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 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.     

Missing value imputation for epistatic MAPs

Background  

Epistatic miniarray profiling (E-MAPs) is a high-throughput approach capable of quantifying aggravating or alleviating genetic interactions between gene pairs. The datasets resulting from E-MAP experiments typically take the form of a symmetric pairwise matrix of interaction scores. These datasets have a significant number of missing values - up to 35% - that can reduce the effectiveness of some data analysis techniques and prevent the use of others. An effective method for imputing interactions would therefore increase the types of possible analysis, as well as increase the potential to identify novel functional interactions between gene pairs. Several methods have been developed to handle missing values in microarray data, but it is unclear how applicable these methods are to E-MAP data because of their pairwise nature and the significantly larger number of missing values. Here we evaluate four alternative imputation strategies, three local (Nearest neighbor-based) and one global (PCA-based), that have been modified to work with symmetric pairwise data.     

Profound influence of microarray scanner characteristics on gene expression ratios: analysis and procedure for correction

Background  

High throughput gene expression data from spotted cDNA microarrays are collected by scanning the signal intensities of the corresponding spots by dedicated fluorescence scanners. The major scanner settings for increasing the spot intensities are the laser power and the voltage of the photomultiplier tube (PMT). It is required that the expression ratios are independent of these settings. We have investigated the relationships between PMT voltage, spot intensities, and expression ratios for different scanners, in order to define an optimal scanning procedure.     

Hybrid clustering for microarray image analysis combining intensity and shape features

Background  

Image analysis is the first crucial step to obtain reliable results from microarray experiments. First, areas in the image belonging to single spots have to be identified. Then, those target areas have to be partitioned into foreground and background. Finally, two scalar values for the intensities have to be extracted. These goals have been tackled either by spot shape methods or intensity histogram methods, but it would be desirable to have hybrid algorithms which combine the advantages of both approaches.     

A robust method for estimating gene expression states using Affymetrix microarray probe level data

Background  

Microarray technology is a high-throughput method for measuring the expression levels of thousand of genes simultaneously. The observed intensities combine a non-specific binding, which is a major disadvantage with microarray data. The Affymetrix GeneChip assigned a mismatch (MM) probe with the intention of measuring non-specific binding, but various opinions exist regarding usefulness of MM measures. It should be noted that not all observed intensities are associated with expressed genes and many of those are associated with unexpressed genes, of which measured values express mere noise due to non-specific binding, cross-hybridization, or stray signals. The implicit assumption that all genes are expressed leads to poor performance of microarray data analyses. We assume two functional states of a gene - expressed or unexpressed - and propose a robust method to estimate gene expression states using an order relationship between PM and MM measures.     

Missing value imputation for microarray gene expression data using histone acetylation information

Background  

It is an important pre-processing step to accurately estimate missing values in microarray data, because complete datasets are required in numerous expression profile analysis in bioinformatics. Although several methods have been suggested, their performances are not satisfactory for datasets with high missing percentages.     

Reverse engineering gene regulatory networks from measurement with missing values

Background

Gene expression time series data are usually in the form of high-dimensional arrays. Unfortunately, the data may sometimes contain missing values: for either the expression values of some genes at some time points or the entire expression values of a single time point or some sets of consecutive time points. This significantly affects the performance of many algorithms for gene expression analysis that take as an input, the complete matrix of gene expression measurement. For instance, previous works have shown that gene regulatory interactions can be estimated from the complete matrix of gene expression measurement. Yet, till date, few algorithms have been proposed for the inference of gene regulatory network from gene expression data with missing values.

Results

We describe a nonlinear dynamic stochastic model for the evolution of gene expression. The model captures the structural, dynamical, and the nonlinear natures of the underlying biomolecular systems. We present point-based Gaussian approximation (PBGA) filters for joint state and parameter estimation of the system with one-step or two-step missing measurements. The PBGA filters use Gaussian approximation and various quadrature rules, such as the unscented transform (UT), the third-degree cubature rule and the central difference rule for computing the related posteriors. The proposed algorithm is evaluated with satisfying results for synthetic networks, in silico networks released as a part of the DREAM project, and the real biological network, the in vivo reverse engineering and modeling assessment (IRMA) network of yeast Saccharomyces cerevisiae.

Conclusion

PBGA filters are proposed to elucidate the underlying gene regulatory network (GRN) from time series gene expression data that contain missing values. In our state-space model, we proposed a measurement model that incorporates the effect of the missing data points into the sequential algorithm. This approach produces a better inference of the model parameters and hence, more accurate prediction of the underlying GRN compared to when using the conventional Gaussian approximation (GA) filters ignoring the missing data points.

     

Missing value imputation in high-dimensional phenomic data: imputable or not,and how?

Background

In modern biomedical research of complex diseases, a large number of demographic and clinical variables, herein called phenomic data, are often collected and missing values (MVs) are inevitable in the data collection process. Since many downstream statistical and bioinformatics methods require complete data matrix, imputation is a common and practical solution. In high-throughput experiments such as microarray experiments, continuous intensities are measured and many mature missing value imputation methods have been developed and widely applied. Numerous methods for missing data imputation of microarray data have been developed. Large phenomic data, however, contain continuous, nominal, binary and ordinal data types, which void application of most methods. Though several methods have been developed in the past few years, not a single complete guideline is proposed with respect to phenomic missing data imputation.

Results

In this paper, we investigated existing imputation methods for phenomic data, proposed a self-training selection (STS) scheme to select the best imputation method and provide a practical guideline for general applications. We introduced a novel concept of “imputability measure” (IM) to identify missing values that are fundamentally inadequate to impute. In addition, we also developed four variations of K-nearest-neighbor (KNN) methods and compared with two existing methods, multivariate imputation by chained equations (MICE) and missForest. The four variations are imputation by variables (KNN-V), by subjects (KNN-S), their weighted hybrid (KNN-H) and an adaptively weighted hybrid (KNN-A). We performed simulations and applied different imputation methods and the STS scheme to three lung disease phenomic datasets to evaluate the methods. An R package “phenomeImpute” is made publicly available.

Conclusions

Simulations and applications to real datasets showed that MICE often did not perform well; KNN-A, KNN-H and random forest were among the top performers although no method universally performed the best. Imputation of missing values with low imputability measures increased imputation errors greatly and could potentially deteriorate downstream analyses. The STS scheme was accurate in selecting the optimal method by evaluating methods in a second layer of missingness simulation. All source files for the simulation and the real data analyses are available on the author’s publication website.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0346-6) contains supplementary material, which is available to authorized users.     

Reuse of imputed data in microarray analysis increases imputation efficiency

Background  

The imputation of missing values is necessary for the efficient use of DNA microarray data, because many clustering algorithms and some statistical analysis require a complete data set. A few imputation methods for DNA microarray data have been introduced, but the efficiency of the methods was low and the validity of imputed values in these methods had not been fully checked.     

Two-stage normalization using background intensities in cDNA microarray data

Background  

In the microarray experiment, many undesirable systematic variations are commonly observed. Normalization is the process of removing such variation that affects the measured gene expression levels. Normalization plays an important role in the earlier stage of microarray data analysis. The subsequent analysis results are highly dependent on normalization. One major source of variation is the background intensities. Recently, some methods have been employed for correcting the background intensities. However, all these methods focus on defining signal intensities appropriately from foreground and background intensities in the image analysis. Although a number of normalization methods have been proposed, no systematic methods have been proposed using the background intensities in the normalization process.     

Probabilistic estimation of microarray data reliability and underlying gene expression

Background  

The availability of high throughput methods for measurement of mRNA concentrations makes the reliability of conclusions drawn from the data and global quality control of samples and hybridization important issues. We address these issues by an information theoretic approach, applied to discretized expression values in replicated gene expression data.     

A comparison of imputation procedures and statistical tests for the analysis of two-dimensional electrophoresis data

Background  

Numerous gel-based softwares exist to detect protein changes potentially associated with disease. The data, however, are abundant with technical and structural complexities, making statistical analysis a difficult task. A particularly important topic is how the various softwares handle missing data. To date, no one has extensively studied the impact that interpolating missing data has on subsequent analysis of protein spots.     

Quality control and quality assessment of data from surface-enhanced laser desorption/ionization (SELDI) time-of flight (TOF) mass spectrometry (MS)

Background

Proteomic profiling of complex biological mixtures by the ProteinChip technology of surface-enhanced laser desorption/ionization time-of-flight (SELDI-TOF) mass spectrometry (MS) is one of the most promising approaches in toxicological, biological, and clinic research. The reliable identification of protein expression patterns and associated protein biomarkers that differentiate disease from health or that distinguish different stages of a disease depends on developing methods for assessing the quality of SELDI-TOF mass spectra. The use of SELDI data for biomarker identification requires application of rigorous procedures to detect and discard low quality spectra prior to data analysis.

Results

The systematic variability from plates, chips, and spot positions in SELDI experiments was evaluated using biological and technical replicates. Systematic biases on plates, chips, and spots were not found. The reproducibility of SELDI experiments was demonstrated by examining the resulting low coefficient of variances of five peaks presented in all 144 spectra from quality control samples that were loaded randomly on different spots in the chips of six bioprocessor plates. We developed a method to detect and discard low quality spectra prior to proteomic profiling data analysis, which uses a correlation matrix to measure the similarities among SELDI mass spectra obtained from similar biological samples. Application of the correlation matrix to our SELDI data for liver cancer and liver toxicity study and myeloma-associated lytic bone disease study confirmed this approach as an efficient and reliable method for detecting low quality spectra.

Conclusion

This report provides evidence that systematic variability between plates, chips, and spots on which the samples were assayed using SELDI based proteomic procedures did not exist. The reproducibility of experiments in our studies was demonstrated to be acceptable and the profiling data for subsequent data analysis are reliable. Correlation matrix was developed as a quality control tool to detect and discard low quality spectra prior to data analysis. It proved to be a reliable method to measure the similarities among SELDI mass spectra and can be used for quality control to decrease noise in proteomic profiling data prior to data analysis.

     

Regularized estimation of large-scale gene association networks using graphical Gaussian models

Background  

Graphical Gaussian models are popular tools for the estimation of (undirected) gene association networks from microarray data. A key issue when the number of variables greatly exceeds the number of samples is the estimation of the matrix of partial correlations. Since the (Moore-Penrose) inverse of the sample covariance matrix leads to poor estimates in this scenario, standard methods are inappropriate and adequate regularization techniques are needed. Popular approaches include biased estimates of the covariance matrix and high-dimensional regression schemes, such as the Lasso and Partial Least Squares.     

Super-sparse principal component analyses for high-throughput genomic data

Background  

Principal component analysis (PCA) has gained popularity as a method for the analysis of high-dimensional genomic data. However, it is often difficult to interpret the results because the principal components are linear combinations of all variables, and the coefficients (loadings) are typically nonzero. These nonzero values also reflect poor estimation of the true vector loadings; for example, for gene expression data, biologically we expect only a portion of the genes to be expressed in any tissue, and an even smaller fraction to be involved in a particular process. Sparse PCA methods have recently been introduced for reducing the number of nonzero coefficients, but these existing methods are not satisfactory for high-dimensional data applications because they still give too many nonzero coefficients.     

MISC: missing imputation for single-cell RNA sequencing data

Background

Single-cell RNA sequencing (scRNA-seq) technology provides an effective way to study cell heterogeneity. However, due to the low capture efficiency and stochastic gene expression, scRNA-seq data often contains a high percentage of missing values. It has been showed that the missing rate can reach approximately 30% even after noise reduction. To accurately recover missing values in scRNA-seq data, we need to know where the missing data is; how much data is missing; and what are the values of these data.

Methods

To solve these three problems, we propose a novel model with a hybrid machine learning method, namely, missing imputation for single-cell RNA-seq (MISC). To solve the first problem, we transformed it to a binary classification problem on the RNA-seq expression matrix. Then, for the second problem, we searched for the intersection of the classification results, zero-inflated model and false negative model results. Finally, we used the regression model to recover the data in the missing elements.

Results

We compared the raw data without imputation, the mean-smooth neighbor cell trajectory, MISC on chronic myeloid leukemia data (CML), the primary somatosensory cortex and the hippocampal CA1 region of mouse brain cells. On the CML data, MISC discovered a trajectory branch from the CP-CML to the BC-CML, which provides direct evidence of evolution from CP to BC stem cells. On the mouse brain data, MISC clearly divides the pyramidal CA1 into different branches, and it is direct evidence of pyramidal CA1 in the subpopulations. In the meantime, with MISC, the oligodendrocyte cells became an independent group with an apparent boundary.

Conclusions

Our results showed that the MISC model improved the cell type classification and could be instrumental to study cellular heterogeneity. Overall, MISC is a robust missing data imputation model for single-cell RNA-seq data.

     

Haplotype frequency estimation error analysis in the presence of missing genotype data

Background  

Increasingly researchers are turning to the use of haplotype analysis as a tool in population studies, the investigation of linkage disequilibrium, and candidate gene analysis. When the phase of the data is unknown, computational methods, in particular those employing the Expectation-Maximisation (EM) algorithm, are frequently used for estimating the phase and frequency of the underlying haplotypes. These methods have proved very successful, predicting the phase-known frequencies from data for which the phase is unknown with a high degree of accuracy. Recently there has been much speculation as to the effect of unknown, or missing allelic data – a common phenomenon even with modern automated DNA analysis techniques – on the performance of EM-based methods. To this end an EM-based program, modified to accommodate missing data, has been developed, incorporating non-parametric bootstrapping for the calculation of accurate confidence intervals.     

Prediction of beta-turns at over 80% accuracy based on an ensemble of predicted secondary structures and multiple alignments

Background  

β-turn is a secondary protein structure type that plays significant role in protein folding, stability, and molecular recognition. To date, several methods for prediction of β-turns from protein sequences were developed, but they are characterized by relatively poor prediction quality. The novelty of the proposed sequence-based β-turn predictor stems from the usage of a window based information extracted from four predicted three-state secondary structures, which together with a selected set of position specific scoring matrix (PSSM) values serve as an input to the support vector machine (SVM) predictor.     

A robust approach based on Weibull distribution for clustering gene expression data

Background

Clustering is a widely used technique for analysis of gene expression data. Most clustering methods group genes based on the distances, while few methods group genes according to the similarities of the distributions of the gene expression levels. Furthermore, as the biological annotation resources accumulated, an increasing number of genes have been annotated into functional categories. As a result, evaluating the performance of clustering methods in terms of the functional consistency of the resulting clusters is of great interest.

Results

In this paper, we proposed the WDCM (Weibull Distribution-based Clustering Method), a robust approach for clustering gene expression data, in which the gene expressions of individual genes are considered as the random variables following unique Weibull distributions. Our WDCM is based on the concept that the genes with similar expression profiles have similar distribution parameters, and thus the genes are clustered via the Weibull distribution parameters. We used the WDCM to cluster three cancer gene expression data sets from the lung cancer, B-cell follicular lymphoma and bladder carcinoma and obtained well-clustered results. We compared the performance of WDCM with k-means and Self Organizing Map (SOM) using functional annotation information given by the Gene Ontology (GO). The results showed that the functional annotation ratios of WDCM are higher than those of the other methods. We also utilized the external measure Adjusted Rand Index to validate the performance of the WDCM. The comparative results demonstrate that the WDCM provides the better clustering performance compared to k-means and SOM algorithms. The merit of the proposed WDCM is that it can be applied to cluster incomplete gene expression data without imputing the missing values. Moreover, the robustness of WDCM is also evaluated on the incomplete data sets.

Conclusions

The results demonstrate that our WDCM produces clusters with more consistent functional annotations than the other methods. The WDCM is also verified to be robust and is capable of clustering gene expression data containing a small quantity of missing values.