University of Texas MD Anderson Cancer Center

Robust Classification of Functional and Quantitative Image Data using Functional Mixed Models

Hongxiao Zhu et al. — Thu, 17 Nov 2011 12:31:38 PST

In this paper, we introduce classification of complex high dimensional functional data in the functional mixed model (FMM) framework. The FMM relates a functional response to a set of scalar predictors through functional fixed and random effects, and therefore is able to account for various factors that affecting the functions and inducing correlations. Classification is performed through training the data by treating the class as one of the fixed effects, and then predicting on the test data using posterior predictive probabilities. Through a Bayesian scheme, we are able to incorporate not only all factors that influencing the functions, but also factors that directly affect class designation. While this classification method is general for all FMM methods, we provide details for two specific Bayesian approaches, the Gaussian, wavelet-based functional mixed model (G-WFMM) and the robust, wavelet-based functional mixed model (R-WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features, and accommodates various nonstationarities. The R-WFMM has the additional advantage of allowing potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down-weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a real mass spectroscopy dataset in pancreatic cancer research. Our results show improved classification when comparing FMM with other typical functional data classification methods and the ad hoc methods that are based on detected spectral peaks.

Statistical Methods for Proteomic Biomarker Discovery Based on Feature Extraction or Functional Modeling Approaches

Jeffrey S. Morris — Tue, 27 Sep 2011 07:36:39 PDT

In recent years, developments in molecular biotechnology have led to the increased promise of detecting and validating biomarkers, or molecular markers that relate to various biological or medical outcomes. Proteomics, the direct study of proteins in biological samples, plays an important role in the biomarker discovery process. These technologies produce complex, high dimensional functional and image data that present many analytical challenges that must be addressed properly for eective comparative proteomics studies that can yield potential biomarkers. Specic challenges include experimental design, preprocessing, feature extraction, and statistical analysis accounting for the inherent multiple testing issues. This paper reviews various computational aspects of comparative proteomic studies, and summarizes contributions I along with numerous collaborators have made. First, there is an overview of comparative proteomics technologies, followed by a discussion of important experimental design and preprocessing issues that must be considered before statistical analysis can be done. Next, the two key approaches to analyzing proteomics data, feature extraction and functional modeling, are described. Feature extraction involves detection and quantication of discrete features like peaks or spots that theoretically correspond to dierent proteins in the sample. After an overview of the feature extraction approach, specic methods for mass spectrometry (Cromwell ) and 2D gel electrophoresis (Pinnacle) are described. The functional modeling approach involves modeling the proteomic data in their entirety as functions or images. A general discussion of the approach is followed by the presentation of a specic method that can be applied, wavelet-based functional mixed models, and its extensions. All methods are illustrated by application to two example proteomic data sets, one from mass spectrometry and one from 2D gel electrophoresis. While the specific methods presented are applied to two specic proteomic technologies, MALDI-TOF and 2D gel electrophoresis, these methods and the other principles discussed in the paper apply much more broadly to other expression proteomics technologies.

Robust, Adaptive Functional Regression in Functional Mixed Model Framework

Hongxiao Zhu et al. — Fri, 11 Mar 2011 12:07:48 PST

Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images),and using other invertible transformations as alternatives to wavelets.

Code for fitting BDSAcgh

Veera Baladandayuthapani — Mon, 11 Oct 2010 14:38:40 PDT

Software for fitting hierarchical spatial functional models

Veera Baladandayuthapani — Mon, 11 Oct 2010 14:35:46 PDT

Matlab code for Bayesian fitting of adaptive P-splines in regression

Veera Baladandayuthapani — Fri, 08 Oct 2010 15:22:00 PDT

Bayesian Random SegmentationModels to Identify Shared Copy Number Aberrations for Array CGH Data

Veera Baladandayuthapani — Mon, 04 Oct 2010 19:22:44 PDT

Members’ Discoveries: Fatal flaws in cancer research

Jeffrey S. Morris — Wed, 26 May 2010 14:52:47 PDT

A recent article published in The Annals of Applied Statistics (AOAS) by two MD Anderson researchers—Keith Baggerly and Kevin Coombes—dissects results from a highly-influential series of medical papers involving genomics-driven personalized cancer therapy, and outlines a series of simple yet fatal flaws that raises serious questions about the veracity of the original results. Having immediate and strong impact, this paper, along with related work, is providing the impetus for new standards of reproducibility in scientific research.

Informatics and Statistics for Analyzing 2-D Gel Electrophoresis Images

Andrew W. Dowsey et al. — Wed, 26 May 2010 14:48:20 PDT

Whilst recent progress in ‘shotgun’ peptide separation by integrated liquid chromatography and mass spectrometry (LC/MS) has enabled its use as a sensitive analytical technique, proteome coverage and reproducibility is still limited and obtaining enough replicate runs for biomarker discovery is a challenge. For these reasons, recent research demonstrates the continuing need for protein separation by two-dimensional gel electrophoresis (2-DE). However, with traditional 2-DE informatics, the digitized images are reduced to symbolic data though spot detection and quantification before proteins are compared for differential expression by spot matching. Recently, a more robust and automated paradigm has emerged where gels are directly aligned in the image domain before spots are detected across the whole image set as a whole. In this chapter we describe the methodology for both approaches and discuss the pitfalls present when reasoning statistically about the differential protein expression discovered.

Statistical Contributions to Proteomic Research

Jeffrey S. Morris et al. — Wed, 26 May 2010 14:39:39 PDT

Proteomic profiling has the potential to impact the diagnosis, prognosis, and treatment of various diseases. A number of different proteomic technologies are available that allow us to look at many proteins at once, and all of them yield complex data that raise significant quantitative challenges. Inadequate attention to these quantitative issues can prevent these studies from achieving their desired goals, and can even lead to invalid results. In this chapter, we describe various ways the involvement of statisticians or other quantitative scientists in the study team can contribute to the success of proteomic research, and we outline some of the key statistical principles that should guide the experimental design and analysis of such studies.