Microarray missing data imputation based on a set theoretic framework and biological knowledge

Identification of Gene Regulatory Networks Using Variational Bayesian Inference in the Presence of Missing Data

The identification of gene regulatory networks (GRN) from gene expression time series data is a challenge and open problem in system biology. This paper considers the structure inference of GRN from the incomplete and noisy gene expression data, which is a not well-studied issue for GRN inference. In this paper, the dynamical behavior of the gene expression process is described by a stochastic nonlinear state-space model with unknown noise information. A variational Bayesian (VB) framework are proposed to estimate the parameters and gene expression levels simultaneously. One of the advantages of this method is that it can easily handle the missing observations by generating the prediction values. Considering the sparsity of GRN, the smoothed gene data are modeled by the extreme gradient boosting tree, and the regulatory interactions among genes are identified by the importance scores based on the tree model. The proposed method is tested on the artificial DREAM4 datasets and one real gene expression dataset of yeast. The comparative results show that the proposed method can effectively recover the regulatory interactions of GRN in the presence of missing observations and outperforms the existing methods for GRN identification.

A comprehensive survey on computational learning methods for analysis of gene expression data

Computational analysis methods including machine learning have a significant impact in the fields of genomics and medicine. High-throughput gene expression analysis methods such as microarray technology and RNA sequencing produce enormous amounts of data. Traditionally, statistical methods are used for comparative analysis of gene expression data. However, more complex analysis for classification of sample observations, or discovery of feature genes requires sophisticated computational approaches. In this review, we compile various statistical and computational tools used in analysis of expression microarray data. Even though the methods are discussed in the context of expression microarrays, they can also be applied for the analysis of RNA sequencing and quantitative proteomics datasets. We discuss the types of missing values, and the methods and approaches usually employed in their imputation. We also discuss methods of data normalization, feature selection, and feature extraction. Lastly, methods of classification and class discovery along with their evaluation parameters are described in detail. We believe that this detailed review will help the users to select appropriate methods for preprocessing and analysis of their data based on the expected outcome.

Efficient technique of microarray missing data imputation using clustering and weighted nearest neighbour

For most bioinformatics statistical methods, particularly for gene expression data classification, prognosis, and prediction, a complete dataset is required. The gene sample value can be missing due to hardware failure, software failure, or manual mistakes. The missing data in gene expression research dramatically affects the analysis of the collected data. Consequently, this has become a critical problem that requires an efficient imputation algorithm to resolve the issue. This paper proposed a technique considering the local similarity structure that predicts the missing data using clustering and top K nearest neighbor approaches for imputing the missing value. A similarity-based spectral clustering approach is used that is combined with the K-means. The spectral clustering parameters, cluster size, and weighting factors are optimized, and after that, missing values are predicted. For imputing each cluster’s missing value, the top K nearest neighbor approach utilizes the concept of weighted distance. The evaluation is carried out on numerous datasets from a variety of biological areas, with experimentally inserted missing values varying from 5 to 25%. Experimental results prove that the proposed imputation technique makes accurate predictions as compared to other imputation procedures. In this paper, for performing the imputation experiments, microarray gene expression datasets consisting of information of different cancers and tumors are considered. The main contribution of this research states that local similarity-based techniques can be used for imputation even when the dataset has varying dimensionality and characteristics.

ANPELA: analysis and performance assessment of the label-free quantification workflow for metaproteomic studies

Label-free quantification (LFQ) with a specific and sequentially integrated workflow of acquisition technique, quantification tool and processing method has emerged as the popular technique employed in metaproteomic research to provide a comprehensive landscape of the adaptive response of microbes to external stimuli and their interactions with other organisms or host cells. The performance of a specific LFQ workflow is highly dependent on the studied data. Hence, it is essential to discover the most appropriate one for a specific data set. However, it is challenging to perform such discovery due to the large number of possible workflows and the multifaceted nature of the evaluation criteria. Herein, a web server ANPELA (https://idrblab.org/anpela/) was developed and validated as the first tool enabling performance assessment of whole LFQ workflow (collective assessment by five well-established criteria with distinct underlying theories), and it enabled the identification of the optimal LFQ workflow(s) by a comprehensive performance ranking. ANPELA not only automatically detects the diverse formats of data generated by all quantification tools but also provides the most complete set of processing methods among the available web servers and stand-alone tools. Systematic validation using metaproteomic benchmarks revealed ANPELA's capabilities in 1 discovering well-performing workflow(s), (2) enabling assessment from multiple perspectives and (3) validating LFQ accuracy using spiked proteins. ANPELA has a unique ability to evaluate the performance of whole LFQ workflow and enables the discovery of the optimal LFQs by the comprehensive performance ranking of all 560 workflows. Therefore, it has great potential for applications in metaproteomic and other studies requiring LFQ techniques, as many features are shared among proteomic studies.

Pharmacometabonomics: data processing and statistical analysis

Individual variations in drug efficacy, side effects and adverse drug reactions are still challenging that cannot be ignored in drug research and development. The aim of pharmacometabonomics is to better understand the pharmacokinetic properties of drugs and monitor the drug effects on specific metabolic pathways. Here, we systematically reviewed the recent technological advances in pharmacometabonomics for better understanding the pathophysiological mechanisms of diseases as well as the metabolic effects of drugs on bodies. First, the advantages and disadvantages of all mainstream analytical techniques were compared. Second, many data processing strategies including filtering, missing value imputation, quality control-based correction, transformation, normalization together with the methods implemented in each step were discussed. Third, various feature selection and feature extraction algorithms commonly applied in pharmacometabonomics were described. Finally, the databases that facilitate current pharmacometabonomics were collected and discussed. All in all, this review provided guidance for researchers engaged in pharmacometabonomics and metabolomics, and it would promote the wide application of metabolomics in drug research and personalized medicine.

Predictive models of medication non-adherence risks of patients with T2D based on multiple machine learning algorithms

OBJECTIVE

Medication adherence plays a key role in type 2 diabetes (T2D) care. Identifying patients with high risks of non-compliance helps individualized management, especially for China, where medical resources are relatively insufficient. However, models with good predictive capabilities have not been studied. This study aims to assess multiple machine learning algorithms and screen out a model that can be used to predict patients' non-adherence risks.

METHODS

A real-world registration study was conducted at Sichuan Provincial People's Hospital from 1 April 2018 to 30 March 2019. Data of patients with T2D on demographics, disease and treatment, diet and exercise, mental status, and treatment adherence were obtained by face-to-face questionnaires. The medication possession ratio was used to evaluate patients' medication adherence status. Fourteen machine learning algorithms were applied for modeling, including Bayesian network, Neural Net, support vector machine, and so on, and balanced sampling, data imputation, binning, and methods of feature selection were evaluated by the area under the receiver operating characteristic curve (AUC). We use two-way cross-validation to ensure the accuracy of model evaluation, and we performed a posteriori test on the sample size based on the trend of AUC as the sample size increase.

RESULTS

A total of 401 patients out of 630 candidates were investigated, of which 85 were evaluated as poor adherence (21.20%). A total of 16 variables were selected as potential variables for modeling, and 300 models were built based on 30 machine learning algorithms. Among these algorithms, the AUC of the best capable one was 0.866±0.082. Imputing, oversampling and larger sample size will help improve predictive ability.

CONCLUSIONS

An accurate and sensitive adherence prediction model based on real-world registration data was established after evaluating data filling, balanced sampling, and so on, which may provide a technical tool for individualized diabetes care.

Classification of Microarray Data

The automatic classification of DNA microarray data is one of the hot topics in the field of bioinformatics, since it is an effective tool for the diagnosis of diseases in patients. The aim of this chapter is to present the most relevant aspects related to the classification of microarrays. We carried out an analysis of the strategies used for the classification of microarray data and a review of the main methods used in the literature. In addition, other related aspects are addressed as the reduction of dimensionality, to try to eliminate redundant information in genes, or the treatment of imbalanced data and missing of data. To conclude, we present an exhaustive review of the main scientific works in journals to show the most successful techniques applied in this discipline as well as the most used datasets to verify their effectiveness.

DrPOCS: Drug Repositioning Based on Projection Onto Convex Sets

Drug repositioning, i.e., identifying new indications for known drugs, has attracted a lot of attentions recently and is becoming an effective strategy in drug development. In literature, several computational approaches have been proposed to identify potential indications of old drugs based on various types of data sources. In this paper, by formulating the drug-disease associations as a low-rank matrix, we propose a novel method, namely DrPOCS, to identify candidate indications of old drugs based on projection onto convex sets (POCS). With the integration of drug structure and disease phenotype information, DrPOCS predicts potential associations between drugs and diseases with matrix completion. Benchmarking results demonstrate that our proposed approach outperforms popular existing approaches with high accuracy. In addition, a number of novel predicted indications are validated with various types of evidences, indicating the predictive power of our proposed approach.

Mining Gene Expression Profile with Missing Values: An Integration of Kernel PCA and Robust Singular Values Decomposition

Background:

Gene expression profiling and transcriptomics provide valuable information about the role of genes that are differentially expressed between two or more samples. It is always important and challenging to analyse High-throughput DNA microarray data with a number of missing values under various experimental conditions. </P><P> Objectives: Graphical data visualizations of the expression of all genes in a particular cell provide holistic views of gene expression patterns, which improve our understanding of cellular systems under normal and pathological conditions. However, current visualization methods are sensitive to missing values, which are frequently observed in microarray-based gene expression profiling, potentially affecting the subsequent statistical analyses.

Methods:

We addressed in this study the problem of missing values with respect to different imputation methods using gene expression biplot (GE biplot), one of the most popular gene visualization techniques. The effects of missing values for mining differentially expressed genes in gene expression data were evaluated using four well-known imputation methods: Robust Singular Value Decomposition (Robust SVD), Column Average (CA), Column Median (CM), and K-nearest Neighbors (KNN). Frobenius norm and absolute distances were used to measure the accuracy of the methods.

Results:

Three numerical experiments were performed using simulated data (i) and publicly available colon cancer (ii) and leukemia data (iii) to analyze the performance of each method. The results showed that CM and KNN performed better than Robust SVD and CA for identifying the index gene profile in the biplot visualization in both the simulation study and the colon cancer and leukemia microarray datasets.

Conclusion:

The impact of missing values on the GE biplot was smaller when the data matrix was imputed by KNN than by CM. This study concluded that KNN performed satisfactorily in generating a GE biplot in the presence of missing values in microarray data.

Discovery of the Consistently Well-Performed Analysis Chain for SWATH-MS Based Pharmacoproteomic Quantification

Sequential windowed acquisition of all theoretical fragment ion mass spectra (SWATH-MS) has emerged as one of the most popular techniques for label-free proteome quantification in current pharmacoproteomic research. It provides more comprehensive detection and more accurate quantitation of proteins comparing with the traditional techniques. The performance of SWATH-MS is highly susceptible to the selection of processing method. Till now, ≥27 methods (transformation, normalization, and missing-value imputation) are sequentially applied to construct numerous analysis chains for SWATH-MS, but it is still not clear which analysis chain gives the optimal quantification performance. Herein, the performances of 560 analysis chains for quantifying pharmacoproteomic data were comprehensively assessed. Firstly, the most complete set of the publicly available SWATH-MS based pharmacoproteomic data were collected by comprehensive literature review. Secondly, substantial variations among the performances of various analysis chains were observed, and the consistently well-performed analysis chains (CWPACs) across various datasets were for the first time generalized. Finally, the log and power transformations sequentially followed by the total ion current normalization were discovered as one of the best performed analysis chains for the quantification of SWATH-MS based pharmacoproteomic data. In sum, the CWPACs identified here provided important guidance to the quantification of proteomic data and could therefore facilitate the cutting-edge research in any pharmacoproteomic studies requiring SWATH-MS technique.

Identification of Boolean Network Models From Time Series Data Incorporating Prior Knowledge

Motivation: Mathematical models take an important place in science and engineering. A model can help scientists to explain dynamic behavior of a system and to understand the functionality of system components. Since length of a time series and number of replicates is limited by the cost of experiments, Boolean networks as a structurally simple and parameter-free logical model for gene regulatory networks have attracted interests of many scientists. In order to fit into the biological contexts and to lower the data requirements, biological prior knowledge is taken into consideration during the inference procedure. In the literature, the existing identification approaches can only deal with a subset of possible types of prior knowledge. Results: We propose a new approach to identify Boolean networks from time series data incorporating prior knowledge, such as partial network structure, canalizing property, positive and negative unateness. Using vector form of Boolean variables and applying a generalized matrix multiplication called the semi-tensor product (STP), each Boolean function can be equivalently converted into a matrix expression. Based on this, the identification problem is reformulated as an integer linear programming problem to reveal the system matrix of Boolean model in a computationally efficient way, whose dynamics are consistent with the important dynamics captured in the data. By using prior knowledge the number of candidate functions can be reduced during the inference. Hence, identification incorporating prior knowledge is especially suitable for the case of small size time series data and data without sufficient stimuli. The proposed approach is illustrated with the help of a biological model of the network of oxidative stress response. Conclusions: The combination of efficient reformulation of the identification problem with the possibility to incorporate various types of prior knowledge enables the application of computational model inference to systems with limited amount of time series data. The general applicability of this methodological approach makes it suitable for a variety of biological systems and of general interest for biological and medical research.

An Iterative Locally Auto-Weighted Least Squares Method for Microarray Missing Value Estimation

Microarray data often contain missing values which significantly affect subsequent analysis. Existing LLSimpute-based imputation methods for dealing with missing data have been shown to be generally efficient. However, all of the LLSimpute-based methods do not consider the different importance of different neighbors of the target gene in the missing value estimation process and treat all the neighbors equally. In this paper, a locally auto-weighted least squares imputation (LAW-LSimpute) method is proposed for missing value estimation, which can automatically weight the neighboring genes based on the importance of the genes. Then, an accelerating strategy is added to the LAW-LSimpute method in order to improve the convergence. Furthermore, an iterative missing value estimation framework of LAW-LSimpute (ILAW-LSimpute) is designed. Experimental results show that the ILAW-LSimpute method is able to reduce the estimation error.

MVIAeval: a web tool for comprehensively evaluating the performance of a new missing value imputation algorithm

BACKGROUND

Missing value imputation is important for microarray data analyses because microarray data with missing values would significantly degrade the performance of the downstream analyses. Although many microarray missing value imputation algorithms have been developed, an objective and comprehensive performance comparison framework is still lacking. To solve this problem, we previously proposed a framework which can perform a comprehensive performance comparison of different existing algorithms. Also the performance of a new algorithm can be evaluated by our performance comparison framework. However, constructing our framework is not an easy task for the interested researchers. To save researchers' time and efforts, here we present an easy-to-use web tool named MVIAeval (Missing Value Imputation Algorithm evaluator) which implements our performance comparison framework.

RESULTS

MVIAeval provides a user-friendly interface allowing users to upload the R code of their new algorithm and select (i) the test datasets among 20 benchmark microarray (time series and non-time series) datasets, (ii) the compared algorithms among 12 existing algorithms, (iii) the performance indices from three existing ones, (iv) the comprehensive performance scores from two possible choices, and (v) the number of simulation runs. The comprehensive performance comparison results are then generated and shown as both figures and tables.

CONCLUSIONS

MVIAeval is a useful tool for researchers to easily conduct a comprehensive and objective performance evaluation of their newly developed missing value imputation algorithm for microarray data or any data which can be represented as a matrix form (e.g. NGS data or proteomics data). Thus, MVIAeval will greatly expedite the progress in the research of missing value imputation algorithms.

An integrative imputation method based on multi-omics datasets

Background

Integrative analysis of multi-omics data is becoming increasingly important to unravel functional mechanisms of complex diseases. However, the currently available multi-omics datasets inevitably suffer from missing values due to technical limitations and various constrains in experiments. These missing values severely hinder integrative analysis of multi-omics data. Current imputation methods mainly focus on using single omics data while ignoring biological interconnections and information imbedded in multi-omics data sets.

Results

In this study, a novel multi-omics imputation method was proposed to integrate multiple correlated omics datasets for improving the imputation accuracy. Our method was designed to: 1) combine the estimates of missing value from individual omics data itself as well as from other omics, and 2) simultaneously impute multiple missing omics datasets by an iterative algorithm. We compared our method with five imputation methods using single omics data at different noise levels, sample sizes and data missing rates. The results demonstrated the advantage and efficiency of our method, consistently in terms of the imputation error and the recovery of mRNA-miRNA network structure.

Conclusions

We concluded that our proposed imputation method can utilize more biological information to minimize the imputation error and thus can improve the performance of downstream analysis such as genetic regulatory network construction.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1122-6) contains supplementary material, which is available to authorized users.

A glance at the applications of Singular Spectrum Analysis in gene expression data

In recent years Singular Spectrum Analysis (SSA) has been used to solve many biomedical issues and is currently accepted as a potential technique in quantitative genetics studies. Presented in this article is a review of recent published genetics studies which have taken advantage of SSA. Since Singular Value Decomposition (SVD) is an important stage of this technique which can also be used as an independent analytical method in gene expression data, we also briefly touch upon some areas of the application of SVD. The review finds that at present, the most prominent area of applying SSA in genetics is filtering and signal extraction, which proves that SSA can be considered as a valuable aid and promising method for genetics analysis.

A hybrid imputation approach for microarray missing value estimation

BACKGROUND

Missing data is an inevitable phenomenon in gene expression microarray experiments due to instrument failure or human error. It has a negative impact on performance of downstream analysis. Technically, most existing approaches suffer from this prevalent problem. Imputation is one of the frequently used methods for processing missing data. Actually many developments have been achieved in the research on estimating missing values. The challenging task is how to improve imputation accuracy for data with a large missing rate.

METHODS

In this paper, induced by the thought of collaborative training, we propose a novel hybrid imputation method, called Recursive Mutual Imputation (RMI). Specifically, RMI exploits global correlation information and local structure in the data, captured by two popular methods, Bayesian Principal Component Analysis (BPCA) and Local Least Squares (LLS), respectively. Mutual strategy is implemented by sharing the estimated data sequences at each recursive process. Meanwhile, we consider the imputation sequence based on the number of missing entries in the target gene. Furthermore, a weight based integrated method is utilized in the final assembling step.

RESULTS

We evaluate RMI with three state-of-art algorithms (BPCA, LLS, Iterated Local Least Squares imputation (ItrLLS)) on four publicly available microarray datasets. Experimental results clearly demonstrate that RMI significantly outperforms comparative methods in terms of Normalized Root Mean Square Error (NRMSE), especially for datasets with large missing rates and less complete genes.

CONCLUSIONS

It is noted that our proposed hybrid imputation approach incorporates both global and local information of microarray genes, which achieves lower NRMSE values against to any single approach only. Besides, this study highlights the need for considering the imputing sequence of missing entries for imputation methods.

Missing value imputation for microarray data: a comprehensive comparison study and a web tool

BACKGROUND

Microarray data are usually peppered with missing values due to various reasons. However, most of the downstream analyses for microarray data require complete datasets. Therefore, accurate algorithms for missing value estimation are needed for improving the performance of microarray data analyses. Although many algorithms have been developed, there are many debates on the selection of the optimal algorithm. The studies about the performance comparison of different algorithms are still incomprehensive, especially in the number of benchmark datasets used, the number of algorithms compared, the rounds of simulation conducted, and the performance measures used.

RESULTS

In this paper, we performed a comprehensive comparison by using (I) thirteen datasets, (II) nine algorithms, (III) 110 independent runs of simulation, and (IV) three types of measures to evaluate the performance of each imputation algorithm fairly. First, the effects of different types of microarray datasets on the performance of each imputation algorithm were evaluated. Second, we discussed whether the datasets from different species have different impact on the performance of different algorithms. To assess the performance of each algorithm fairly, all evaluations were performed using three types of measures. Our results indicate that the performance of an imputation algorithm mainly depends on the type of a dataset but not on the species where the samples come from. In addition to the statistical measure, two other measures with biological meanings are useful to reflect the impact of missing value imputation on the downstream data analyses. Our study suggests that local-least-squares-based methods are good choices to handle missing values for most of the microarray datasets.

CONCLUSIONS

In this work, we carried out a comprehensive comparison of the algorithms for microarray missing value imputation. Based on such a comprehensive comparison, researchers could choose the optimal algorithm for their datasets easily. Moreover, new imputation algorithms could be compared with the existing algorithms using this comparison strategy as a standard protocol. In addition, to assist researchers in dealing with missing values easily, we built a web-based and easy-to-use imputation tool, MissVIA (http://cosbi.ee.ncku.edu.tw/MissVIA), which supports many imputation algorithms. Once users upload a real microarray dataset and choose the imputation algorithms, MissVIA will determine the optimal algorithm for the users' data through a series of simulations, and then the imputed results can be downloaded for the downstream data analyses.

WIMP: web server tool for missing data imputation

The imputation of unknown or missing data is a crucial task on the analysis of biomedical datasets. There are several situations where it is necessary to classify or identify instances given incomplete vectors, and the existence of missing values can much degrade the performance of the algorithms used for the classification/recognition. The task of learning accurately from incomplete data raises a number of issues some of which have not been completely solved in machine learning applications. In this sense, effective missing value estimation methods are required. Different methods for missing data imputations exist but most of the times the selection of the appropriate technique involves testing several methods, comparing them and choosing the right one. Furthermore, applying these methods, in most cases, is not straightforward, as they involve several technical details, and in particular in cases such as when dealing with microarray datasets, the application of the methods requires huge computational resources. As far as we know, there is not a public software application that can provide the computing capabilities required for carrying the task of data imputation. This paper presents a new public tool for missing data imputation that is attached to a computer cluster in order to execute high computational tasks. The software WIMP (Web IMPutation) is a public available web site where registered users can create, execute, analyze and store their simulations related to missing data imputation.

Time series analysis as input for clinical predictive modeling: modeling cardiac arrest in a pediatric ICU

Background

Thousands of children experience cardiac arrest events every year in pediatric intensive care units. Most of these children die. Cardiac arrest prediction tools are used as part of medical emergency team evaluations to identify patients in standard hospital beds that are at high risk for cardiac arrest. There are no models to predict cardiac arrest in pediatric intensive care units though, where the risk of an arrest is 10 times higher than for standard hospital beds. Current tools are based on a multivariable approach that does not characterize deterioration, which often precedes cardiac arrests. Characterizing deterioration requires a time series approach. The purpose of this study is to propose a method that will allow for time series data to be used in clinical prediction models. Successful implementation of these methods has the potential to bring arrest prediction to the pediatric intensive care environment, possibly allowing for interventions that can save lives and prevent disabilities.

Methods

We reviewed prediction models from nonclinical domains that employ time series data, and identified the steps that are necessary for building predictive models using time series clinical data. We illustrate the method by applying it to the specific case of building a predictive model for cardiac arrest in a pediatric intensive care unit.

Results

Time course analysis studies from genomic analysis provided a modeling template that was compatible with the steps required to develop a model from clinical time series data. The steps include: 1) selecting candidate variables; 2) specifying measurement parameters; 3) defining data format; 4) defining time window duration and resolution; 5) calculating latent variables for candidate variables not directly measured; 6) calculating time series features as latent variables; 7) creating data subsets to measure model performance effects attributable to various classes of candidate variables; 8) reducing the number of candidate features; 9) training models for various data subsets; and 10) measuring model performance characteristics in unseen data to estimate their external validity.

Conclusions

We have proposed a ten step process that results in data sets that contain time series features and are suitable for predictive modeling by a number of methods. We illustrated the process through an example of cardiac arrest prediction in a pediatric intensive care setting.

Incorporating Nonlinear Relationships in Microarray Missing Value Imputation

Microarray gene expression data often contain missing values. Accurate estimation of the missing values is important for downstream data analyses that require complete data. Nonlinear relationships between gene expression levels have not been well-utilized in missing value imputation. We propose an imputation scheme based on nonlinear dependencies between genes. By simulations based on real microarray data, we show that incorporating nonlinear relationships could improve the accuracy of missing value imputation, both in terms of normalized root-mean-squared error and in terms of the preservation of the list of significant genes in statistical testing. In addition, we studied the impact of artificial dependencies introduced by data normalization on the simulation results. Our results suggest that methods relying on global correlation structures may yield overly optimistic simulation results when the data have been subjected to row (gene)-wise mean removal.

Integrative analysis of transcriptomic and proteomic data of Shewanella oneidensis: missing value imputation using temporal datasets

Despite significant improvements in recent years, proteomic datasets currently available still suffer from large number of missing values. Integrative analyses based upon incomplete proteomic and transcriptomic datasets could seriously bias the biological interpretation. In this study, we applied a non-linear data-driven stochastic gradient boosted trees (GBT) model to impute missing proteomic values using a temporal transcriptomic and proteomic dataset of Shewanella oneidensis. In this dataset, genes' expression was measured after the cells were exposed to 1 mM potassium chromate for 5, 30, 60, and 90 min, while protein abundance was measured for 45 and 90 min. With the ultimate objective to impute protein values for experimentally undetected samples at 45 and 90 min, we applied a serial set of algorithms to capture relationships between temporal gene and protein expression. This work follows four main steps: (1) a quality control step for gene expression reliability, (2) mRNA imputation, (3) protein prediction, and (4) validation. Initially, an S control chart approach is performed on gene expression replicates to remove unwanted variability. Then, we focused on the missing measurements of gene expression through a nonlinear Smoothing Splines Curve Fitting. This method identifies temporal relationships among transcriptomic data at different time points and enables imputation of mRNA abundance at 45 min. After mRNA imputation was validated by biological constrains (i.e. operons), we used a data-driven GBT model to impute protein abundance for the proteins experimentally undetected in the 45 and 90 min samples, based on relevant predictors such as temporal mRNA gene expression data and cellular functional roles. The imputed protein values were validated using biological constraints such as operon and pathway information through a permutation test to investigate whether dispersion measures are indeed smaller for known biological groups than for any set of random genes. Finally, we demonstrated that such missing value imputation improved characterization of the temporal response of S. oneidensis to chromate.

Missing Value Estimation for Compound-Target Activity Data

Relationships between drug targets and associated diseases have traditionally been investigated by means of sequence similarity, comparative protein modeling, and pathway analysis. Recently, a complementary paradigm has emerged to link targets and drugs via biological responses within activity data and visualize findings in networks. It has been indicated that one of the obstacles towards the identification of novel interactions is the sparsity of available data. In this article, we provide a survey of estimation methods that address the challenge of data sparsity. Each method is described in terms of its advantages and limitations, and an exemplary application on compound-target activity data is demonstrated. With such imputation methods in-hand, the opportunity to combine efforts in molecular informatics can be realized, yielding novel insights into ligand-target space.

Multiconstrained gene clustering based on generalized projections

Background

Gene clustering for annotating gene functions is one of the fundamental issues in bioinformatics. The best clustering solution is often regularized by multiple constraints such as gene expressions, Gene Ontology (GO) annotations and gene network structures. How to integrate multiple pieces of constraints for an optimal clustering solution still remains an unsolved problem.

Results

We propose a novel multiconstrained gene clustering (MGC) method within the generalized projection onto convex sets (POCS) framework used widely in image reconstruction. Each constraint is formulated as a corresponding set. The generalized projector iteratively projects the clustering solution onto these sets in order to find a consistent solution included in the intersection set that satisfies all constraints. Compared with previous MGC methods, POCS can integrate multiple constraints from different nature without distorting the original constraints. To evaluate the clustering solution, we also propose a new performance measure referred to as Gene Log Likelihood (GLL) that considers genes having more than one function and hence in more than one cluster. Comparative experimental results show that our POCS-based gene clustering method outperforms current state-of-the-art MGC methods.

Conclusions

The POCS-based MGC method can successfully combine multiple constraints from different nature for gene clustering. Also, the proposed GLL is an effective performance measure for the soft clustering solutions.

Comparative analysis of missing value imputation methods to improve clustering and interpretation of microarray experiments

Background

Microarray technologies produced large amount of data. In a previous study, we have shown the interest of k-Nearest Neighbour approach for restoring the missing gene expression values, and its positive impact of the gene clustering by hierarchical algorithm. Since, numerous replacement methods have been proposed to impute missing values (MVs) for microarray data. In this study, we have evaluated twelve different usable methods, and their influence on the quality of gene clustering. Interestingly we have used several datasets, both kinetic and non kinetic experiments from yeast and human.

Results

We underline the excellent efficiency of approaches proposed and implemented by Bo and co-workers and especially one based on expected maximization (EM_array). These improvements have been observed also on the imputation of extreme values, the most difficult predictable values. We showed that the imputed MVs have still important effects on the stability of the gene clusters. The improvement on the clustering obtained by hierarchical clustering remains limited and, not sufficient to restore completely the correct gene associations. However, a common tendency can be found between the quality of the imputation method and the gene cluster stability. Even if the comparison between clustering algorithms is a complex task, we observed that k-means approach is more efficient to conserve gene associations.

Conclusions

More than 6.000.000 independent simulations have assessed the quality of 12 imputation methods on five very different biological datasets. Important improvements have so been done since our last study. The EM_array approach constitutes one efficient method for restoring the missing expression gene values, with a lower estimation error level. Nonetheless, the presence of MVs even at a low rate is a major factor of gene cluster instability. Our study highlights the need for a systematic assessment of imputation methods and so of dedicated benchmarks. A noticeable point is the specific influence of some biological dataset.

How to improve postgenomic knowledge discovery using imputation

While microarrays make it feasible to rapidly investigate many complex biological problems, their multistep fabrication has the proclivity for error at every stage. The standard tactic has been to either ignore or regard erroneous gene readings as missing values, though this assumption can exert a major influence upon postgenomic knowledge discovery methods like gene selection and gene regulatory network (GRN) reconstruction. This has been the catalyst for a raft of new flexible imputation algorithms including local least square impute and the recent heuristic collateral missing value imputation, which exploit the biological transactional behaviour of functionally correlated genes to afford accurate missing value estimation. This paper examines the influence of missing value imputation techniques upon postgenomic knowledge inference methods with results for various algorithms consistently corroborating that instead of ignoring missing values, recycling microarray data by flexible and robust imputation can provide substantial performance benefits for subsequent downstream procedures.

Discovering biclusters in gene expression data based on high-dimensional linear geometries

Background

In DNA microarray experiments, discovering groups of genes that share similar transcriptional characteristics is instrumental in functional annotation, tissue classification and motif identification. However, in many situations a subset of genes only exhibits consistent pattern over a subset of conditions. Conventional clustering algorithms that deal with the entire row or column in an expression matrix would therefore fail to detect these useful patterns in the data. Recently, biclustering has been proposed to detect a subset of genes exhibiting consistent pattern over a subset of conditions. However, most existing biclustering algorithms are based on searching for sub-matrices within a data matrix by optimizing certain heuristically defined merit functions. Moreover, most of these algorithms can only detect a restricted set of bicluster patterns.

Results

In this paper, we present a novel geometric perspective for the biclustering problem. The biclustering process is interpreted as the detection of linear geometries in a high dimensional data space. Such a new perspective views biclusters with different patterns as hyperplanes in a high dimensional space, and allows us to handle different types of linear patterns simultaneously by matching a specific set of linear geometries. This geometric viewpoint also inspires us to propose a generic bicluster pattern, i.e. the linear coherent model that unifies the seemingly incompatible additive and multiplicative bicluster models. As a particular realization of our framework, we have implemented a Hough transform-based hyperplane detection algorithm. The experimental results on human lymphoma gene expression dataset show that our algorithm can find biologically significant subsets of genes.

Conclusion

We have proposed a novel geometric interpretation of the biclustering problem. We have shown that many common types of bicluster are just different spatial arrangements of hyperplanes in a high dimensional data space. An implementation of the geometric framework using the Fast Hough transform for hyperplane detection can be used to discover biologically significant subsets of genes under subsets of conditions for microarray data analysis.

Missing value imputation improves clustering and interpretation of gene expression microarray data

Background

Missing values frequently pose problems in gene expression microarray experiments as they can hinder downstream analysis of the datasets. While several missing value imputation approaches are available to the microarray users and new ones are constantly being developed, there is no general consensus on how to choose between the different methods since their performance seems to vary drastically depending on the dataset being used.

Results

We show that this discrepancy can mostly be attributed to the way in which imputation methods have traditionally been developed and evaluated. By comparing a number of advanced imputation methods on recent microarray datasets, we show that even when there are marked differences in the measurement-level imputation accuracies across the datasets, these differences become negligible when the methods are evaluated in terms of how well they can reproduce the original gene clusters or their biological interpretations. Regardless of the evaluation approach, however, imputation always gave better results than ignoring missing data points or replacing them with zeros or average values, emphasizing the continued importance of using more advanced imputation methods.

Conclusion

The results demonstrate that, while missing values are still severely complicating microarray data analysis, their impact on the discovery of biologically meaningful gene groups can – up to a certain degree – be reduced by using readily available and relatively fast imputation methods, such as the Bayesian Principal Components Algorithm (BPCA).

Which missing value imputation method to use in expression profiles: a comparative study and two selection schemes

Background

Gene expression data frequently contain missing values, however, most down-stream analyses for microarray experiments require complete data. In the literature many methods have been proposed to estimate missing values via information of the correlation patterns within the gene expression matrix. Each method has its own advantages, but the specific conditions for which each method is preferred remains largely unclear. In this report we describe an extensive evaluation of eight current imputation methods on multiple types of microarray experiments, including time series, multiple exposures, and multiple exposures × time series data. We then introduce two complementary selection schemes for determining the most appropriate imputation method for any given data set.

Results

We found that the optimal imputation algorithms (LSA, LLS, and BPCA) are all highly competitive with each other, and that no method is uniformly superior in all the data sets we examined. The success of each method can also depend on the underlying "complexity" of the expression data, where we take complexity to indicate the difficulty in mapping the gene expression matrix to a lower-dimensional subspace. We developed an entropy measure to quantify the complexity of expression matrixes and found that, by incorporating this information, the entropy-based selection (EBS) scheme is useful for selecting an appropriate imputation algorithm. We further propose a simulation-based self-training selection (STS) scheme. This technique has been used previously for microarray data imputation, but for different purposes. The scheme selects the optimal or near-optimal method with high accuracy but at an increased computational cost.

Conclusion

Our findings provide insight into the problem of which imputation method is optimal for a given data set. Three top-performing methods (LSA, LLS and BPCA) are competitive with each other. Global-based imputation methods (PLS, SVD, BPCA) performed better on mcroarray data with lower complexity, while neighbour-based methods (KNN, OLS, LSA, LLS) performed better in data with higher complexity. We also found that the EBS and STS schemes serve as complementary and effective tools for selecting the optimal imputation algorithm.

The properties of high-dimensional data spaces: implications for exploring gene and protein expression data

High-throughput genomic and proteomic technologies are widely used in cancer research to build better predictive models of diagnosis, prognosis and therapy, to identify and characterize key signalling networks and to find new targets for drug development. These technologies present investigators with the task of extracting meaningful statistical and biological information from high-dimensional data spaces, wherein each sample is defined by hundreds or thousands of measurements, usually concurrently obtained. The properties of high dimensionality are often poorly understood or overlooked in data modelling and analysis. From the perspective of translational science, this Review discusses the properties of high-dimensional data spaces that arise in genomic and proteomic studies and the challenges they can pose for data analysis and interpretation.

Unsupervised feature selection under perturbations: meeting the challenges of biological data

MOTIVATION

Feature selection methods aim to reduce the complexity of data and to uncover the most relevant biological variables. In reality, information in biological datasets is often incomplete as a result of untrustworthy samples and missing values. The reliability of selection methods may therefore be questioned.

METHOD

Information loss is incorporated into a perturbation scheme, testing which features are stable under it. This method is applied to data analysis by unsupervised feature filtering (UFF). The latter has been shown to be a very successful method in analysis of gene-expression data.

RESULTS

We find that the UFF quality degrades smoothly with information loss. It remains successful even under substantial damage. Our method allows for selection of a best imputation method on a dataset treated by UFF. More importantly, scoring features according to their stability under information loss is shown to be correlated with biological importance in cancer studies. This scoring may lead to novel biological insights.

Robust imputation method for missing values in microarray data

BACKGROUND

When analyzing microarray gene expression data, missing values are often encountered. Most multivariate statistical methods proposed for microarray data analysis cannot be applied when the data have missing values. Numerous imputation algorithms have been proposed to estimate the missing values. In this study, we develop a robust least squares estimation with principal components (RLSP) method by extending the local least square imputation (LLSimpute) method. The basic idea of our method is to employ quantile regression to estimate the missing values, using the estimated principal components of a selected set of similar genes.

RESULTS

Using the normalized root mean squares error, the performance of the proposed method was evaluated and compared with other previously proposed imputation methods. The proposed RLSP method clearly outperformed the weighted k-nearest neighbors imputation (kNNimpute) method and LLSimpute method, and showed competitive results with Bayesian principal component analysis (BPCA) method.

CONCLUSION

Adapting the principal components of the selected genes and employing the quantile regression model improved the robustness and accuracy of missing value imputation. Thus, the proposed RLSP method is, according to our empirical studies, more robust and accurate than the widely used kNNimpute and LLSimpute methods.

Spectral estimation in unevenly sampled space of periodically expressed microarray time series data

BACKGROUND

Periodogram analysis of time-series is widespread in biology. A new challenge for analyzing the microarray time series data is to identify genes that are periodically expressed. Such challenge occurs due to the fact that the observed time series usually exhibit non-idealities, such as noise, short length, and unevenly sampled time points. Most methods used in the literature operate on evenly sampled time series and are not suitable for unevenly sampled time series.

RESULTS

For evenly sampled data, methods based on the classical Fourier periodogram are often used to detect periodically expressed gene. Recently, the Lomb-Scargle algorithm has been applied to unevenly sampled gene expression data for spectral estimation. However, since the Lomb-Scargle method assumes that there is a single stationary sinusoid wave with infinite support, it introduces spurious periodic components in the periodogram for data with a finite length. In this paper, we propose a new spectral estimation algorithm for unevenly sampled gene expression data. The new method is based on signal reconstruction in a shift-invariant signal space, where a direct spectral estimation procedure is developed using the B-spline basis. Experiments on simulated noisy gene expression profiles show that our algorithm is superior to the Lomb-Scargle algorithm and the classical Fourier periodogram based method in detecting periodically expressed genes. We have applied our algorithm to the Plasmodium falciparum and Yeast gene expression data and the results show that the algorithm is able to detect biologically meaningful periodically expressed genes.

CONCLUSION

We have proposed an effective method for identifying periodic genes in unevenly sampled space of microarray time series gene expression data. The method can also be used as an effective tool for gene expression time series interpolation or resampling.

A meta-data based method for DNA microarray imputation

Background

DNA microarray experiments are conducted in logical sets, such as time course profiling after a treatment is applied to the samples, or comparisons of the samples under two or more conditions. Due to cost and design constraints of spotted cDNA microarray experiments, each logical set commonly includes only a small number of replicates per condition. Despite the vast improvement of the microarray technology in recent years, missing values are prevalent. Intuitively, imputation of missing values is best done using many replicates within the same logical set. In practice, there are few replicates and thus reliable imputation within logical sets is difficult. However, it is in the case of few replicates that the presence of missing values, and how they are imputed, can have the most profound impact on the outcome of downstream analyses (e.g. significance analysis and clustering). This study explores the feasibility of imputation across logical sets, using the vast amount of publicly available microarray data to improve imputation reliability in the small sample size setting.

Results

We download all cDNA microarray data of Saccharomyces cerevisiae, Arabidopsis thaliana, and Caenorhabditis elegans from the Stanford Microarray Database. Through cross-validation and simulation, we find that, for all three species, our proposed imputation using data from public databases is far superior to imputation within a logical set, sometimes to an astonishing degree. Furthermore, the imputation root mean square error for significant genes is generally a lot less than that of non-significant ones.

Conclusion

Since downstream analysis of significant genes, such as clustering and network analysis, can be very sensitive to small perturbations of estimated gene effects, it is highly recommended that researchers apply reliable data imputation prior to further analysis. Our method can also be applied to cDNA microarray experiments from other species, provided good reference data are available.