematic for the analysis of microarray data. Imputation methods have been compared in terms of the similarity between imputed and true values in simulation experiments and not of their influence on the final analysis. The focus has been on missing at random, while entries are missing also not at random. RESULTS: We investigate the influence of imputation on the detection of differentially expressed genes from cDNA microarray data. We apply ANOVA for microarrays and SAM and look to the differentially expressed genes that are lost because of imputation. We show that this new measure provides useful information that the traditional root mean squared error cannot capture. We also show that the type of missingness matters: imputing 5% missing not at random has the same effect as imputing 10-30% missing at random. We propose a new method for imputation (LinImp), fitting a simple linear model for each channel separately, and compare it with the widely used KNNimpute method. For 10% missing at random, KNNimpute leads to twice as many lost differentially expressed genes as LinImp. AVAILABILITY: The R package for LinImp is available at http://folk.uio.no/idasch/imp.     

Missing value estimation for DNA microarray gene expression data by Support Vector Regression imputation and orthogonal coding scheme

Background  

Gene expression profiling has become a useful biological resource in recent years, and it plays an important role in a broad range of areas in biology. The raw gene expression data, usually in the form of large matrix, may contain missing values. The downstream analysis methods that postulate complete matrix input are thus not applicable. Several methods have been developed to solve this problem, such as K nearest neighbor impute method, Bayesian principal components analysis impute method, etc. In this paper, we introduce a novel imputing approach based on the Support Vector Regression (SVR) method. The proposed approach utilizes an orthogonal coding input scheme, which makes use of multi-missing values in one row of a certain gene expression profile and imputes the missing value into a much higher dimensional space, to obtain better performance.     

Improving the statistical detection of regulated genes from microarray data using intensity-based variance estimation

Background  

Gene microarray technology provides the ability to study the regulation of thousands of genes simultaneously, but its potential is limited without an estimate of the statistical significance of the observed changes in gene expression. Due to the large number of genes being tested and the comparatively small number of array replicates (e.g., N = 3), standard statistical methods such as the Student's t-test fail to produce reliable results. Two other statistical approaches commonly used to improve significance estimates are a penalized t-test and a Z-test using intensity-dependent variance estimates.     

SVDMAN--singular value decomposition analysis of microarray data

SUMMARY: We have developed two novel methods for Singular Value Decomposition analysis (SVD) of microarray data. The first is a threshold-based method for obtaining gene groups, and the second is a method for obtaining a measure of confidence in SVD analysis. Gene groups are obtained by identifying elements of the left singular vectors, or gene coefficient vectors, that are greater in magnitude than the threshold W N(-1/2), where N is the number of genes, and W is a weight factor whose default value is 3. The groups are non-exclusive and may contain genes of opposite (i.e. inversely correlated) regulatory response. The confidence measure is obtained by systematically deleting assays from the data set, interpolating the SVD of the reduced data set to reconstruct the missing assay, and calculating the Pearson correlation between the reconstructed assay and the original data. This confidence measure is applicable when each experimental assay corresponds to a value of parameter that can be interpolated, such as time, dose or concentration. Algorithms for the grouping method and the confidence measure are available in a software application called SVD Microarray ANalysis (SVDMAN). In addition to calculating the SVD for generic analysis, SVDMAN provides a new means for using microarray data to develop hypotheses for gene associations and provides a measure of confidence in the hypotheses, thus extending current SVD research in the area of global gene expression analysis.     

Kalman filtering for disease-state estimation from microarray data

MOTIVATION: In this paper, we propose using the Kalman filter (KF) as a pre-processing step in microarray-based molecular diagnosis. Incorporating the expression covariance between genes is important in such classification problems, since this represents the functional relationships that govern tissue state. Failing to fulfil such requirements may result in biologically implausible class prediction models. Here, we show that employing the KF to remove noise (while retaining meaningful covariance and thus being able to estimate the underlying biological state from microarray measurements) yields linearly separable data suitable for most classification algorithms. RESULTS: We demonstrate the utility and performance of the KF as a robust disease-state estimator on publicly available binary and multi-class microarray datasets in combination with the most widely used classification methods to date. Moreover, using popular graphical representation schemes we show that our filtered datasets also have an improved visualization capability.     

An ensemble approach to microarray data-based gene prioritization after missing value imputation

MOTIVATION: Microarrays have been widely used to discover novel disease related genes. Some types of microarray, such as cDNA arrays, usually contain a considerable portion of missing values. When missing value imputation and gene prioritization are sequentially conducted, it is necessary to consider the distribution space of prioritization scores due to the existence of missing values. We propose an ensemble approach to address this issue. A bootstrap procedure enables us to generate a resample multivariate distribution of the prioritization scores and then to obtain the expected prioritization scores. RESULTS: We used a published microarray two-sample data set to illustrate our approach. We focused on the following issues after missing value imputation: (i) concordance of gene prioritization and (ii) control of true and false positives. We compared our approach with the traditional non-ensemble approach to missing value imputation. We also evaluated the performance of non-imputation approach when the theoretical test distribution was available. The results showed that the ensemble imputation approach provided clearly improved performances in the concordance of gene prioritization and the control of true/false positives, especially when sample sizes were about 5-10 per group and missing rates were about 10-20%, which was a common situation for cDNA microarray studies. AVAILABILITY: The Matlab codes are freely available at http://home.gwu.edu/~ylai/research/Missing.     

Towards better accuracy for missing value estimation of epistatic miniarray profiling data by a novel ensemble approach

Epistatic miniarray profiling (E-MAP) is a powerful tool for analyzing gene functions and their biological relevance. However, E-MAP data suffers from large proportion of missing values, which often results in misleading and biased analysis results. It is urgent to develop effective missing value estimation methods for E-MAP. Although several independent algorithms can be applied to achieve this goal, their performance varies significantly on different datasets, indicating different algorithms having their own advantages and disadvantages. In this paper, we propose a novel ensemble approach EMDI based on the high-level diversity to impute missing values that consists of two global and four local base estimators. Experimental results on five E-MAP datasets show that EMDI outperforms all single base algorithms, demonstrating an appropriate combination providing complementarity among different methods. Comparison results between several fusion strategies also demonstrate that the proposed high-level diversity scheme is superior to others. EMDI is freely available at www.csbio.sjtu.edu.cn/bioinf/EMDI/.