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

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusion</p> <p>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).</p

Transposable regularized covariance models with an application to missing data imputation

Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so-called transposable regularized covariance models allow for maximum likelihood estimation of the mean and nonsingular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS314 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Algorithmic Techniques in Gene Expression Processing. From Imputation to Visualization

The amount of biological data has grown exponentially in recent decades. Modern biotechnologies, such as microarrays and next-generation sequencing, are capable to produce massive amounts of biomedical data in a single experiment. As the amount of the data is rapidly growing there is an urgent need for reliable computational methods for analyzing and visualizing it. This thesis addresses this need by studying how to efficiently and reliably analyze and visualize high-dimensional data, especially that obtained from gene expression microarray experiments. First, we will study the ways to improve the quality of microarray data by replacing (imputing) the missing data entries with the estimated values for these entries. Missing value imputation is a method which is commonly used to make the original incomplete data complete, thus making it easier to be analyzed with statistical and computational methods. Our novel approach was to use curated external biological information as a guide for the missing value imputation. Secondly, we studied the effect of missing value imputation on the downstream data analysis methods like clustering. We compared multiple recent imputation algorithms against 8 publicly available microarray data sets. It was observed that the missing value imputation indeed is a rational way to improve the quality of biological data. The research revealed differences between the clustering results obtained with different imputation methods. On most data sets, the simple and fast k-NN imputation was good enough, but there were also needs for more advanced imputation methods, such as Bayesian Principal Component Algorithm (BPCA). Finally, we studied the visualization of biological network data. Biological interaction networks are examples of the outcome of multiple biological experiments such as using the gene microarray techniques. Such networks are typically very large and highly connected, thus there is a need for fast algorithms for producing visually pleasant layouts. A computationally efficient way to produce layouts of large biological interaction networks was developed. The algorithm uses multilevel optimization within the regular force directed graph layout algorithm.Siirretty Doriast

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

Incomplete Data Analysis

This chapter discusses missing-value problems from the perspective of machine learning. Missing values frequently occur during data acquisition. When a dataset contains missing values, nonvectorial data are generated. This subsequently causes a serious problem in pattern recognition models because nonvectorial data need further data wrangling before models are built. In view of such, this chapter reviews the methodologies of related works and examines their empirical effectiveness. At present, a great deal of effort has been devoted in this field, and those works can be roughly divided into two types — Multiple imputation and single imputation, where the latter can be further classified into subcategories. They include deletion, fixed-value replacement, K-Nearest Neighbors, regression, tree-based algorithms, and latent component-based approaches. In this chapter, those approaches are introduced and commented. Finally, numerical examples are provided along with recommendations on future development

Prediction with Missing Data

Missing information is inevitable in real-world data sets. While imputation is well-suited and theoretically sound for statistical inference, its relevance and practical implementation for out-of-sample prediction remains unsettled. We provide a theoretical analysis of widely used data imputation methods and highlight their key deficiencies in making accurate predictions. Alternatively, we propose adaptive linear regression, a new class of models that can be directly trained and evaluated on partially observed data, adapting to the set of available features. In particular, we show that certain adaptive regression models are equivalent to impute-then-regress methods where the imputation and the regression models are learned simultaneously instead of sequentially. We validate our theoretical findings and adaptive regression approach with numerical results with real-world data sets

Data analysis tools for mass spectrometry proteomics

ABSTRACT Proteins are large biomolecules which consist of amino acid chains. They differ from one another in their amino acid sequences, which are mainly dictated by the nucleotide sequence of their corresponding genes. Proteins fold into specific threedimensional structures that determine their activity. Because many of the proteins act as catalytes in biochemical reactions, they are considered as the executive molecules in the cells and therefore their research is fundamental in biotechnology and medicine. Currently the most common method to investigate the activity, interactions, and functions of proteins on a large scale, is high-throughput mass spectrometry (MS). The mass spectrometers are used for measuring the molecule masses, or more specifically, their mass-to-charge ratios. Typically the proteins are digested into peptides and their masses are measured by mass spectrometry. The masses are matched against known sequences to acquire peptide identifications, and subsequently, the proteins from which the peptides were originated are quantified. The data that are gathered from these experiments contain a lot of noise, leading to loss of relevant information and even to wrong conclusions. The noise can be related, for example, to differences in the sample preparation or to technical limitations of the analysis equipment. In addition, assumptions regarding the data might be wrong or the chosen statistical methods might not be suitable. Taken together, these can lead to irreproducible results. Developing algorithms and computational tools to overcome the underlying issues is of most importance. Thus, this work aims to develop new computational tools to address these problems. In this PhD Thesis, the performance of existing label-free proteomics methods are evaluated and new statistical data analysis methods are proposed. The tested methods include several widely used normalization methods, which are thoroughly evaluated using multiple gold standard datasets. Various statistical methods for differential expression analysis are also evaluated. Furthermore, new methods to calculate differential expression statistic are developed and their superior performance compared to the existing methods is shown using a wide set of metrics. The tools are published as open source software packages.TIIVISTELMÄ Proteiinit ovat aminohappoketjuista muodostuvia isoja biomolekyylejä. Ne eroavat toisistaan aminohappojen järjestyksen osalta, mikä pääosin määräytyy proteiineja koodaavien geenien perusteella. Lisäksi proteiinit laskostuvat kolmiulotteisiksi rakenteiksi, jotka osaltaan määrittelevät niiden toimintaa. Koska proteiinit toimivat katalyytteinä biokemiallisissa reaktioissa, niillä katsotaan olevan keskeinen rooli soluissa ja siksi myös niiden tutkimusta pidetään tärkeänä. Tällä hetkellä yleisin menetelmä laajamittaiseen proteiinien aktiivisuuden, interaktioiden sekä funktioiden tutkimiseen on suurikapasiteettinen massaspektrometria (MS). Massaspektrometreja käytetään mittaamaan molekyylien massoja – tai tarkemmin massan ja varauksen suhdetta. Tyypillisesti proteiinit hajotetaan peptideiksi massojen mittausta varten. Massaspektrometrillä havaittuja massoja verrataan tunnetuista proteiinisekvensseistä koottua tietokantaa vasten, jotta peptidit voidaan tunnistaa. Peptidien myötä myös proteiinit on mahdollista päätellä ja kvantitoida. Kokeissa kerätty data sisältää normaalisti runsaasti kohinaa, joka saattaa johtaa olennaisen tiedon hukkumiseen ja jopa pahimmillaan johtaa vääriin johtopäätöksiin. Tämä kohina voi johtua esimerkiksi näytteen käsittelystä johtuvista eroista tai mittalaitteiden teknisistä rajoitteista. Lisäksi olettamukset datan luonteesta saattavat olla virheellisiä tai käytetään datalle soveltumattomia tilastollisia malleja. Pahimmillaan tämä johtaa tilanteisiin, joissa tutkimuksen tuloksia ei pystytä toistamaan. Erilaisten laskennallisten työkalujen sekä algoritmien kehittäminen näiden ongelmien ehkäisemiseksi onkin ensiarvoisen tärkeää tutkimusten luotettavuuden kannalta. Tässä työssä keskitytäänkin sovelluksiin, joilla pyritään ratkaisemaan tällä osa-alueella ilmeneviä ongelmia. Tutkimuksessa vertaillaan yleisesti käytössä olevia kvantitatiivisen proteomiikan ohjelmistoja ja yleisimpiä datan normalisointimenetelmiä, sekä kehitetään uusia datan analysointityökaluja. Menetelmien keskinäiset vertailut suoritetaan useiden sellaisten standardiaineistojen kanssa, joiden todellinen sisältö tiedetään. Tutkimuksessa vertaillaan lisäksi joukko tilastollisia menetelmiä näytteiden välisten erojen havaitsemiseen sekä kehitetään kokonaan uusia tehokkaita menetelmiä ja osoitetaan niiden parempi suorituskyky suhteessa aikaisempiin menetelmiin. Kaikki tutkimuksessa kehitetyt työkalut on julkaistu avoimen lähdekoodin sovelluksina

Dealing with missing values in DNA microarray

Ph.DDOCTOR OF PHILOSOPH