Identifying Biomarkers from Mass Spectrometry Data with Ordinal Outcome

In recent years, there has been an increased interest in using protein mass spectroscopy to identify molecular markers that discriminate diseased from healthy individuals. Existing methods are tailored towards classifying observations into nominal categories. Sometimes, however, the outcome of interest may be measured on an ordered scale. Ignoring this natural ordering results in some loss of information. In this paper, we propose a Bayesian model for the analysis of mass spectrometry data with ordered outcome. The method provides a unified approach for identifying relevant markers and predicting class membership. This is accomplished by building a stochastic search variable selection method within an ordinal outcome model. We apply the methodology to mass spectrometry data on ovarian cancer cases and healthy individuals. We also utilize wavelet-based techniques to remove noise from the mass spectra prior to analysis. We identify protein markers associated with being healthy, having low grade ovarian cancer, or being a high grade case. For comparison, we repeated the analysis using conventional classification procedures and found improved predictive accuracy with our method

KONSTRUKCJA I WERYFIKACJA MATEMATYCZNEGO MODELU DANYCH WIDM MASOWYCH

The article presents issues concerning construction, adjustment and implementation of mass spectrometry mathematical model based on Gaussians and Mixture Models and the mean spectrum. This task is essential to the analysis and it needs specification of many parameters of the model.Artykuł przedstawia kwestie związane z konstrukcją, dopasowaniem i implementacją modelu matematycznego widm masowych opartego o rozkłady normalne i mieszaniny rozkładów oraz o widmo średnie. To zadanie jest kluczowe dla analizy, wymaga też określenia wielu parametrów modelu

An adaptive ensemble learner function via bagging and rank aggregation with applications to high dimensional data.

An ensemble consists of a set of individual predictors whose predictions are combined. Generally, different classification and regression models tend to work well for different types of data and also, it is usually not know which algorithm will be optimal in any given application. In this thesis an ensemble regression function is presented which is adapted from Datta et al. 2010. The ensemble function is constructed by combining bagging and rank aggregation that is capable of changing its performance depending on the type of data that is being used. In the classification approach, the results can be optimized with respect to performance measures such as accuracy, sensitivity, specificity and area under the curve (AUC) whereas in the regression approach, it can be optimized with respect to measures such as mean square error and mean absolute error. The ensemble classifier and ensemble regressor performs at the level of the best individual classifier or regression model. For complex high-dimensional datasets, it may be advisable to combine a number of classification algorithms or regression algorithms rather than using one specific algorithm

Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Underdetermined blind separation of nonnegative dependent sources consists in decomposing set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture-wise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization (NMF) therein. Thus, original problem is converted into new one with increased number of mixtures, increased number of dependent sources and higher-order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, that is the case for mass spectra of analytes, sparseness constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of ten dependent components from five mixtures and to extraction of ten dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples

Inferential stability in systems biology

The modern biological sciences are fraught with statistical difficulties. Biomolecular stochasticity, experimental noise, and the “large p, small n” problem all contribute to the challenge of data analysis. Nevertheless, we routinely seek to draw robust, meaningful conclusions from observations. In this thesis, we explore methods for assessing the effects of data variability upon downstream inference, in an attempt to quantify and promote the stability of the inferences we make. We start with a review of existing methods for addressing this problem, focusing upon the bootstrap and similar methods. The key requirement for all such approaches is a statistical model that approximates the data generating process. We move on to consider biomarker discovery problems. We present a novel algorithm for proposing putative biomarkers on the strength of both their predictive ability and the stability with which they are selected. In a simulation study, we find our approach to perform favourably in comparison to strategies that select on the basis of predictive performance alone. We then consider the real problem of identifying protein peak biomarkers for HAM/TSP, an inflammatory condition of the central nervous system caused by HTLV-1 infection. We apply our algorithm to a set of SELDI mass spectral data, and identify a number of putative biomarkers. Additional experimental work, together with known results from the literature, provides corroborating evidence for the validity of these putative biomarkers. Having focused on static observations, we then make the natural progression to time course data sets. We propose a (Bayesian) bootstrap approach for such data, and then apply our method in the context of gene network inference and the estimation of parameters in ordinary differential equation models. We find that the inferred gene networks are relatively unstable, and demonstrate the importance of finding distributions of ODE parameter estimates, rather than single point estimates

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

New Statistical Algorithms for the Analysis of Mass Spectrometry Time-Of-Flight Mass Data with Applications in Clinical Diagnostics

Mass spectrometry (MS) based techniques have emerged as a standard forlarge-scale protein analysis. The ongoing progress in terms of more sensitive machines and improved data analysis algorithms led to a constant expansion of its fields of applications. Recently, MS was introduced into clinical proteomics with the prospect of early disease detection using proteomic pattern matching. Analyzing biological samples (e.g. blood) by mass spectrometry generates mass spectra that represent the components (molecules) contained in a sample as masses and their respective relative concentrations. In this work, we are interested in those components that are constant within a group of individuals but differ much between individuals of two distinct groups. These distinguishing components that dependent on a particular medical condition are generally called biomarkers. Since not all biomarkers found by the algorithms are of equal (discriminating) quality we are only interested in a small biomarker subset that - as a combination - can be used as a fingerprint for a disease. Once a fingerprint for a particular disease (or medical condition) is identified, it can be used in clinical diagnostics to classify unknown spectra. In this thesis we have developed new algorithms for automatic extraction of disease specific fingerprints from mass spectrometry data. Special emphasis has been put on designing highly sensitive methods with respect to signal detection. Thanks to our statistically based approach our methods are able to detect signals even below the noise level inherent in data acquired by common MS machines, such as hormones. To provide access to these new classes of algorithms to collaborating groups we have created a web-based analysis platform that provides all necessary interfaces for data transfer, data analysis and result inspection. To prove the platform's practical relevance it has been utilized in several clinical studies two of which are presented in this thesis. In these studies it could be shown that our platform is superior to commercial systems with respect to fingerprint identification. As an outcome of these studies several fingerprints for different cancer types (bladder, kidney, testicle, pancreas, colon and thyroid) have been detected and validated. The clinical partners in fact emphasize that these results would be impossible with a less sensitive analysis tool (such as the currently available systems). In addition to the issue of reliably finding and handling signals in noise we faced the problem to handle very large amounts of data, since an average dataset of an individual is about 2.5 Gigabytes in size and we have data of hundreds to thousands of persons. To cope with these large datasets, we developed a new framework for a heterogeneous (quasi) ad-hoc Grid - an infrastructure that allows to integrate thousands of computing resources (e.g. Desktop Computers, Computing Clusters or specialized hardware, such as IBM's Cell Processor in a Playstation 3)

The Affine Uncertainty Principle, Associated Frames and Applications in Signal Processing

Uncertainty relations play a prominent role in signal processing, stating that a signal can not be simultaneously concentrated in the two related domains of the corresponding phase space. In particular, a new uncertainty principle for the affine group, which is directly related to the wavelet transform has lead to a new minimizing waveform. In this thesis, a frame construction is proposed which leads to approximately tight frames based on this minimizing waveform. Frame properties such as the diagonality of the frame operator as well as lower and upper frame bounds are analyzed. Additionally, three applications of such frame constructions are introduced: inpainting of missing audio data, detection of neuronal spikes in extracellular recorded data and peak detection in MALDI imaging data