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PubMed1998

Robust mean and covariance structure analysis.

Covariance structure analysis is used to evaluate hypothesized influences among unmeasured latent and observed variables. As implemented, it is not robust to outliers and bad data. Several robust methods in model fitting and testing are proposed. These include direct estimation of M-estimators of structured parameters and a two-stage procedure based on robust M- and S-estimators of population covariances. The large sample properties of these estimators are obtained. The equivalence between a direct M-estimator and a two-stage estimator based on an M-estimator of population covariance is established when sampling from an elliptical distribution. Two test statistics are presented in judging the adequacy of a hypothesized model; both are asymptotically distribution free if using distribution free weight matrices. So these test statistics possess both finite sample and large sample robustness. The two-stage procedures can be easily adapted into standard software packages by modifying existing asymptotically distribution free procedures. To demonstrate the two-stage procedure, S-estimator and M-estimators under different weight functions are calculated for some real data sets.

Analysis of Variance↗
PubMed1978

Sexual dimorphism of skeletal robusticity in several mammalian orders.

This study tries to determine whether a phylogenetic trend exists in the sexual dimorphism of skeletal robusticity and whether domestication has an effect on it. The problems were studied in the metatarsals of marsupials, insectivores, rodents and primates including Homo, and in various skeletal sections of wild and domesticated rats and dogs. No clear phylogenetic trend could be found and domestication cannot be shown to have an effect on diminishing skeletal robusticity. Sexual dimorphism of skeletal robusticity seems to be highly species-specific and to have a mosaic distribution in a given taxon. Conclusions on phylogenetic trends of sexual dimorphism of skeletal robusticity and the effect of culture on it seem to be premature.

Animals↗
PubMed2006

Detecting outliers when fitting data with nonlinear regression - a new method based on robust nonlinear regression and the false discovery rate.

BACKGROUND: Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. RESULTS: We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1-3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. CONCLUSION: Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.

Computer Simulation↗
PubMed2005

A random sampling approach for robust estimation of tissue-to-plasma ratio from extremely sparse data.

his study was performed to develop a new nonparametric approach for the estimation of robust tissue-to-plasma ratio from extremely sparsely sampled paired data (ie, one sample each from plasma and tissue per subject). Tissue-to-plasma ratio was estimated from paired/unpaired experimental data using independent time points approach, area under the curve (AUC) values calculated with the naïve data averaging approach, and AUC values calculated using sampling based approaches (eg, the pseudoprofile-based bootstrap [PpbB] approach and the random sampling approach [our proposed approach]). The random sampling approach involves the use of a 2-phase algorithm. The convergence of the sampling/resampling approaches was investigated, as well as the robustness of the estimates produced by different approaches. To evaluate the latter, new data sets were generated by introducing outlier(s) into the real data set. One to 2 concentration values were inflated by 10% to 40% from their original values to produce the outliers. Tissue-to-plasma ratios computed using the independent time points approach varied between 0 and 50 across time points. The ratio obtained from AUC values acquired using the naive data averaging approach was not associated with any measure of uncertainty or variability. Calculating the ratio without regard to pairing yielded poorer estimates. The random sampling and pseudoprofile-based bootstrap approaches yielded tissue-to-plasma ratios with uncertainty and variability. However, the random sampling approach, because of the 2-phase nature of its algorithm, yielded more robust estimates and required fewer replications. Therefore, a 2-phase random sampling approach is proposed for the robust estimation of tissue-to-plasma ratio from extremely sparsely sampled data.

Algorithms↗
PubMed2004

Topology and robustness in the Drosophila segment polarity network.

A complex hierarchy of genetic interactions converts a single-celled Drosophila melanogaster egg into a multicellular embryo with 14 segments. Previously, von Dassow et al. reported that a mathematical model of the genetic interactions that defined the polarity of segments (the segment polarity network) was robust (von Dassow et al. 2000). As quantitative information about the system was unavailable, parameters were sampled randomly. A surprisingly large fraction of these parameter sets allowed the model to maintain and elaborate on the segment polarity pattern. This robustness is due to the positive feedback of gene products on their own expression, which induces individual cells in a model segment to adopt different stable expression states (bistability) corresponding to different cell types in the segment polarity pattern. A positive feedback loop will only yield multiple stable states when the parameters that describe it satisfy a particular inequality. By testing which random parameter sets satisfy these inequalities, I show that bistability is necessary to form the segment polarity pattern and serves as a strong predictor of which parameter sets will succeed in forming the pattern. Although the original model was robust to parameter variation, it could not reproduce the observed effects of cell division on the pattern of gene expression. I present a modified version that incorporates recent experimental evidence and does successfully mimic the consequences of cell division. The behavior of this modified model can also be understood in terms of bistability in positive feedback of gene expression. I discuss how this topological property of networks provides robust pattern formation and how large changes in parameters can change the specific pattern produced by a network.

Animals↗
PubMed2004

Robust H(infinity) output feedback control for a class of uncertain Lur'e systems with time-delays.

In this work, the analysis of robust stability and design of robust H infinity output feedback controllers for a class of Lur'e systems with both time-delays and parameter uncertainties were studied. A robust H infinity output feedback controller based on Linear Matrix Inequalities (LMIs) was developed to guarantee the robust stability and H infinity performance of the resultant closed-loop system. The presented design approach is based on the application of descriptor model transformation and Park's inequality for the bounding of cross terms and is expected to be less conservative compared to reported design methods. Finally, illustrative examples are advanced to demonstrate the superiority of the obtained method.

Algorithms↗
PubMed1999

Viral RNA and evolved mutational robustness.

Many properties of organisms show great robustness against mutations. Whether this robustness is an evolved property or intrinsic to genetic systems is by and large unknown. An evolutionary origin of robustness would require a rethinking of key concepts in the field of molecular evolution, such as gene-specific neutral mutation rates, or the context-independence of deleterious mutations. We provide evidence that mutational robustness of the genome of RNA viruses to mutational changes in secondary structure has evolved. J. Exp. Zool. ( Mol. Dev. Evol.) 285:119-127, 1999.

Animals↗
PubMed2000

Robust gamma oscillations in networks of inhibitory hippocampal interneurons.

Recent experiments suggest that inhibitory networks of interneurons can synchronize the neuronal discharge in in vitro hippocampal slices. Subsequent theoretical work has shown that strong synchronization by mutual inhibition is only moderately robust against neuronal heterogeneities in the current drive, provided by activation of metabotropic glutamate receptors. In vivo neurons display greater variability in the interspike intervals due to the presence of synaptic noise. Noise and heterogeneity affect synchronization properties differently. In this paper we study, using model simulations, how robust synchronization can be in the presence of synaptic noise and neuronal heterogeneity. We find that stochastic weak synchronization (SWS) (i.e. when neurons spike within a short interval from each other, but not necessarily at each period) is produced with at least a minimum amount of noise and that it is much more robust than strong synchronization (i.e. when neurons spike at each period). The statistics produced by the SWS population discharge are consistent with previous experimental data. We also find robust SWS in the gamma-frequency range (20-80 Hz) for a stronger synaptic coupling compared with previous models and for networks with 10-1000 neurons.

Animals↗
PubMed2006

[Rapid and robust partial least squares regression and its application to NIR spectroscopy analysis].

Modern near infrared spectroscopy (NIRS), as an indirect analytical technique, is used to carriy out quantitative analysis of unknown samples by establishing a model with calibration samples. Taking into account the low sensitivity and poor disturbance rejection of NIRS, a new robust version of the SIMPLS algorithm was constructed from a robust covariance matrix for high-dimensional data and robust linear regression in the present paper. Because SIMPLS was based on the empirical cross-covariance matrix between the response variables and the regressors and on linear least squares regression, the results were affected by abnormal observations in the data set. In order to eliminate their negative impact on the accuracy and reliability of the model, a simple multivariate outlier-detection procedure and a robust estimator for the covariance matrix were embedded in the SIMPLS regression framework, based on the use of information obtained from projections onto the directions that maximize and minimize the kurtosis coefficient of the projected data. Finally, application of the proposed kurtosis-SIMPLS method to the NIR analysis was presented with a comparison to the SIMPLS. The results show that kurtosis-SIMPLS method not only finds out the very outliers from the data set with less computational cost, but also holds better prediction performance and steady capability for the normal samples.

English Abstract↗
PubMed1995

Robust elementwise estimation of a dispersion matrix.

Most of the existing robust methods for estimating a covariance or correlation matrix involve a multivariate approach in which matrix elements are estimated via simultaneous manipulation of all variables. These methods are generally based on complex iterative algorithms and hence are rather difficult to implement. The purpose of this article is to recommend an easy to implement noniterative robust method for estimating a dispersion matrix, based on an elementwise estimation approach. Simple expressions are provided for robust estimators of variances and covariances based, in part, on a modified A-estimator of scale discussed previously by Lax (1985, Journal of the American Statistical Association 80, 736-741). A Monte Carlo study is used to compare the performance of the proposed noniterative method with that of some iterative procedures studied in the literature. A numerical example involving robust estimation of variance components is presented as an application of the proposed methodology.

Analysis of Variance↗
PubMed1996

Robustness and power of analysis of covariance applied to data distorted from normality by floor effects: homogeneous regression slopes.

We investigate through computer simulations the robustness and power of two group analysis of covariance test applied to small samples distorted normality by floor effects when the regression slopes are homogeneous. We consider four parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regression slopes and two t-tests on unadjusted means and on difference scores. Under the null hypothesis of no difference in means, we estimated actual significance levels by comparing observed test statistics to appropriate values from the F and t distributions for nominal significance levels of 0.10, 0.05, 0.02 and 0.01. We estimated power by similar comparisons under various alternative hypothesis. The hierarchical approach (that adjusts for non-homogeneous slopes if found significant), the test that assumes homogeneous regression slopes, and the test that estimates separate regression slopes in each treatment were robust. In general, each test produced power at least equal to that expected from normal theory. The textbook approach, which does not test for mean differences when there is significant non-homogeneity, was conservative but also had good power. The t-tests were robust but had poorer power properties than the above procedures.

Analysis of Variance↗
PubMed1996

A robust method for proportional hazards regression.

In this paper we give an informal introduction to a robust method for survival analysis which is based on a modification of the usual partial likelihood estimator (PLE). Large sample results lead us to expect reduced bias for this robust estimator compared with the PLE whenever there are even slight violations of the model. In this paper we investigate three types of violation: (a) varying dependency structure of survival time and covariates over the sample; (b) omission of influential covariates, and (c) errors in the covariates. The simulations presented support the above expectation. Analyses of data sets from cancer epidemiology and from a clinical trial in lung cancer illustrate that a better fit and additional insights may be gained using robust estimators.

Algorithms↗
PubMed1984

The effects of simulated increases in body weight for 60 days on robusticity and mineral content of limb bones of hypophysectomized rats.

The purpose of this investigation was to subject separate male and female groups of weanling hypophysectomized rats each to a specific 10% simulated increase in body weight using constant centrifugation, ranging from 1.1G to 2.0G, to study changes in bone robusticity and bone mineral content. (In this paper, "G" is the acceleration due to gravity.) After 60 days of centrifugation at 24 rpm, the rats were killed and the humerus, radius, ulna, femur, and tibia were removed, cleared of soft tissues, weighed, measured, decalcified with EDTA, and reweighed. Bone robusticity was determined using the ponderal index: P.I. = bone length divided by 3 square root bone weight; and bone mineral content (BMC) was determined using the formula: BMC = [(Wu - Wd) divided by Wu] X 100. Tukey's Studentized Multiple Range T Test was used. The data suggest that, for both male and female hypophysectomized rats, bone robusticity is decreased with simulated increases in body weight; also, for males, a bimodal curve describing the relationship between BMC and simulated increases in body weight is suggested.

Animals↗
PubMed1984

The effects of simulated increases in body weight from birth on bone robusticity of limb bones of rats.

Groups of newborn rats were each subjected to a specific 10% simulated increase in body weight, ranging from 1.1G to 2.0G, to study changes in bone robusticity. (In this paper, "G" is the acceleration due to gravity.) Constant centrifugation was used. At 90 days of age, the rats were killed and the humerus, radius, ulna, femur, and tibia were removed, weighed, and measured. Bone robusticity was calculated using the ponderal index: bone length/3 square root bone weight. Tukey's Multiple Range Test was used. The data suggest that, for both males and females, bone robusticity is increased with simulated increases in body weight.

Animals↗
PubMed2004

Robust control of initiation of prokaryotic chromosome replication: essential considerations for a minimal cell.

A genomically and chemically detailed mathematical model of a "minimal cell" would be useful to understand better the "design logic" of cellular regulation. A "minimal cell" will be a prokaryote with the minimum number of genes necessary for growth and replication in an ideal environment (i.e., preformed precursors, constant temperature, etc.). The Cornell single-cell model of Escherichia coli serves as the basic framework upon which a minimal cell model can be constructed. A critical issue for any cell model is to describe a mechanism for control of initiation of chromosome replication. There is strong evidence that the essence of chromosome replication control is highly conserved in eubacteria and even extends to the archae. A generalized mechanism is possible based on binding of the protein DnaA-ATP to the origin of replication (oriC) as a primary control. Other features, such as regulatory inactivation of DnaA (RIDA) by conversion of DnaA-ATP to DnaA-ADP and titration of DnaA by binding to other DnaA boxes on the chromosome, have emerged as critical elements in obtaining a functional system to control initiation of chromosome synthesis. We describe a biologically realistic model of chromosome replication initiation control embedded in a complete whole-cell model that explicitly links the external environment to the mechanism of replication control. The base model is deterministic and then modified to include stochastic variation in the components for replication control. The stochastic model allows evaluation of the model's robustness, employing a low standard deviation of interinitiation time as a measure of robustness. Four factors were examined: DnaA synthesis rate; DnaA-ATP binding sites at oriC; the binding rate of DnaA-ATP to the nonfunctional DnaA boxes; and the effect of changing the number of nonfunctional binding sites. The observed DnaA synthesis rate (2000 molecules/cell) and the number of DnaA binding sites per origin (30) are close to the values predicted by the model to provide good control (low variance of interinitiation time), with a reasonable expenditure of cell resources. At relatively high binding rates for DnaA-ATP to the DnaA boxes (10(16) M(-1) s(-1)), increasing the number of DnaA binding sites to about 300, improved control (but little further improvement was seen by extension to 1000 boxes); however, at a low binding rate (10(10) M(-1) s(-1)), an increase in DnaA boxes had an adverse effect on control. The combination of all four factors is probably necessary to obtain a robust control system. Although this mechanism of replication initiation control is highly conserved, it is not clear if simpler control in a minimal cell might exist based on experimental observations with Mycoplasma. This issue is discussed in this investigation.

Bacterial Proteins↗
PubMed2005

Pattern robustness of diagnostic gene expression signatures in leukemia.

Microarray technology has been proposed as an addition to the methods in current use for diagnosing leukemia. Before a new technology can be used in a diagnostic setting, the method has to be shown to produce robust results. It is known that, given the technical aspects of specimen sampling and target preparation, global gene expression patterns can change dramatically. Various parameters such as RNA degradation, shipment time, sample purity, and patient age can principally influence measured gene expression. However, thus far, no information has been available on the robustness of a diagnostic gene expression signature. We demonstrate here that for a subset of acute leukemia, expression profiling is applicable in a diagnostic setting, considering various influencing parameters. With the use of a set of differentially expressed genes, that is, a diagnostic gene expression signature, four genetically defined acute myeloid leukemia subtypes with recurrent chromosomal aberrations can clearly be identified. In addition, we show that preparation by different operators and using different sample-handling procedures did not impair the robustness of diagnostic expression signatures. In conclusion, our results provide additional support for the applicability of microarrays in a diagnostic setting, and we have been encouraged to enroll patients in a prospective study in which microarrays will be tested as an additional routine diagnostic method in parallel with standard diagnostic procedures.

Adult↗
PubMed1987

Robust inference for variance components models in families ascertained through probands: I. Conditioning on proband's phenotype.

A robust approach for estimating standard errors of variance components by using quantitative phenotypes from families ascertained through a proband with an extreme phenotypic value is presented. Estimators that use the multivariate normal distribution as a "working likelihood" are obtained by computing conditional ln-likelihoods, conditional first and second derivatives in a Newton-Raphson approach. Robust estimates of standard errors about the estimators are also provided. Tests of hypotheses are based on a modification of the score test, which allows the assumption of multivariate normality to be relaxed. Conditional goodness-of-fit statistics are proposed that can be used to examine the fit of separate pedigrees to the overall model. This robust approach for estimating the standard errors for variance components by conditioning on the proband's phenotype will allow general inferences to be made from the analysis of families ascertained through probands with extreme or unusual phenotypes and should be most appropriate for studying many physiological traits that may be intrinsically nonnormal.

Analysis of Variance↗
PubMed2001

A robust multipoint linkage statistic (tlod) for mapping complex trait loci.

Classical parametric two-point linkage analysis is a powerful analysis tool, however there are clear disadvantages too, including the sensitivity to allele frequency mis-specification. Conversely, multipoint linkage analysis is not sensitive to allele frequency mis-specification, but it is sensitive to genetic model mis-specification. Göring and Terwilliger [Am J Hum Genet 66:1095-106, 2000] proposed a new robust multipoint statistic that increased the robustness of multipoint analyses. In this paper we have referred to this new statistic as the tlod. We applied this new statistic to the Genetic Analysis Workshop (GAW) 12 data using affected status (AFF) as the phenotype of interest. The heterogeneity tlod and two-point hlod scores correlated highly across the genome (p < 0.0001), as expected, but the het-tlod had a lower number false positives. In addition, the tlod analysis handled missing data better, as would be expected for a multipoint method. When one-third of the genotype data was removed (dead people) the tlod analysis was less affected than the two-point analysis. When tlod scores were compared with multipoint lod scores in true gene locations, the robustness of the tlod to model mis-specification was clearly evident. When the "best" replicate from the general population was analyzed, a borderline genome-wide significant two-point hlod result (3.6) was found 4 cM from MG6 and MG7 on chromosome 6. The heterogeneity tlod score was lower than the two-point hlod score (1.8), but greater than the heterogeneity multipoint lod score (0.4). However, when replicate 1 of the isolated population was analyzed none of the true gene locations were identified with either statistic.

Chromosome Mapping↗