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PubMed2004

Robust multipoint identical-by-descent mapping for affected relative pairs.

The genetic mapping of complex traits has been challenging and has required new statistical methods that are robust to misspecified models. Liang et al. proposed a robust multipoint method that can be used to simultaneously estimate, on the basis of sib-pair linkage data, both the position of a trait locus on a chromosome and its effect on disease status. The advantage of their method is that it does not require specification of an underlying genetic model, so estimation of the position of a trait locus on a specified chromosome and of its standard error is robust to a wide variety of genetic mechanisms. If multiple loci influence the trait, the method models the marginal effect of a locus on a specified chromosome. The main critical assumption is that there is only one trait locus on the chromosome of interest. We extend this method to different types of affected relative pairs (ARPs) by two approaches. One approach is to estimate the position of a trait locus yet allow unconstrained trait-locus effects across different types of ARPs. This robust approach allows for differences in sharing alleles identical-by-descent across different types of ARPs. Some examples for which an unconstrained model would apply are differences due to secular changes in diagnostic methods that can change the frequency of phenocopies among different types of relative pairs, environmental factors that modify the genetic effect, epistasis, and variation in marker-information content. However, this unconstrained model requires a parameter for each type of relative pair. To reduce the number of parameters, we propose a second approach that models the marginal effect of a susceptibility locus. This constrained model is robust for a trait caused by either a single locus or by multiple loci without epistasis. To evaluate the adequacy of the constrained model, we developed a robust score statistic. These methods are applied to a prostate cancer-linkage study, which emphasizes their potential advantages and limitations.

Chromosome Mapping↗
PubMed2004

Robust sparse hyperplane classifiers: application to uncertain molecular profiling data.

Molecular profiling studies can generate abundance measurements for thousands of transcripts, proteins, metabolites, or other species in, for example, normal and tumor tissue samples. Treating such measurements as features and the samples as labeled data points, sparse hyperplanes provide a statistical methodology for classifying data points into one of two categories (classification and prediction) and defining a small subset of discriminatory features (relevant feature identification). However, this and other extant classification methods address only implicitly the issue of observed data being a combination of underlying signals and noise. Recently, robust optimization has emerged as a powerful framework for handling uncertain data explicitly. Here, ideas from this field are exploited to develop robust sparse hyperplanes, i.e., classification and relevant feature identification algorithms that are resilient to variation in the data. Specifically, each data point is associated with an explicit data uncertainty model in the form of an ellipsoid parameterized by a center and covariance matrix. The task of learning a robust sparse hyperplane from such data is formulated as a second order cone program (SOCP). Gaussian and distribution-free data uncertainty models are shown to yield SOCPs that are equivalent to the SCOP based on ellipsoidal uncertainty. The real-world utility of robust sparse hyperplanes is demonstrated via retrospective analysis of breast cancer related transcript profiles. Data-dependent heuristics are used to compute the parameters of each ellipsoidal data uncertainty model. The generalization performance of a specific implementation, designated "robust LIKNON," is better than its nominal counterpart. Finally, the strengths and limitations of robust sparse hyperplanes are discussed.

Breast Neoplasms↗
PubMed2005

Fast robust correlation.

A new, fast, statistically robust, exhaustive, translational image-matching technique is presented: fast robust correlation. Existing methods are either slow or non-robust, or rely on optimization. Fast robust correlation works by expressing a robust matching surface as a series of correlations. Speed is obtained by computing correlations in the frequency domain. Computational cost is analyzed and the method is shown to be fast. Speed is comparable to conventional correlation and, for large images, thousands of times faster than direct robust matching. Three experiments demonstrate the advantage of the technique over standard correlation.

Algorithms↗
PubMed2005

Time-delay- and time-reversal-based robust Capon beamformers for ultrasound imaging.

Currently, the nonadaptive delay-and-sum (DAS) beamformer is extensively used for ultrasound imaging, despite the fact that it has lower resolution and worse interference suppression capability than the adaptive standard Capon beamformer (SCB) if the steering vector corresponding to the signal of interest (SOI) is accurately known. The main problem which restricts the use of SCB, however, is that SCB lacks robustness against steering vector errors that are inevitable in practice. Whenever this happens, the performance of SCB may hecome worse than that of DAS. Therefore, a robust adaptive beamformer is desirable to maintain the robustness of DAS and adaptivity of SCB. In this paper we consider a recent promising robust Capon beamformer (RCB) for ultrasound imaging. We propose two ways of implementing RCB, one based on time delay and the other based on time reversal. RCB extends SCB by allowing the array steering vector to be within an uncertainty set. Hence, it restores the appeal of SCB including its high resolution and superb interference suppression capabilities, and also retains the attractiveness of DAS including its robustness against steering vector errors. The time-delay-based RCB can tolerate the misalignment of data samples and the time-reversal-based RCB can withstand the uncertainty of the Green's function. Both time-delay-based RCB and time-reversal-based RCB can be efficiently computed at a comparable cost to SCB. The excellent performances of the proposed robust adaptive beamforming approaches are demonstrated via a number of simulated and experimental examples.

Algorithms↗
PubMed2004

Robust adaptive-scale parametric model estimation for computer vision.

Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the Two-Step Scale estimator (TSSE) and the Adaptive Scale Sample Consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines Random Sample Consensus (RANSAC) and TSSE: using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 percent outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than Least Median Squares (LMedS), Residual Consensus (RESC), and Adaptive Least Kth order Squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.

Algorithms↗
PubMed2004

A similarity-based robust clustering method.

This paper presents an alternating optimization clustering procedure called a similarity-based clustering method (SCM). It is an effective and robust approach to clustering on the basis of a total similarity objective function related to the approximate density shape estimation. We show that the data points in SCM can self-organize local optimal cluster number and volumes without using cluster validity functions or a variance-covariance matrix. The proposed clustering method is also robust to noise and outliers based on the influence function and gross error sensitivity analysis. Therefore, SCM exhibits three robust clustering characteristics: 1) robust to the initialization (cluster number and initial guesses), 2) robust to cluster volumes (ability to detect different volumes of clusters), and 3) robust to noise and outliers. Several numerical data sets and actual data are used in the SCM to show these good aspects. The computational complexity of SCM is also analyzed. Some experimental results of comparing the proposed SCM with the existing methods show the superiority of the SCM method.

Algorithms↗
PubMed1999

Robustness of the latent variable model for correlated binary data.

The marginal regression model offers a useful alternative to conditional approaches to analyzing binary data (Liang, Zeger, and Qaqish, 1992, Journal of the Royal Statistical Society, Series B 54, 3-40). Instead of modelling the binary data directly as do Liang and Zeger (1986, Biometrika 73, 13-22), the parametric marginal regression model developed by Qu et al. (1992, Biometrics 48, 1095-1102) assumes that there is an underlying multivariate normal vector that gives rise to the observed correlated binary outcomes. Although this parametric approach provides a flexible way to model different within-cluster correlation structures and does not restrict the parameter space, it is of interest to know how robust the parameter estimates are with respect to choices of the latent distribution. We first extend the latent modelling to include multivariate t-distributed latent vectors and assess the robustness in this class of distributions. Then we show through a simulation that the parameter estimates are robust with respect to the latent distribution even if latent distribution is skewed. In addtion to this empirical evidence for robustness, we show through the iterative algorithm that the robustness of the regression coefficents with respect to misspecifications of covariance structure in Liang and Zeger's model in fact indicates robustness with respect to underlying distributional assumptions of the latent vector in the latent variable model.

Algorithms↗
PubMed2001

Tests against qualitative interaction: exact critical values and robust tests.

Consider a study to evaluate treatment A with a placebo in two or more groups of patients. If treatment A is beneficial to one group of patients and harmful to another, then we say that there is qualitative interaction or crossover interaction between patient groups and the treatments. Gail and Simon (1985, Biometrics 41, 361-372) developed a large-sample procedure for this testing problem. Their test has received favorable coverage in the literature. In this article, we obtain corresponding exact finite sample results for normal error distribution and provide a table of critical values. The test statistic is similar to the familiar F-ratio, and its p-value is equal to a weighted sum of tail areas of F-distributions. The computations to implement this are simple. A simulation study shows that the exact critical values provided here for normal error distribution are preferable to the asymptotic critical values for a wide range of error distributions. We also develop tests that are power robust against long-tailed error distributions. Our robust test uses M-estimators instead of the least squares estimators. We show that the efficiency robustness of the M-estimator translates to power robustness of the corresponding test. Therefore, our robust tests are better if outliers are expected. A simulation study illustrates the substantial power advantages of our robust tests.

Antihypertensive Agents↗
PubMed2003

Improving robustness of active noise control in ducts.

A robust active noise controller (ANC) is proposed here for finite ducts. While the H(infinity) control theory provides theoretical ground and numerical algorithms to design robust controllers, it is important for an engineer to design and formulate a robust controller so that the objective is more achievable and the H(infinity) constraints less restrictive without sacrificing robustness. A new robust ANC is designed this way with an extra actuator to improve achievable performance and introduce more degrees of freedom to controller parameters. The new strategy relaxes H(infinity) constraints without sacrificing robustness and enables the ANC to tolerate a wide variety of errors and uncertainties including truncation errors between a finite model and an infinite field. Theoretical analysis, numerical examples, and experimental results are presented to demonstrate the improved performance of the proposed ANC when subject to a certain level of uncertainties in a duct.

Journal Article↗
PubMed2000

Feedback path variability modeling for robust hearing aids.

Acoustic feedback is a common problem in hearing aids with vented earmolds. Hearing aids designed to work under normal conditions become unstable when the feedback path varies under changing conditions. A comprehensive study of the variability of the feedback path under various conditions and for different users is presented in this paper. A multiplicative uncertainty bound widely used in H-infinity robust control is suggested to model the variations, which is then used to formulate a robust stability condition for the hearing aid. The upper limit of the closed-loop acoustic gain of the hearing aid for maintaining robust stability is also derived. Examples of robust constant amplification hearing aids, which maintain stability in the face of the given variations in the feedback path, are presented. The robust stability condition is also suggested as a tool to design more robust digital, hearing aids.

Acoustic Stimulation↗
PubMed1999

Testing for linkage under robust genetic models.

Robust genetic models are used to assess linkage between a quantitative trait and genetic variation at a specific locus using allele-sharing data. Little is known about the relative performance of different possible significance tests under these models. Under the robust variance components model approach there are several alternatives: standard Wald and likelihood ratio tests, a quasilikelihood Wald test, and a Monte Carlo test. This paper reports on the relative performance (significance level and power) of the robust sibling pair test and the different alternatives under the robust variance components model. Simulations show that (1) for a fixed sample size of nuclear families, the variance components model approach is more powerful than the robust sibling pair approach; (2) when the number of nuclear families is at least approximately 100 and heritability at the trait locus is moderate to high (>0.20) all tests based on the variance components model are equally effective; (3) when the number of nuclear families is less than approximately 100 or heritability at the trait locus is low (<0. 20), on balance, the Monte Carlo test provides the best power and is the most valid. The different testing procedures are applied to determine which are able to detect the known association between low density lipoprotein cholesterol and the common genotypes at the locus encoding apolipoprotein E. Results from this application show that the robust sibling pair method may be more effective in practice than that indicated by simulations.

Alleles↗
PubMed2006

Effect of random and hub gene disruptions on environmental and mutational robustness in Escherichia coli.

BACKGROUND: Genome-wide profiling has allowed the regulatory interaction networks of many organisms to be visualised and the pattern of connections between genes to be studied. These networks are non-random, following a power-law distribution with a small number of well-connected 'hubs' and many genes with only one or a few connections. Theoretical work predicts that power-law networks display several unique properties. One of the most biologically interesting of these is an intrinsic robustness to disturbance such that removal of a random gene will have little effect on network function. Conversely, targeted removal of a hub gene is expected to have a large effect. RESULTS: We compared the response of Escherichia coli to environmental and mutational stress following disruption of random or hub genes. We found that disruption of random genes had less effect on robustness to environmental stress than did the targeted disruption of hub genes. In contrast, random disruption strains were slightly less robust to the effect of mutational stress than were hub disruption strains. When we compared the effect of each disruption on environmental and mutational stress, we found a negative relationship, such that strains that were more environmentally robust tended to be less robust to mutational stress. CONCLUSION: Our results demonstrate that mutant strains of E. coli respond differently to stress, depending on whether random or hub genes are disrupted. This difference indicates that the power-law distribution of regulatory interactions has biological significance, making random disruptions less deleterious to organisms facing environmental stress. That E. coli can reduce the effect of environmental stress without reducing the phenotypic effect of additional mutations, indicates that robustness and evolvability need not be antagonistic.

Anti-Bacterial Agents↗
PubMed2005

Quantifying the robustness of a broth-based model for predicting Listeria monocytogenes growth in meat and poultry products.

Given the importance of Listeria monocytogenes as a risk factor in meat and poultry products, there is a need to evaluate the relative robustness of predictive growth models applied to meat products. The U.S. Department of Agriculture-Agricultural Research Service Pathogen Modeling Program is a tool widely used by the food industry to estimate pathogen growth, survival, and inactivation in food. However, the robustness of the Pathogen Modeling Program broth-based L. monocytogenes growth model in meat and poultry application has not, to our knowledge, been specifically evaluated. In the present study, this model was evaluated against independent data in terms of predicted microbial counts and covered a range of conditions inside and outside the original model domain. The robustness index was calculated as the ratio of the standard error of prediction (root mean square error of the model against an independent data set not used to create the model) to the standard error of calibration (root mean square error of the model against the data set used to create the model). Inside the calibration domain of the Pathogen Modeling Program, the best robustness index for application to meat products was 0.37; the worst was 3.96. Outside the domain, the best robustness index was 0.40, and the worst was 1.22. Product type influenced the robustness index values (P < 0.01). In general, the results indicated that broth-based predictive models should be validated against independent data in the domain of interest; otherwise, significant predictive errors can occur.

Animals↗
PubMedDate not supplied

Robust methods in bioequivalence assay; preliminary results.

The aim of this study is to compare four statistical methods for outlier identification in Bioequivalence tests. The methods are based in four confidence intervals, 'parametric','non- parametric','robust with the asymptotic distribution of the M-estimator' and 'robust with the bootstrap distribution'. The drug we used was Diltiazen, in a two sequence randomized crossover study design. The pharmacokinetic parameters measured were the area under the plasma concentration curve (AUC), and the peak drug concentration (CMAX). Time to peak drug concentration (TMAX), was not used here in order to separate the efficiency of the methods from the efficiency of the measurements. The methods were applied to simulated and experimental data. We made two simulations, one with normal data and another one with outliers data. When simulating normal data all methods showed similar profiles and high power. On the contrary, when simulating experiments with outliers data, the parametric method showed low power, whereas robust methods showed just a slight decrement in power. When we analyzed experimental data of AUC, if we used the parametric method (recommended by U.S.P), we were not able to conclude Bioequivalence, but with the other methods, this was possible. This disagreement between parametric and robust procedures was a sign of outliers data. We conclude that the robust methods in bioequivalence assays help us in the identification of outliers as observations with weight equal zero.

Adult↗
PubMed2005

Robustness, evolvability, and neutrality.

Biological systems, from macromolecules to whole organisms, are robust if they continue to function, survive, or reproduce when faced with mutations, environmental change, and internal noise. I focus here on biological systems that are robust to mutations and ask whether such systems are more or less evolvable, in the sense that they can acquire novel properties. The more robust a system is, the more mutations in it are neutral, that is, without phenotypic effect. I argue here that such neutral change--and thus robustness--can be a key to future evolutionary innovation, if one accepts that neutrality is not an essential feature of a mutation. That is, a once neutral mutation may cause phenotypic effects in a changed environment or genetic background. I argue that most, if not all, neutral mutations are of this sort, and that the essentialist notion of neutrality should be abandoned. This perspective reconciles two opposing views on the forces dominating organismal evolution, natural selection and random drift: neutral mutations occur and are especially abundant in robust systems, but they do not remain neutral indefinitely, and eventually become visible to natural selection, where some of them lead to evolutionary innovations.

Animals↗
PubMed2004

Robust control in bacterial regulatory circuits.

Robust control refers to regulatory systems that are insensitive to perturbations to the intra- or extra-cellular environment. It is generally believed that most cell regulatory circuits should possess some degree of robustness. Examples of robust control and the underlying mechanisms for achieving this robustness are only beginning to be uncovered. Various forms of robustness are associated with circuits based on negative and/or positive feedback, bi-functional enzymes, protein oligomerization and discrete or continuous control.

Bacteria↗
PubMed2000

Design of robust discrete control with desirable quadratic stability

In this paper, a design of robust discrete control with desirable quadratic stability is proposed. The design procedure is the extended discrete version of the continuous robust quadratic stabilization technique proposed by Gu et al. [K. Gu, Y.H. Chen, M.A. Zohdy, N.K. Loh, Quadratic stabilizability of uncertain systems: a two level optimization setup, Automatica 27 (1) (1991) 161-165.]. The effect of the sampling time selection, and the effect of the domain on the robustness, is examined. The presented algorithm is applied to a discrete mass spring system, and a discrete simplified car steering system to demonstrate the feasibility of the procedure, and the effect of the time sampling on the robustness. The robustness increases in both examples considered, as the sampling time decreases to some degree.

Journal Article↗
PubMed2002

Identification and robust control of an experimental servo motor.

In this work, the design of a robust controller for an experimental laboratory-scale position control system based on a dc motor drive as well as the corresponding identification and robust stability analysis are presented. In order to carry out the robust design procedure, first, a classic closed-loop identification technique is applied and then, the parametrization by internal model control is used. The model uncertainty is evaluated under both parametric and global representation. For the latter case, an interesting discussion about the conservativeness of this description is presented by means of a comparison between the uncertainty disk and the critical perturbation radius approaches. Finally, conclusions about the performance of the experimental system with the robust controller are discussed using comparative graphics of the controlled variable and the Nyquist stability margin as a robustness measurement.

Computer Simulation↗