Biomedical subjects

Edward R Dougherty

Publications and source records attributed to Edward R Dougherty.

10 recordsLinked to original sources

PubMed2003

Corrected small-sample estimation of the Bayes error.

MOTIVATION: A major problem of pattern classification is estimation of the Bayes error when only small samples are available. One way to estimate the Bayes error is to design a classifier based on some classification rule applied to sample data, estimate the error of the designed classifier, and then use this estimate as an estimate of the Bayes error. Relative to the Bayes error, the expected error of the designed classifier is biased high, and this bias can be severe with small samples. RESULTS: This paper provides a correction for the bias by subtracting a term derived from the representation of the estimation error. It does so for Boolean classifiers, these being defined on binary features. Although the general theory applies to any Boolean classifier, a model is introduced to reduce the number of parameters. A key point is that the expected correction is conservative. Properties of the corrected estimate are studied via simulation. The correction applies to binary predictors because they are mathematically identical to Boolean classifiers. In this context the correction is adapted to the coefficient of determination, which has been used to measure nonlinear multivariate relations between genes and design genetic regulatory networks. An application using gene-expression data from a microarray experiment is provided on the website http://gspsnap.tamu.edu/smallsample/ (user:'smallsample', password:'smallsample)').

Algorithms↗

PubMed2003

Gene selection: a Bayesian variable selection approach.

UNLABELLED: Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.

Algorithms↗

PubMed2002

Inference from clustering with application to gene-expression microarrays.

There are many algorithms to cluster sample data points based on nearness or a similarity measure. Often the implication is that points in different clusters come from different underlying classes, whereas those in the same cluster come from the same class. Stochastically, the underlying classes represent different random processes. The inference is that clusters represent a partition of the sample points according to which process they belong. This paper discusses a model-based clustering toolbox that evaluates cluster accuracy. Each random process is modeled as its mean plus independent noise, sample points are generated, the points are clustered, and the clustering error is the number of points clustered incorrectly according to the generating random processes. Various clustering algorithms are evaluated based on process variance and the key issue of the rate at which algorithmic performance improves with increasing numbers of experimental replications. The model means can be selected by hand to test the separability of expected types of biological expression patterns. Alternatively, the model can be seeded by real data to test the expected precision of that output or the extent of improvement in precision that replication could provide. In the latter case, a clustering algorithm is used to form clusters, and the model is seeded with the means and variances of these clusters. Other algorithms are then tested relative to the seeding algorithm. Results are averaged over various seeds. Output includes error tables and graphs, confusion matrices, principal-component plots, and validation measures. Five algorithms are studied in detail: K-means, fuzzy C-means, self-organizing maps, hierarchical Euclidean-distance-based and correlation-based clustering. The toolbox is applied to gene-expression clustering based on cDNA microarrays using real data. Expression profile graphics are generated and error analysis is displayed within the context of these profile graphics. A large amount of generated output is available over the web.

Computational Biology↗

PubMed2002

Strong feature sets from small samples.

For small samples, classifier design algorithms typically suffer from overfitting. Given a set of features, a classifier must be designed and its error estimated. For small samples, an error estimator may be unbiased but, owing to a large variance, often give very optimistic estimates. This paper proposes mitigating the small-sample problem by designing classifiers from a probability distribution resulting from spreading the mass of the sample points to make classification more difficult, while maintaining sample geometry. The algorithm is parameterized by the variance of the spreading distribution. By increasing the spread, the algorithm finds gene sets whose classification accuracy remains strong relative to greater spreading of the sample. The error gives a measure of the strength of the feature set as a function of the spread. The algorithm yields feature sets that can distinguish the two classes, not only for the sample data, but for distributions spread beyond the sample data. For linear classifiers, the topic of the present paper, the classifiers are derived analytically from the model, thereby providing an enormous savings in computation time. The algorithm is applied to cancer classification via cDNA microarrays. In particular, the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the algorithm is used to find gene sets whose expressions can be used to classify BRCA1 and BRCA2 tumors.

Breast Neoplasms↗

PubMed2002

Gene perturbation and intervention in probabilistic Boolean networks.

MOTIVATION: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as cancer. We consider the general question of the potential effect of individual genes on the global dynamical network behavior, both from the view of random gene perturbation as well as intervention in order to elicit desired network behavior. RESULTS: Using a recently introduced class of models, called Probabilistic Boolean Networks (PBNs), this paper develops a model for random gene perturbations and derives an explicit formula for the transition probabilities in the new PBN model. This result provides a building block for performing simulations and deriving other results concerning network dynamics. An example is provided to show how the gene perturbation model can be used to compute long-term influences of genes on other genes. Following this, the problem of intervention is addressed via the development of several computational tools based on first-passage times in Markov chains. The consequence is a methodology for finding the best gene with which to intervene in order to most likely achieve desirable network behavior. The ideas are illustrated with several examples in which the goal is to induce the network to transition into a desired state, or set of states. The corresponding issue of avoiding undesirable states is also addressed. Finally, the paper turns to the important problem of assessing the effect of gene perturbations on long-run network behavior. A bound on the steady-state probabilities is derived in terms of the perturbation probability. The result demonstrates that states of the network that are more 'easily reachable' from other states are more stable in the presence of gene perturbations. Consequently, these are hypothesized to correspond to cellular functional states. AVAILABILITY: A library of functions written in MATLAB for simulating PBNs, constructing state-transition matrices, computing steady-state distributions, computing influences, modeling random gene perturbations, and finding optimal intervention targets, as described in this paper, is available on request from is@ieee.org.

Chromosome Mapping↗

PubMed2002

Probabilistic Boolean Networks: a rule-based uncertainty model for gene regulatory networks.

MOTIVATION: Our goal is to construct a model for genetic regulatory networks such that the model class: (i) incorporates rule-based dependencies between genes; (ii) allows the systematic study of global network dynamics; (iii) is able to cope with uncertainty, both in the data and the model selection; and (iv) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes. RESULTS: We introduce Probabilistic Boolean Networks (PBN) that share the appealing rule-based properties of Boolean networks, but are robust in the face of uncertainty. We show how the dynamics of these networks can be studied in the probabilistic context of Markov chains, with standard Boolean networks being special cases. Then, we discuss the relationship between PBNs and Bayesian networks--a family of graphical models that explicitly represent probabilistic relationships between variables. We show how probabilistic dependencies between a gene and its parent genes, constituting the basic building blocks of Bayesian networks, can be obtained from PBNs. Finally, we present methods for quantifying the influence of genes on other genes, within the context of PBNs. Examples illustrating the above concepts are presented throughout the paper.

Cell Cycle↗

PubMed2002

Ratio statistics of gene expression levels and applications to microarray data analysis.

MOTIVATION: Expression-based analysis for large families of genes has recently become possible owing to the development of cDNA microarrays, which allow simultaneous measurement of transcript levels for thousands of genes. For each spot on a microarray, signals in two channels must be extracted from their backgrounds. This requires algorithms to extract signals arising from tagged mRNA hybridized to arrayed cDNA locations and algorithms to determine the significance of signal ratios. RESULTS: This paper focuses on estimation of signal ratios from the two channels, and the significance of those ratios. The key issue is the determination of whether a ratio is significantly high or low in order to conclude whether the gene is upregulated or downregulated. The paper builds on an earlier study that involved a hypothesis test based on a ratio statistic under the supposition that the measured fluorescent intensities subsequent to image processing can be assumed to reflect the signal intensities. Here, a refined hypothesis test is considered in which the measured intensities forming the ratio are assumed to be combinations of signal and background. The new method involves a signal-to-noise ratio, and for a high signal-to-noise ratio the new test reduces (with close approximation) to the original test. The effect of low signal-to-noise ratio on the ratio statistics constitutes the main theme of the paper. Finally, and in this vein, a quality metric is formulated for spots. This measure can be used to decide whether or not a spot ratio should be deleted, or to adjust various measurements to reflect confidence in the quality of the measurement. CONTACT: e-dougherty@tamu.edu

Cell Line↗

PubMed2002

Morphological spot counting from stacked images for automated analysis of gene copy numbers by fluorescence in situ hybridization.

Fluorescence in situ hybridization (FISH) is a molecular diagnostic technique in which a fluorescent labeled probe hybridizes to a target nucleotide sequence of deoxyribose nucleic acid. Upon excitation, each chromosome containing the target sequence produces a fluorescent signal (spot). Because fluorescent spot counting is tedious and often subjective, automated digital algorithms to count spots are desirable. New technology provides a stack of images on multiple focal planes throughout a tissue sample. Multiple-focal-plane imaging helps overcome the biases and imprecision inherent in single-focal-plane methods. This paper proposes an algorithm for global spot counting in stacked three-dimensional slice FISH images without the necessity of nuclei segmentation. It is designed to work in complex backgrounds, when there are agglomerated nuclei, and in the presence of illumination gradients. It is based on the morphological top-hat transform, which locates intensity spikes on irregular backgrounds. After finding signals in the slice images, the algorithm groups these together to form three-dimensional spots. Filters are employed to separate legitimate spots from fluorescent noise. The algorithm is set in a comprehensive toolbox that provides visualization and analytic facilities. It includes simulation software that allows examination of algorithm performance for various image and algorithm parameter settings, including signal size, signal density, and the number of slices.

Algorithms↗

PubMed2002

Simulation of cDNA microarrays via a parameterized random signal model.

cDNA microarrays provide simultaneous expression measurements for thousands of genes that are the result of processing images to recover the average signal intensity from a spot composed of pixels covering the area upon which the cDNA detector has been put down. The accuracy of the signal measurement depends on using an appropriate algorithm to process the images. This includes determining spot locations and processing the data in such a way as to take into account spot geometry, background noise, and various kinds of noise that degrade the signal. This paper presents a stochastic model for microarray images. There are over 20 model parameters, each governed by a probability distribution, that control the signal intensity, spot geometry, spot drift, background effects, and the many kinds of noise that affect microarray images owing to the manner in which they are formed. The model can be used to analyze the performance of image algorithms designed to measure the true signal intensity because the ground truth (signal intensity) for each spot is known. The levels of foreground noise, background noise, and spot distortion can be set, and algorithms can be evaluated under varying conditions.

Algorithms↗

PubMed2002

Identification of combination gene sets for glioma classification.

One goal for the gene expression profiling of cancer tissues is to identify signature genes that robustly distinguish different types or grades of tumors. Such signature genes would ideally provide a molecular basis for classification and also yield insight into the molecular events underlying different cancer phenotypes. This study applies a recently developed algorithm to identify not only single classifier genes but also gene sets (combinations) for use as glioma classifiers. Classifier genes identified by this algorithm are shown to be strong features by conservatively and collectively considering the misclassification errors of the feature sets. Applying this approach to a test set of 25 patients, we have identified the best single genes and two- to three-gene combinations for distinguishing four types of glioma: (a) oligodendroglioma; (b) anaplastic oligodendroglioma; (c) anaplastic astrocytoma; and (d) glioblastoma multiforme. Some of the identified genes, such as insulin-like growth factor-binding protein 2, have been confirmed to be associated with one of the tumor types. Using combinations of genes, the classification error rate can be significantly lowered. In many instances, neither of the individual genes of a two-gene set performs well as an accurate classifier, but the combination of the two genes forms a robust classifier with a small error rate. Two-gene and three-gene combinations thus provide robust classifiers possessing the potential to translate expression microarray results into diagnostic histopathological assays for clinical utilization.

Algorithms↗