Computational Methods for Data Integration and Imputation of Missing Values in Omics Datasets

Molecular profiling of different omic-modalities (e.g., DNA methylomics, transcriptomics, proteomics) in biological systems represents the basis for research and clinical decision-making. Measurement-specific biases, so-called batch effects, often hinder the integration of independently acquired datasets, and missing values further hamper the applicability of typical data processing algorithms. In addition to careful experimental design, well-defined standards in data acquisition and data exchange, the alleviation of these phenomena particularly requires a dedicated data integration and preprocessing pipeline. This review aims to give a comprehensive overview of computational methods for data integration and missing value imputation for omic data analyses. We provide formal definitions for missing value mechanisms and propose a novel statistical taxonomy for batch effects, especially in the presence of missing data. Based on an automated document search and systematic literature review, we describe 32 distinct data integration methods from five main methodological categories, as well as 37 algorithms for missing value imputation from five separate categories. Additionally, this review highlights multiple quantitative evaluation methods to aid researchers in selecting a suitable set of methods for their work. Finally, this work provides an integrated discussion of the relevance of batch effects and missing values in omics with corresponding method recommendations. We then propose a comprehensive three-step workflow from the study conception to final data analysis and deduce perspectives for future research. Eventually, we present a comprehensive flow chart as well as exemplary decision trees to aid practitioners in the selection of specific approaches for imputation and data integration in their studies.

NMF-Based Approach for Missing Values Imputation of Mass Spectrometry Metabolomics Data

In mass spectrometry (MS)-based metabolomics, missing values (NAs) may be due to different causes, including sample heterogeneity, ion suppression, spectral overlap, inappropriate data processing, and instrumental errors. Although a number of methodologies have been applied to handle NAs, NA imputation remains a challenging problem. Here, we propose a non-negative matrix factorization (NMF)-based method for NA imputation in MS-based metabolomics data, which makes use of both global and local information of the data. The proposed method was compared with three commonly used methods: k-nearest neighbors (kNN), random forest (RF), and outlier-robust (ORI) missing values imputation. These methods were evaluated from the perspectives of accuracy of imputation, retrieval of data structures, and rank of imputation superiority. The experimental results showed that the NMF-based method is well-adapted to various cases of data missingness and the presence of outliers in MS-based metabolic profiles. It outperformed kNN and ORI and showed results comparable with the RF method. Furthermore, the NMF method is more robust and less susceptible to outliers as compared with the RF method. The proposed NMF-based scheme may serve as an alternative NA imputation method which may facilitate biological interpretations of metabolomics data.

A Layered KNN-SVM Approach to Predict Missing Values of Functional Requirements in Product Customization

The conversion from functional requirements (FRs) to design parameters is the foundation of product customization. However, original customer needs usually result in incomplete FRs, limited by customers’ incomprehension on the design requirements of these products. As the incomplete FRs may undermine the design activities afterwards, managers need to develop an effective approach to predict the missing values of the FR. This study proposes an integrative approach to obtain the complete FR. The k nearest neighbor (KNN) algorithm is employed to predict the missing continuous variables in FR, using the improved distance formula for two incomplete FRs. Support vector machine (SVM) classifiers are adopted to classify the missing categorical variables in FR, combined with directed acyclic graph for multi-class classification. KNN and SVM are then integrated into a multi-layer framework to predict the missing values of FR, where categorical and continuous variables both exist. A case study on the elevator customization is conducted to verify that KNN-SVM is feasible in accurate prediction of elevator FR values. Furthermore, KNN-SVM outperforms other five single and five composite methods, with average reduction in root mean squared error (RMSE) of 39% and 21% against KNN and KNN-Tree, respectively.

Microarray Missing Value Imputation: A Regularized Local Learning Method

Microarray experiments on gene expression inevitably generate missing values, which impedes further downstream biological analysis. Therefore, it is key to estimate the missing values accurately. Most of the existing imputation methods tend to suffer from the over-fitting problem. In this study, we propose two regularized local learning methods for microarray missing value imputation. Motivated by the grouping effect of L2 regularization, after selecting the target gene, we train an L2 Regularized Local Least Squares imputation model (RLLSimpute_L2) on the target gene and its neighbors to estimate the missing values of the target gene. Furthermore, RLLSimpute_L2 imputes the missing values in an ascending order based on the associated missing rate with each target gene. This contributes to fully utilizing the previously estimated values. Besides L2, we further explore L1 regularization and propose an L1 Regularized Local Least Squares imputation model (RLLSimpute_L1). To evaluate their effectiveness, we conducted extensive experimental studies on six benchmark datasets covering both time series and non-time series cases. Nine state-of-the-art imputation methods are compared with RLLSimpute_L2 and RLLSimpute_L1 in terms of three performance metrics. The comparative experimental results indicate that RLLSimpute_L2 outperforms its competitors by achieving smaller imputation errors and better structure preservation of differentially expressed genes.

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.

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.