Missing value imputation for microarray data: a comprehensive comparison study and a web tool
© Chiu et al.; licensee BioMed Central Ltd. 2013
Published: 13 December 2013
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.
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.
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.
Gene expression microarray (DNA chip) technology is a powerful tool for modern biomedical research. It could monitor relative expression of thousands of genes under a variety of experimental conditions. Therefore, it has been used widely in numerous studies over a broad range of biological disciplines, such as cell cycle regulation, stress responses, cancer diagnosis, functional gene discovery, specific therapy, and drug dynamic identification [1–9]. Although microarray technology has been used for several years, expression data still contain missing values due to various reasons such as scratches on the slide, spotting problems, poor hybridization, inadequate resolution, fabrication errors and so on.
Basically, microarray data contain 1-10% missing values that could affect up to 95% of genes . The occurrence of missing values in microarray data disadvantageously influences downstream analyses, such as discovery of differentially expressed genes [11, 12], construction of gene regulatory networks [13, 14], supervised classification of clinical samples , gene cluster analysis [10, 16], and biomarker detection.
One straightforward solution to solve the missing value problem is to repeat the microarray experiments, but that is very costly and inefficient. Another solution is to remove genes (rows) with one or more missing values before downstream analysis, but it is easily seen that part of important information would be lost. Hence, advanced algorithms must be developed to accurately impute the missing values.
Using modern mathematical and computational techniques can effectively impute missing values. Early approaches included replacing missing values by zero, row average or row median . Recently, many studies found that merging information from various biological data can significantly improve the missing values estimation. Liew et al. categorized the existing algorithms into four different classes: (1) local algorithms, (2) global algorithms, (3) hybrid algorithms, and (4) knowledge assisted algorithms [18, 19].
The first category includes k nearest neighbors (KNN) , iterative k nearest neighbors (IKNN) , sequential k nearest neighbors (SKNN) , least squares adaptive (LSA) , local least squares (LLS) , iterative local-least-squares (ILLS) , sequential local-least-squares (SLLS) , and etc. The second category includes Bayesian principal component analysis (BPCA) , singular value decomposition (SVD) , partial least squares (PLS) and so on. The third category includes LinCmb . The fourth category integrates domain knowledge (Gene Ontology  and multiple external datasets ) or external information into the imputation process. Projection onto convex sets (POCS) , GOimpute, histone acetylation information aided imputation (HAIimpute) , weighted nearest neighbors imputation (WeNNI)  and integrative missing value estimation (iMISS)  belong to the knowledge assisted approach algorithms. In this study, we did not use the hybrid algorithms and the knowledge assisted algorithms because their programs are not freely available or cannot be easily modified.
In the past few years, several papers have preliminary and objective analyses for the systematic evaluation of different imputation algorithms [32–35]. The weaknesses of these studies are as follows. First, few microarray datasets were used . Second, few independent rounds of the imputed procedure were performed (usually 10 times). Third, single performance measure was used [33, 34]. Here, we present a fair and comprehensive evaluation to assess the performances of different imputation algorithms on different datasets using different performance measures.
Considering that datasets from different species and types of datasets may have different effects on the performance of imputation algorithms, we chose thirteen different datasets from two species (Saccharomyces cerevisiae and Homo sapiens), which could be categorized into three different types (time series, non-time series and mixed type), for our analyses.
For time series datasets, we selected the yeast cell cycle data (including the alpha factor arrest and elutriation datasets) from , and Shapira04A and Shapira04B datasets, which were two different time series datasets (both measured the effect of oxidative stress on the yeast cell cycle) from . We also chose the human cell cycle data called Human HeLa from . For non-time series datasets, we chose the datasets (Ogawa, BohenSH and BohenLC) from  and . Ogawa's data was retrieved from the study of phosphophate accumulation and poly-phosphophate metabolism and the BohenSH was retrieved from follicular lymphoma lymph node and normal lymph node and spleen samples on SH microarrays and the BohenLC was retrieved from 24 independent follicular lymphoma lymph node samples on LC microarrays. For mixed type datasets, we chose the datasets from Lymphoma  (focused on two experimental subsets corresponding to Blood B cells and Thymic T cells), Baldwin , Yoshimoto02 , Brauer05  and Ronen05 .
Collection of missing value imputation algorithms
In this paper, we present a comprehensive evaluation on the performance of nine imputation algorithms on a wide variety of types and sizes of microarray datasets. We assessed the performance of different algorithms on each dataset. Algorithms used can be divided into two categories: local imputation algorithms and global imputation algorithms.
Missing value imputation methods used in this study
K-nearest neighbors (KNN)
Iterative K-nearest-neighbors (IKNN)
Sequential K-nearest-neighbors (SKNN)
Least squares adaptive (LSA)
Local least squares (LLS)
Iterative local least squares (ILLS)
Sequential local least squares (SLLS)
Bayesian principal component analysis (BPCA)
Singular value decomposition (SVD)
We used three performance indices (normalized root mean squared error, cluster pair proportions and biomarker list concordance index) to assess the performance of imputation algorithms. Based on the type of information used in the index, we categorized these three indices into three different types: (i) statistic index, (ii) clustering index and (iii) differentially expressed genes index.
(i) Statistic index
For the statistic index, we used the normalized root mean squared error (NRMSE) to evaluate the performance of the imputation algorithms. Lower the value of the statistic index, better the algorithm performs.
where y guess and y answer are vectors, the elements of y guess are the imputed values, the elements of y answer are the known answer values, and variance[y answer ] is the variance of y answer .
(ii) Clustering index
An important data analysis in the microarray data is the gene clustering. In this study, k-means was used to do gene clustering for the complete datasets and the imputed datasets. We used cluster pair proportions (CPP)  as a clustering index to evaluate the performance of the algorithms. The numbers of clusters for each dataset was 10. Higher the value of the clustering index, better the algorithm performs.
(iii) Differentially expressed genes index
An important data analysis in the microarray is the identification of differentially expressed genes. In this study, SAM was used to identify differentially expressed genes for the complete dataset and the imputed dataset. We used biomarker list concordance index (BLCI)  as the differentially expressed genes index to evaluate the performance of the algorithms.
where B CD is the significantly differentially expressed genes from the complete data, and B ID is the significantly differentially expressed genes from the imputed data. is the complement set of B C D , and is the complement set of B ID .
Results and discussion
We used (i) thirteen different datasets coming from two organisms (human and yeast), (ii) 110 independent rounds per experiment, and (iii) three kinds of indices to assess nine different algorithms. We thought that the performances of algorithms should be evaluated using measures which can reflect the impact of imputation on downstream analysis. The cluster pair proportions (CPP) is used to assess the results of clustering analysis and the biomarker list concordance index (BLCI) is used to assess the results of identifying differentially expressed genes. Therefore, we used not only normalized root mean squared error (NRMSE), but also CPP and BLCI to evaluate the performance of each algorithm. Such a comprehensive comparison can provide an explicit direction for practitioners and researchers for advanced studies.
In our numerical experiments, thirteen real microarray datasets were used as benchmark datasets and nine algorithms including KNN, SKNN, IKNN, LS, LLS, ILLS, SLLS, BPCA and SVD were used.
The performances of imputation algorithms
In this paper, we compared the performances of imputation algorithms using microarrays of various data types to determine the optimal algorithm. Time series, non-time series and mixed type datasets were used as benchmark datasets, and the performance of each algorithm was evaluated using different measures mentioned above. Furthermore, robustness of an imputation algorithm was also disscussed. We compared robustness of an algorithm between various conditions, such as types of datasets and datasets from samples of different organisms.
The ranking of imputation algorithms for different data types
Performance of imputation algorithms on time series data
The performances (average rank) of algorithms are estimated by different indices. The optimal algorithm is ILLS using NRMSE (average rank = 2.12), the optimal algorithms are ILLS and LLS using CPP (average rank = 3.56) and the optimal algorithm is SLLS using BLCI (average rank = 2.04). To precisely understand the performances of the algorithms on time series datasets, we averaged each average rank of the algorithms using the different indices as the average rank of the algorithms using the average index on time series datasets. The performance of LLS-like algorithms perform well using the average index. The top two of LLS-like algorithms are SLLS and ILLS. The average rank of SLLS is 2.76 and the average rank of ILLS is 2.79.
Performance of imputation algorithms on non-time series data
Performance of imputation algorithms on mixed type data
Performance of imputation algorithms on all data
The optimal algorithm determined by using various indices for different types of datasets.
Robustness of each imputation algorithm
Tuikkala et al. demonstrated that BPCA is the best imputation method on most of datasets , while de Brevern et al. indicated that KNN constitutes one efficient method for restoring the missing values with a low error level . According to our experiences, BPCA does not always perform well on all benchmark datasets, and the performance of KNN is usually worse than that of other methods for most of time, which means that KNN cannot accurately estimate missing values to improve downstream analysis. Integrating the results of the previous studies with our experiences, it strongly suggests that the optimal imputation algorithms for different types of datasets may be different. Therefore, it is necessary to compare the robustness of each imputation method, which is useful for choosing an optimal algorithm for most of the researchers, especially when they cannot ensure the type of their dataset.
Robustness against different data types
Robustness against data from different species
An easy-to-use web tool for missing value imputation
To find an optimal method to solve the missing value problem efficiently, we conducted a comprehensive performance comparison of various missing value imputation algorithms in this work. First, we investigated the impact of different types of microarray data on the performance of imputation methods. Three types of microarray data (time series, non-time series and mixed type) were used as benchmark datasets, and the performance of each algorithm was evaluated using three kinds of measures (NRMSE, CPP and BLCI) and the average of these measures (called the average index). These measures are originally used for different purposes. NRMSE is for estimation of deviation between the estimated values and the real values, CPP is for evaluation of clustering results, and BLCI is for assessing the results of finding differentially expressed genes. Our results suggest that, for time series data, ILLS and SLLS have better performances if one wants to do clustering analysis or find differentially expressed genes. For non-time series data, LS is the best algorithm when the performance is evaluated using NRMSE, while SKNN is better than the others if one wants to conduct downstream microarray data analysis. For mixed type data, ILLS is the best choice if one wants to find differentially expressed genes, but LS would be better for the other two purposes.
Then we investigated whether the microarray data from different species would affect the performance of various imputation methods or not. Our results indicate that what kind of species a dataset comes from does not have any obvious effect on the performance of imputation methods. This means that when one is dealing with missing values, what he needs to consider is not the species that the dataset comes from, but the type of the dataset. Besides, we used a distinct illustration to display the relationship between different types of datasets, which is helpful to reveal the robustness of these imputation methods and is useful for researchers to choose an optimal algorithm for their datasets. Besides, to assist experiment practioners in solving missing value problems directly before data analysis, we developed a web-based imputation tool. In this web tool, only 3 steps are needed, and then users could easily obtain a complete dataset imputed by the optimal algorithm.
This study was supported by the National Cheng Kung University and Taiwan National Science Council NSC 99-2628-B-006-015-MY3.
The full funding for the publication fee came from Taiwan National Science Council and College of Electrical Engineering and Computer Science, National Cheng Kung University.
This article has been published as part of BMC Systems Biology Volume 7 Supplement 6, 2013: Selected articles from the 24th International Conference on Genome Informatics (GIW2013). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/7/S6.
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