- Research
- Open Access
Missing value imputation for microarray data: a comprehensive comparison study and a web tool
- Chia-Chun Chiu^{1},
- Shih-Yao Chan^{1},
- Chung-Ching Wang^{1} and
- Wei-Sheng Wu^{1}Email author
https://doi.org/10.1186/1752-0509-7-S6-S12
© Chiu et al.; licensee BioMed Central Ltd. 2013
- Published: 13 December 2013
Abstract
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.
Keywords
- microarray
- missing value
- imputation
- evaluation
Background
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 [10]. 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 [15], 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 [17]. 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) [17], iterative k nearest neighbors (IKNN) [20], sequential k nearest neighbors (SKNN) [21], least squares adaptive (LSA) [22], local least squares (LLS) [23], iterative local-least-squares (ILLS) [24], sequential local-least-squares (SLLS) [25], and etc. The second category includes Bayesian principal component analysis (BPCA) [26], singular value decomposition (SVD) [17], partial least squares (PLS) and so on. The third category includes LinCmb [11]. The fourth category integrates domain knowledge (Gene Ontology [27] and multiple external datasets [18]) or external information into the imputation process. Projection onto convex sets (POCS) [28], GOimpute, histone acetylation information aided imputation (HAIimpute) [29], weighted nearest neighbors imputation (WeNNI) [30] and integrative missing value estimation (iMISS) [31] 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 [32]. 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.
Methods
Datasets
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 [36], 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 [37]. We also chose the human cell cycle data called Human HeLa from [38]. For non-time series datasets, we chose the datasets (Ogawa, BohenSH and BohenLC) from [39] and [40]. 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 [41] (focused on two experimental subsets corresponding to Blood B cells and Thymic T cells), Baldwin [42], Yoshimoto02 [43], Brauer05 [44] and Ronen05 [45].
Benchmark datasets.
Datasets | ||||
---|---|---|---|---|
Name | Full Dim. | Used Dim. | Category | Species |
Ogawa | 6263*8 | 3069*8 | Non-time series | S.cerevisiae |
Brauer05 | 6133*60 | 706*60 | Mixed type | S.cerevisiae |
Ronen05 | 6987*26 | 2998*26 | Mixed type | S.cerevisiae |
Yoshimoto02 | 6166*24 | 4380*24 | Mixed type | S.cerevisiae |
Spahira04A | 4771*23 | 2970*23 | Time series | S.cerevisiae |
Spahira04B | 4771*14 | 3340*14 | Time series | S.cerevisiae |
Spellman ELU | 6178*14 | 5766*14 | Time series | S.cerevisiae |
Spellman AFA | 6178*18 | 4489*18 | Time series | S.cerevisiae |
BohenSH | 2364*24 | 623*24 | Non-time series | H.sapiens |
BohenLC | 13121*24 | 615*24 | Non-time series | H.sapiens |
Lymphoma | 4026*16 | 2209*16 | Mixed type | H.sapiens |
Baldwin | 16838*39 | 6850*39 | Mixed type | H.sapiens |
Human HeLa | 1134*19 | 920*19 | Time series | H.sapiens |
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
Methods | Author | Programming Language | Year |
---|---|---|---|
Local algorithm | |||
K-nearest neighbors (KNN) | Troyanskaya O. | C | 2001 |
Iterative K-nearest-neighbors (IKNN) | Bras L.P. | R | 2007 |
Sequential K-nearest-neighbors (SKNN) | Kim K.Y. | R | 2004 |
Least squares adaptive (LSA) | Bø T.H. | Java | 2004 |
Local least squares (LLS) | Kim H. | Matlab | 2005 |
Iterative local least squares (ILLS) | Cai Z. | Matlab | 2006 |
Sequential local least squares (SLLS) | Zhang X | R | 2008 |
Global algorithm | |||
Bayesian principal component analysis (BPCA) | Oba S. | R | 2003 |
Singular value decomposition (SVD) | Troyanskaya O. | R | 2001 |
Performance indices
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) [10] 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) [47] 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. ${B}_{CD}^{C}$ is the complement set of B_{ C D }, and ${B}_{ID}^{C}$ 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.
Simulation setting
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.
Index | Data | Best algorithm |
---|---|---|
NRMSE | Time series | ILLS |
Non-time series | LS | |
Mixed type | LS | |
All Data | LS | |
CPP | Time series | ILLS, LLS |
Non-time series | SKNN | |
Mixed type | LS | |
All data | ILLS | |
BLCI | Time series | SLLS |
Non-time series | SKNN | |
Mixed type | ILLS | |
All data | SLLS | |
Average index | Time series | SLLS |
Non-time series | LS | |
Mixed type | ILLS | |
All data | ILLS |
Robustness of each imputation algorithm
Tuikkala et al. demonstrated that BPCA is the best imputation method on most of datasets [33], while de Brevern et al. indicated that KNN constitutes one efficient method for restoring the missing values with a low error level [10]. 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
Conclusions
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.
Declarations
Acknowledgements
This study was supported by the National Cheng Kung University and Taiwan National Science Council NSC 99-2628-B-006-015-MY3.
Declarations
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.
Authors’ Affiliations
References
- Wu W, Li W, Chen B: Computational reconstruction of transcriptional regulatory modules of the yeast cell cycle. BMC Bioinformatics. 2006, 7: 421-10.1186/1471-2105-7-421.PubMed CentralView ArticlePubMedGoogle Scholar
- Rowicka M, Kudlicki A, Tu B, Otwinowski Z: High-resolution timing of cell cycle-regulated gene expression. Proc Natl Acad Sci USA. 2007, 104: 16892-16897. 10.1073/pnas.0706022104.PubMed CentralView ArticlePubMedGoogle Scholar
- Wu W, Li W, Chen B: Identifying regulatory targets of cell cycle transcription factors using gene expression and ChIP-chip data. BMC Bioinformatics. 2007, 8: 188-10.1186/1471-2105-8-188.PubMed CentralView ArticlePubMedGoogle Scholar
- Futschik M, Herzel H: Are we overestimating the number of cell-cycling genes? The impact of background models on time-series analysis. Bioinformatics. 2008, 24: 1063-1069. 10.1093/bioinformatics/btn072.View ArticlePubMedGoogle Scholar
- Wu W, Li W: Systematic identification of yeast cell cycle transcription factors using multiple data sources. BMC Bioinformatics. 2008, 9: 522-10.1186/1471-2105-9-522.PubMed CentralView ArticlePubMedGoogle Scholar
- Siegal-Gaskins D, Ash J, Crosson S: Model-based deconvolution of cell cycle time-series data reveals gene expression details at high resolution. PLoS Comput Biol. 2009, 5: e1000460-10.1371/journal.pcbi.1000460.PubMed CentralView ArticlePubMedGoogle Scholar
- Wang H, Wang Y, Wu W: Yeast cell cycle transcription factors identification by variable selection criteria. Gene. 2011, 485: 172-176. 10.1016/j.gene.2011.06.001.View ArticlePubMedGoogle Scholar
- Gasch A, Spellman P, Kao C, Carmel-Harel O, Eisen M, Storz G, Botstein D, Brown P: Genomic expression programs in the response of yeast cells to environmental changes. Mol Biol Cell. 2000, 11: 4241-4257. 10.1091/mbc.11.12.4241.PubMed CentralView ArticlePubMedGoogle Scholar
- Wu W, Li W: Identifying gene regulatory modules of heat shock response in yeast. BMC Genomics. 2008, 9: 439-10.1186/1471-2164-9-439.PubMed CentralView ArticlePubMedGoogle Scholar
- de Brevern AG, Hazout S, Malpertuy A: Influence of microarrays experiments missing values on the stability of gene groups by hierarchical clustering. BMC Bioinformatics. 2004, 5: 114-10.1186/1471-2105-5-114.PubMed CentralView ArticlePubMedGoogle Scholar
- Jörnsten R, Wang HY, Welsh WJ, Ouyang M: DNA microarray data imputation and significance analysis of differential expression. Bioinformatics. 2005, 21 (22): 4155-4161. 10.1093/bioinformatics/bti638.View ArticlePubMedGoogle Scholar
- Scheel I, Aldrin M, Glad IK, Sørum R, Lyng H, Frigessi A: The influence of missing value imputation on detection of differentially expressed genes from microarray data. Bioinformatics. 2005, 21 (23): 4272-4279. 10.1093/bioinformatics/bti708.View ArticlePubMedGoogle Scholar
- Sehgal MSB, Gondal I, Dooley LS, Coppel R: How to improve postgenomic knowledge discovery using imputation. EURASIP Journal on Bioinformatics and Systems Biology. 2009, 2009: 717136-PubMed CentralView ArticleGoogle Scholar
- Zhang Y, Xuan J, Reyes BGdl, Clarke R, Ressom HW: Reverse engineering module networks by PSO-RNN hybrid modeling. BMC Genomics. 2009, 10 (Suppl 1): S15-10.1186/1471-2164-10-S1-S15.PubMed CentralView ArticlePubMedGoogle Scholar
- Wang D, Lv Y, Guo Z, Li X, Li Y, Zhu J, Yang D, Xu J, Wang C, Rao S, Yang B: Effects of replacing the unreliable cDNA microarray measurements on the disease classification based on gene expression profiles and functional modules. Bioinformatics. 2006, 22 (23): 2883-2889. 10.1093/bioinformatics/btl339.View ArticlePubMedGoogle Scholar
- Ouyang M, Welsh WJ, Georgopoulos P: Gaussian mixture clustering and imputation of microarray data. Bioinformatics. 2004, 20 (6): 917-923. 10.1093/bioinformatics/bth007.View ArticlePubMedGoogle Scholar
- Troyanskaya O, Cantor M, Sherlock G, Brown P, Hastie T, Tibshirani R, Botstein D, Altman RB: Missing value estimation methods for DNA microarrays. Bioinformatics (Oxford, England). 2001, 17 (6): 520-525. 10.1093/bioinformatics/17.6.520.View ArticleGoogle Scholar
- Liew AWC, Law NF, Yan H: Missing value imputation for gene expression data: computational techniques to recover missing data from available information. Briefings in bioinformatics. 2011, 12 (5): 498-513. 10.1093/bib/bbq080.View ArticlePubMedGoogle Scholar
- Moorthy K, Mohamad MS, Deris S: A review on missing value imputation algorithms for microarray gene expression data. Advance in Bioinformatics. 2013,Google Scholar
- Brãs LP, Menezes JC: Improving cluster-based missing value estimation of DNA microarray data. Biomolecular engineering. 2007, 24 (2): 273-282. 10.1016/j.bioeng.2007.04.003.View ArticlePubMedGoogle Scholar
- Kim KY, Kim BJ, Yi GS: Reuse of imputed data in microarray analysis increases imputation efficiency. BMC Bioinformatics. 2004, 5: 160-10.1186/1471-2105-5-160.PubMed CentralView ArticlePubMedGoogle Scholar
- Bø TH, Dysvik B, Jonassen I: LSimpute: accurate estimation of missing values in microarray data with least squares methods. Nucleic Acids Research. 2004, 32 (3): e34-10.1093/nar/gnh026.PubMed CentralView ArticlePubMedGoogle Scholar
- Kim H, Golub GH, Park H: Missing value estimation for DNA microarray gene expression data: local least squares imputation. Bioinformatics. 2005, 21 (2): 187-198. 10.1093/bioinformatics/bth499.View ArticlePubMedGoogle Scholar
- Cai Z, Heydari M, Lin G: Iterated local least squares microarray missing value imputation. Journal of bioinformatics and computational biology. 2006, 4 (5): 935-957. 10.1142/S0219720006002302.View ArticlePubMedGoogle Scholar
- Zhang X, Song X, Wang H, Zhang H: Sequential local least squares imputation estimating missing value of microarray data. Computers in biology and medicine. 2008, 38 (10): 1112-1120. 10.1016/j.compbiomed.2008.08.006.View ArticlePubMedGoogle Scholar
- Oba S, Sato Ma, Takemasa I, Monden M, Matsubara Ki, Ishii S: A Bayesian missing value estimation method for gene expression profile data. Bioinformatics. 2003, 19 (16): 2088-2096. 10.1093/bioinformatics/btg287.View ArticlePubMedGoogle Scholar
- Jelizarow M, Guillemot V, Tenenhaus A, Strimmer K, Boulesteix AL: Over-optimism in bioinformatics: an illustration. Bioinformatics. 2010, 26 (16): 1990-1998. 10.1093/bioinformatics/btq323.View ArticlePubMedGoogle Scholar
- Gan X, Liew AWC, Yan H: Microarray missing data imputation based on a set theoretic framework and biological knowledge. Nucleic Acids Research. 2006, 34 (5): 1608-1619. 10.1093/nar/gkl047.PubMed CentralView ArticlePubMedGoogle Scholar
- Xiang Q, Dai X, Deng Y, He C, Wang J, Feng J, Dai Z: Missing value imputation for microarray gene expression data using histone acetylation information. BMC Bioinformatics. 2008, 9: 252-10.1186/1471-2105-9-252.PubMed CentralView ArticlePubMedGoogle Scholar
- Johansson P, Häkkinen J: Improving missing value imputation of microarray data by using spot quality weights. BMC Bioinformatics. 2006, 7: 306-10.1186/1471-2105-7-306.PubMed CentralView ArticlePubMedGoogle Scholar
- Hu J, Li H, Waterman MS, Zhou XJ: Integrative missing value estimation for microarray data. BMC Bioinformatics. 2006, 7: 449-10.1186/1471-2105-7-449.PubMed CentralView ArticlePubMedGoogle Scholar
- Brock GN, Shaffer JR, Blakesley RE, Lotz MJ, Tseng GC: Which missing value imputation method to use in expression profiles: a comparative study and two selection schemes. BMC Bioinformatics. 2008, 9: 12-10.1186/1471-2105-9-12.PubMed CentralView ArticlePubMedGoogle Scholar
- Tuikkala J, Elo LL, Nevalainen OS, Aittokallio T: Missing value imputation improves clustering and interpretation of gene expression microarray data. BMC Bioinformatics. 2008, 9: 202-10.1186/1471-2105-9-202.PubMed CentralView ArticlePubMedGoogle Scholar
- Celton M, Malpertuy A, Lelandais G, Brevern AGd: Comparative analysis of missing value imputation methods to improve clustering and interpretation of microarray experiments. BMC Genomics. 2010, 11: 15-10.1186/1471-2164-11-15.PubMed CentralView ArticlePubMedGoogle Scholar
- Rao SSS, Shepherd LA, Bruno AE, Liu S, Miecznikowski JC: Comparing imputation procedures for Affymetrix gene expression datasets using MAQC datasets. Current Bioinformatics. 2013,Google Scholar
- Spellman PT, Sherlock G, Zhang MQ, Iyer VR, Anders K, Eisen MB, Brown PO, Botstein D, Futcher B: Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Molecular Biology of the Cell. 1998, 9 (12): 3273-3297. 10.1091/mbc.9.12.3273.PubMed CentralView ArticlePubMedGoogle Scholar
- Shapira M, Segal E, Botstein D: Disruption of yeast forkhead-associated cell cycle transcription by oxidative stress. Molecular Biology of the Cell. 2004, 15 (12): 5659-5669. 10.1091/mbc.E04-04-0340.PubMed CentralView ArticlePubMedGoogle Scholar
- Whitfield ML, Sherlock G, Saldanha AJ, Murray JI, Ball CA, Alexander KE, Matese JC, Perou CM, Hurt MM, Brown PO, Botstein D: Identification of genes periodically expressed in the human cell cycle and their expression in tumors. Molecular biology of the cell. 2002, 13 (6): 1977-2000. 10.1091/mbc.02-02-0030..PubMed CentralView ArticlePubMedGoogle Scholar
- Ogawa N, DeRisi J, Brown PO: New components of a system for phosphate accumulation and polyphosphate metabolism in Saccharomyces cerevisiae revealed by genomic expression analysis. Molecular biology of the cell. 2000, 11 (12): 4309-4321. 10.1091/mbc.11.12.4309.PubMed CentralView ArticlePubMedGoogle Scholar
- Bohen SP, Troyanskaya OG, Alter O, Warnke R, Botstein D, Brown PO, Levy R: Variation in gene expression patterns in follicular lymphoma and the response to rituximab. Proceedings of the National Academy of Sciences of the United States of America. 2003, 100 (4): 1926-1930. 10.1073/pnas.0437875100.PubMed CentralView ArticlePubMedGoogle Scholar
- Alizadeh AA, Eisen MB, Davis RE, Ma C, Lossos IS, Rosenwald A, Boldrick JC, Sabet H, Tran T, Yu X, Powell JI, Yang L, Marti GE, Moore T, Hudson JJ, Lu L, Lewis DB, Tibshirani R, Sherlock G, Chan WC, Greiner TC, Weisenburger DD, Armitage JO, Warnke R, Levy R, Wilson W, Grever MR, Byrd JC, Botstein D, Brown PO, Staudt LM: Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature. 2000, 403 (6769): 503-511. 10.1038/35000501.View ArticlePubMedGoogle Scholar
- Baldwin DN, Vanchinathan V, Brown PO, Theriot JA: A gene-expression program reflecting the innate immune response of cultured intestinal epithelial cells to infection by Listeria monocytogenes. Genome Biology. 2002, 4: R2-10.1186/gb-2002-4-1-r2.PubMed CentralView ArticlePubMedGoogle Scholar
- Yoshimoto H, Saltsman K, Gasch AP, Li HX, Ogawa N, Botstein D, Brown PO, Cyert MS: Genome-wide analysis of gene expression regulated by the calcineurin/Crz1p signaling pathway in Saccharomyces cerevisiae. The Journal of biological chemistry. 2002, 277 (34): 31079-31088. 10.1074/jbc.M202718200.View ArticlePubMedGoogle Scholar
- Brauer MJ, Saldanha AJ, Dolinski K, Botstein D: Homeostatic adjustment and metabolic remodeling in glucose-limited yeast cultures. Molecular Biology of the Cell. 2005, 16 (5): 2503-2517. 10.1091/mbc.E04-11-0968.PubMed CentralView ArticlePubMedGoogle Scholar
- Ronen M, Botstein D: Transcriptional response of steady-state yeast cultures to transient perturbations in carbon source. Proceedings of the National Academy of Sciences of the United States of America. 2006, 103 (2): 389-394. 10.1073/pnas.0509978103.PubMed CentralView ArticlePubMedGoogle Scholar
- Sehgal MSB, Gondal I, Dooley LS: Collateral missing value imputation: a new robust missing value estimation algorithm for microarray data. Bioinformatics (Oxford, England). 2005, 21 (10): 2417-2423. 10.1093/bioinformatics/bti345.View ArticleGoogle Scholar
- Oh S, Kang DD, Brock GN, Tseng GC: Biological impact of missing-value imputation on downstream analyses of gene expression profiles. Bioinformatics. 2011, 27: 78-86. 10.1093/bioinformatics/btq613.PubMed CentralView ArticlePubMedGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.