Robust Regression Approach Research Articles

Inferring gene regulatory relationships with a high-dimensional robust approach

Gene expression (GE) levels have important biological and clinical implications. They are regulated by copy number alterations (CNAs). Modeling the regulatory relationships between GEs and CNAs facilitates understanding disease biology and can also have values in translational medicine. The expression level of a gene can be regulated by its cis-acting as well as trans-acting CNAs, and the set of trans-acting CNAs is usually not known, which poses a high-dimensional selection and estimation problem. Most of the existing studies share a common limitation in that they cannot accommodate long-tailed distributions or contamination of GE data. In this study, we develop a high-dimensional robust regression approach to infer the regulatory relationships between GEs and CNAs. A high-dimensional regression model is used to accommodate the effects of both cis-acting and trans-acting CNAs. A density power divergence loss function is used to accommodate long-tailed GE distributions and contamination. Penalization is adopted for regularized estimation and selection of relevant CNAs. The proposed approach is effectively realized using a coordinate descent algorithm. Simulation shows that it has competitive performance compared to the nonrobust benchmark and the robust LAD (least absolute deviation) approach. We analyze TCGA (The Cancer Genome Atlas) data on cutaneous melanoma and study GE-CNA regulations in the RAP (regulation of apoptosis) pathway, which further demonstrates the satisfactory performance of the proposed approach.

A Ranking Method Based on the Aggregate Distance Measure Function in the Value Space

The aim of this paper is to introduce a new MCDA method for ranking a finite set of alternatives evaluated on multiple criteria. The proposed method uses the idea of the robust ordinal regression (ROR) approach to establish the ranking scores determined by the distance measure function, however not in the criteria space, but in the value space. The preference model is composed of a set of additive value functions compatible with the preference information provided by the decision maker (DM). From among many forms of an additive preference model, we consider the model having as simple form as possible, i.e., the model that is the “closest to linear”. We define an achievement scalarizing function representing closeness to the ideal solution in the value space. A set of mix-integer linear programming (MILP) problems is then solved to determine the minimum distance scores of each alternative on the set of compatible value functions. Then, the obtained distance scores are used to rank all alternatives. A hypothetical case study is then performed to illustrate the proposed method. Finally, the result of our method is discussed and compared with results obtained by other methods based on the distance measure function (i.e., TOPSIS and VIKOR).

A new method for robust mixture regression.

Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity and wide applicability, may fail in the presence of severe outliers. Using a sparse, case-specific, and scale-dependent mean-shift mixture model parameterization, we propose a robust mixture regression approach for simultaneously conducting outlier detection and robust parameter estimation. A penalized likelihood approach is adopted to induce sparsity among the mean-shift parameters so that the outliers are distinguished from the remainder of the data, and a generalized Expectation-Maximization (EM) algorithm is developed to perform stable and efficient computation. The proposed approach is shown to have strong connections with other robust methods including the trimmed likelihood method and M-estimation approaches. In contrast to several existing methods, the proposed methods show outstanding performance in our simulation studies.

Is Alaska an Aberration or the Worst Case? A Robust Regression Approach to Understanding Inter-State Variations of Forcible Rape

ABSTRACTAlaska’s rape rate perennially exceeds that of all other states. This study considers Alaska’s socioeconomic extremes—its frontier demography, its externally dependent resource economy, and its military presence—as explanations for inter-state variations of sexual violence. Robust regression procedures that accommodate extreme values were used to account for the effects of measures capturing Alaska’s unique socioeconomic qualities on state-level rape rates. The results showing that other economically dependent states with frontier demographic structures also report elevated rape rates indicate that despite its endemic levels of sexual violence, Alaska is not an aberration but is instead the worst case possible.

Robust ordinal regression for decision under risk and uncertainty

We apply the Robust Ordinal Regression (ROR) approach to decision under risk and uncertainty. ROR is a methodology proposed within multiple criteria decision aiding (MCDA) with the aim of taking into account the whole set of instances of a given preference model, for example instances of a value function, which are compatible with preference information supplied by the Decision Maker (DM) in terms of some holistic preference comparisons of alternatives. ROR results in two preference relations, necessary and possible; the necessary weak preference relation holds if an alternative is at least as good as another one for all instances compatible with the DM’s preference information, while the possible weak preference relation holds if an alternative is at least as good as another one for at least one compatible instance. To apply ROR to decision under risk and uncertainty we have to reformulate such a problem in terms of MCDA. This is obtained by considering as criteria a set of quantiles of the outcome distribution, which are meaningful for the DM. We illustrate our approach in a didactic example based on the celebrated newsvendor problem.

Gender diversity in the governance of the Nigerian securities market

Purpose – The purpose of the paper is to identify the key determinants of stock market performance in Nigeria. More specifically, it is an attempt to determine the effect of gender diversity in leadership roles on the performance of the stock market in Nigeria. Design/methodology/approach – The paper uses annual data from 1980 through 2011 to model the development and performance of the Nigerian stock market through a modified Calderon-Rossell approach. Specifically, the leadership role of women in the governance of the stock market is investigated. Robust regression approach is used to avoid complications associated with the violations of the assumptions underlying the application of ordinary least squares regression. Findings – The empirical analysis shows that level of income, real exchange rate, liquidity, banking sector development, institutional quality, macroeconomic stability and gender are important determinants of stock market performance in the Nigerian stock market. Further, the results indicate that at worst, gender diversity does not play into stock market performance in Nigeria, and at its best, the appointment of women in the management of the Nigerian Stock Exchange is associated with better performance. Originality/value – The paper contributes to the empirical literature on the role of gender diversity and financial performance. The contribution of this paper is the inclusion of gender as an institutional factor among the determinants of stock market performance in Nigeria.

Abstract 5302: Genome-wide methylation analysis reveals multiple epigenetic subtypes of acute myeloid leukemia

Abstract Background: Acute myeloid leukemia (AML) is a highly heterogeneous malignancy for which known molecular features, while useful, are inadequate for determining the likelihood of durable remission following chemotherapy. Our study examines multiple DNA methylation patterns associated with AML curability and clinical features, and expands on preliminary work relating epigenomic phenotype to survival. Methods: To measure genome-wide CpG methylation we used Digital Restriction Enzyme Analysis of Methylation (DREAM) on a cohort of 101 AML samples and 25 normal blood controls. We used methylation data from 194 patient samples from The Cancer Genome Atlas (TCGA) on the Illumina Infinium HumanMethylation450 platform as validation. Statistical analysis was done using R. Results: DREAM analysis of 3,003 CpG sites (with standard deviation > 20% across AML cases) revealed three distinct DNA methylation patterns by hierarchical clustering. A group of 22 AML cases demonstrated significant hypermethylation at many loci compared to normal blood, consistent with a CpG Island Methylator Phenotype (CIMP). Kaplan-Meier analysis demonstrated that CIMP-AML cases had significantly longer OS than either non-CIMP cluster (median OS, years: CIMP = 14, hypomethylator = 1.47, non-CIMP-2 = 1.04, log-rank p = 0.0021). In this dataset CIMP was prognostic independent of cytogenetic risk, and antecedent hematologic malignancy (AHD). We also found that CIMP-AML was significantly enriched in IDH1/2 mutations (32% of CIMP-AML vs. 9% of non-CIMP-AML, p = 0.02). Differential methylation analysis to characterize the specific CpG sites within the genome that define CIMP-AML demonstrated widespread hypermethylation predominantly at CGIs. Using a robust Cox regression approach, we identified candidate markers of CIMP in our DREAM dataset (sensitivity = 73%, specificity = 100%). We validated the presence of CIMP-AML in independent data from TCGA which demonstrated a consistent pattern regarding survival (median OS, years: CIMP = 2, non-CIMP = 1, log-rank p = 0.0109), and the enrichment of IDH1/2 mutations (30% of CIMP-AML vs. 14% of non-CIMP-AML, p = 0.02). Our DREAM analysis also revealed a distinct cluster of AML cases with a hypomethylator phenotype (HMP). This novel HMP-AML subtype was more common than CIMP, and was associated with intermediate OS. Differential methylation analysis revealed that HMP-AML is defined by loss of methylation predominantly at non-CGIs. HMP-AML demonstrated a relative enrichment for DNMT3A mutations (24% of HMP-AML vs. 7% of non-HMP-AML, p = 0.10). Conclusions: We propose that CIMP-AML is associated with CGI hypermethylation, IDH1/2 mutations, and favorable prognosis. Our Cox regression strategy identified a small group candidate biomarkers of CIMP-AML. In addition, we identified a novel HMP-AML phenotype associated with non-CGI hypomethylation, DNMT3A mutations, and an intermediate prognosis. Citation Format: Andrew D. Kelly, Heike Kroeger, Jumpei Yamazaki, Rodolphe Taby, Frank Neumann, Justin T. Lee, Rong He, Shoudan Liang, Yue Lu, Matteo Cesaroni, Sherry A. Pierce, Steven M. Kornblau, Carlos E. Bueso-Ramos, Farhad Ravandi, Hagop M. Kantarjian, Jaroslav Jelinek, Jean-Pierre J. Issa. Genome-wide methylation analysis reveals multiple epigenetic subtypes of acute myeloid leukemia. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 5302. doi:10.1158/1538-7445.AM2015-5302

A robust regression based classifier with determination of optimal feature set

This paper proposes a robust regression approach for different classification problems using determination of optimal feature set values. Three different data sets are used to test and evaluate the proposed algorithm. In robust regression stage, the number of vector of regression coefficients is equal to the number of attributes in classification application. In optimization stage, the optimum values of the each of features in classification problem are determined by using genetic algorithm. The high classification accuracy with low number of reference data is the valuable property of proposed method. Simulation results show that proposed classification approach based on robust regression has high accuracy rate. All Rights Reserved © 2015 Universidad Nacional Autonoma de Mexico, Centro de Ciencias Aplicadas y Desarrollo Tecnologico. This is an open access item distributed under the Creative Commons CC License BY-NC-ND 4.0.

A robust multiple-locus method for quantitative trait locus analysis of non-normally distributed multiple traits.

Linear regression-based quantitative trait loci/association mapping methods such as least squares commonly assume normality of residuals. In genetics studies of plants or animals, some quantitative traits may not follow normal distribution because the data include outlying observations or data that are collected from multiple sources, and in such cases the normal regression methods may lose some statistical power to detect quantitative trait loci. In this work, we propose a robust multiple-locus regression approach for analyzing multiple quantitative traits without normality assumption. In our method, the objective function is least absolute deviation (LAD), which corresponds to the assumption of multivariate Laplace distributed residual errors. This distribution has heavier tails than the normal distribution. In addition, we adopt a group LASSO penalty to produce shrinkage estimation of the marker effects and to describe the genetic correlation among phenotypes. Our LAD-LASSO approach is less sensitive to the outliers and is more appropriate for the analysis of data with skewedly distributed phenotypes. Another application of our robust approach is on missing phenotype problem in multiple-trait analysis, where the missing phenotype items can simply be filled with some extreme values, and be treated as outliers. The efficiency of the LAD-LASSO approach is illustrated on both simulated and real data sets.

Multicriteria decision support for the evaluation of agricultural units in Greece

One of the main objectives of the common agricultural policy (CAP) is the increase of productivity of agricultural units. CAP is set and reformed in the frame of providing financial support to producers in primary sector via a single payment schema as a direct funding based on the land area, where farmers obtain ‘entitlements’. In Greece the total area is taken into account to the financial aid as form of direct payment. Therefore, the production is significantly decreased. In this paper the evaluation of agricultural units is proposed using the robust ordinal regression approach, and a case study dealing with the evaluation of Greek farmers in the industry of the juicing citrus is conducted. The method is used as an evaluation tool for financial aid to the farmers, towards the new policy, thus making the production-based approach more effective and objective. An additive evaluation model is proposed based on a consistent family of criteria composed by input and output criteria. The phenomenon of “Sofa Farmers” could be eliminated, since farmers would be financially aided after been evaluated. Finally, in order to obtain robust conclusions, post-optimality analyses are applied by computing complementary robustness measures.

Analysis of Mining Engineering Data Using Robust Estimators in the Presence of Outliers

Ordinary least squares (OLS) regression is an estimation technique widely used in mining research to model relationship among a dependent variable and a set of explanatory variables. However, OLS is based on strong assumption such as normality of the error term, exogeneity of explanatory variables, linearity between regression coefficients, and homoscedasticity. When one or more of the assumption are not held, OLS can lead to biased and inefficient estimates of the true population parameters. Using biased estimates of the population parameters may result in serious problems in mining decision making, especially if key decisions are based on the biased parameter estimates. One of the main reasons that can lead OLS to provide biased estimates is the presence of outlier data points in the sampled population. In this paper, we focus on alternatives to the OLS estimator, which are more robust (or resistant) to the presence of outliers. Two case studies were conducted to compare OLS and robust regression approaches namely L1-estimation, M-estimation, least trimmed squares, least median squares, and MM-estimation. The case studies showed that inference based on OLS in the presence of outliers could lead to bad decisions if regression coefficients are not interpreted correctly. Robust regression approach can provide estimates useful even if a dataset is contaminated with outliers.

Gendered key events in the life course: effects on changes in travel mode choice over time

This paper studies changes in travel mode specific trip rates after life course (and accessibility) related key events from a gender perspective. It is theoretically informed by the mobility biographies approach, and by gender/travel studies. The data used is the German Mobility Panel (GMP) 1994 to 2010 in which households and their members are asked three times in three subsequent years to report the trips they made over a week. The changes reported are regressed to key events over the life course, cohort effects and period effects, while sociodemographics and spatial context attributes are controlled. A cluster–robust regression approach is used to account for the non-independent character of panel observations. Significant effects were found for some key events, including the birth of a child, entry into the labour market, and changes in spatial context, accessibility and mobility. Some effects differed distinctly between men and women, suggesting that men and women are differently affected by life course events. However, taken together the associations found, as well as their gender differences are rather limited. Hence, key events over the life course seem to be only loosely associated with travel mode specific trip rates.

A Refined Strategy for Removing Composite Errors of SAR Interferogram

In standard differential synthetic aperture radar interferometry, there could still be a residual tilt (orbital error) in the interferometric phase due to inaccurate baseline estimation. We demonstrated theoretically that the orbital errors were partially elevation dependent. On the basis of this, we introduced an elevation-dependent item to the conventional polynomial model to simulate, and therefore, compensate the orbital errors, as well as the small scale topographic and/or topography-related phase errors. Robust regression approach was suggested to determine the parameters of the proposed model. The model was validated with both synthetic and real ALOS PALSAR data of the Zhouqu, China mudslide. The synthetic test indicated that upon applying the refined model, the accuracies of phase measurements were improved by nearly two times, compared to those using conventional linear and quadratic models. The real data experiment indicated that after utilizing the refined model, the correlation between the interferogram and the digital elevation model of Zhouqu reduced to about 1/5 of those using linear and quadratic models. This demonstrates that the elevation-dependent phase components have been largely removed by the new model. More importantly, the interferogram corrected by the new model visibly disclosed the deformation area affected by the Zhouqu mudslide.

Influence of the limit of detection on classification using otolith elemental signatures

Otolith elemental composition is a commonly used tool in the classification of fish stocks. Lower detection limits associated with trace element analysis techniques are the source of much debate among fisheries biologists. Using empirical data from Atlantic herring (Clupea harengus) from two separate origins in the British Isles, we addressed methods of treating data at or falling below detection limits and the implications of each treatment for discrimination and classification analysis. Estimating actual values of non-detected concentrations, through imputation, is now a plausible and simply applied strategy and should be considered as an alternative to constant replacement. We compare a robust regression approach to estimating values for non-detects alongside a variety of constant replacement methods. We also show the value of a highly censored variable in understanding population discrimination; despite 40% of readings for one element being non-detects, we found that its removal was detrimental to the discriminatory power of the analysis.

Correlation of Water Vapor Permeability with Microstructure Characteristics of Building Materials Using Robust Chemometrics

This paper studies various microstructure parameters of natural and artificial building materials and aims to their correlation to the water vapor permeability. Three categories of building materials were investigated: stones, bricks, and plasters. Mercury intrusion porosimetry was applied in order to obtain the materials microstructure characteristics, a variety of pore size distributions and pore structure measurements, such as total porosity. The water vapor permeability of materials was determined experimentally according to ASTM standard E96-00. A robust principal component regression approach, coupled with multiple outlier detection, was applied in order to correlate water vapor permeability values to pore size distributions. A good quality correlation model was found by utilizing relative specific pore volume and relative specific pore surface distributions, whereas using pore structure measurements, such as total porosity, the correlation results were very poor. From the results, specific ranges of pore size distribution, corresponding to pores radius sizes greater than \(10\,\upmu \text{ m }\) and between 1.778 and \(0.421\,\upmu \text{ m }\), contribute to the water vapor permeability of the materials.

Simultaneous robust estimation of multi-response surfaces in the presence of outliers

A robust approach should be considered when estimating regression coefficients in multi-response problems. Many models are derived from the least squares method. Because the presence of outlier data is unavoidable in most real cases and because the least squares method is sensitive to these types of points, robust regression approaches appear to be a more reliable and suitable method for addressing this problem. Additionally, in many problems, more than one response must be analyzed; thus, multi-response problems have more applications. The robust regression approach used in this paper is based on M-estimator methods. One of the most widely used weighting functions used in regression estimation is Huber’s function. In multi-response surfaces, an individual estimation of each response can cause a problem in future deductions because of separate outlier detection schemes. To address this obstacle, a simultaneous independent multi-response iterative reweighting (SIMIR) approach is suggested. By presenting a coincident outlier index (COI) criterion while considering a realistic number of outliers in a multi-response problem, the performance of the proposed method is illustrated. Two well-known cases are presented as numerical examples from the literature. The results show that the proposed approach performs better than the classic estimation, and the proposed index shows efficiency of the proposed approach.

IB1001, an Investigational Recombinant Factor IX, Pharmacokinetics in Pediatric Patients with Hemophilia B.

AbstractAbstract 2225 IntroductionIB1001 is a recombinant factor IX product being investigated for the treatment and prevention of bleeding in individuals with hemophilia B. Pharmacokinetics (PK) in adults (>12 years) demonstrated that IB1001 had results similar to the currently available recombinant FIX with respect to parameters such as terminal phase half-life and incremental recovery.We report the interim findings from a PK assessment in children <12 years, with severe hemophilia B (FIX <2%), >50 prior exposure days to FIX, and no history of or currently detectable inhibitor to FIX. MethodsNon-randomized, open-label PK study with patients receiving 75±5 IU/kg of IB1001 following a washout period of ≥4 days from a previous FIX infusion. Factor IX levels were determined pre-infusion and at 15–30 minutes, 4–6, 24–26, and 68–72 hours post-infusion. Additional samples could be drawn at 1–3 and 10–14 hours.Calculated PK parameters were: half-life (β-phase t1/2, determined using a robust regression approach [Lee ML et al. XVIth ISTH Congress, Florence, Italy, 1997]) but generally assuming a single compartmental model because of the small number of points, maximum plasma concentration (Cmax), in vivo recovery (IVR) and AUC(0-∞) (determined by the trapezoidal rule). In addition, the AUC(0-t) and mean residence time (MRT) were calculated. ResultsSubjectt 1/2 α (hr)t 1/2 β (hr)MRT (hr)Cmax (IU/dl)In vivo Recovery (IU/dl)AUC0-∞ (IU/dl/hr)AUC0-t (IU/dl/hr)Age (years)Subjects 6 - 12 Years of Age32001n/a17.722630.8414611359912001n/a17.521.2570.76113810627.532003720.724580.77106797711.135002n/a33.655220.2960541010mean±SD (median)22.4±7.6 (19.2)30.6±16.3 (23)50±19 (57.5)0.66±0.25 (0.765)1068±353 (1102.5)952±397 (1019.5)9.4±1.5 (9.5)Subjects < 6 Years of Age4001n/a7.612.1600.8942941235001n/a16.319.5640.8512171147432002n/a21.929.4400.539868704.5mean±SD (median)15.3±7.2 (16.3)20.3±8.7 (19.5)55±13 (60)0.73±0.17 (0.8)1048±148 (986)986±144 (941)3.5±1.3 (4)When compared to the findings previously reported with IB1001 in adult (≥12 years of age) subjects (Martinowitz U et al. Haemophilia, 18, 2012), the results in pediatric patients demonstrate a more rapid metabolism of factor IX as is indicated by the shorter terminal half-life (mean±SD of 19.3±7.8 h versus 29.6±18.2 h in adults) and the smaller AUC0-∞ (mean±SD of 1059±264 versus 1668±598 in adults). In addition, the in vivo recovery was lower (mean±SD of 0.69±0.21) versus that seen in adults (mean±SD of 0.98±0.22). These results are similar to those reported by Berntorp et al (Haemophilia, 7, 2001) with nonacog alfa. ConclusionsThe pharmacokinetics of IB1001 has previously been shown to be non-inferior to nonacog alfa, another recombinant factor IX, in hemophilia B individuals >12 years of age. The current study is intended to provide information on children <12 and, particularly, <6 years of age. IB1001 is metabolized faster and has a lower recovery than the comparable findings in patients >12 years of age. Although the study is ongoing, these may represent important implications for the potential use of IB1001 in pediatric patients. Disclosures:Gomperts:Inspiration Biopharmaceuticals Inc: Consultancy. Apte:Inspiration Biopharmacauticals Inc: Research Funding. Chaudhuri:Inspiration Biopharmaceuticals Inc: Research Funding. John:Inspiration Biopharmaceuticals Inc: Research Funding. Ramanan:Inspiration Biopharmaceuticals Inc: Research Funding. Liesner:Inspiration Biopharmaceuticals Inc: Research Funding. Shapiro:Inspiration Biopharmaceuticals Inc: Honoraria, Research Funding. Mills:Inspiration Biopharmaceuticals Inc: Employment. Lee:Inspiration Biopharmaceuticals Inc: Employment.

Institutional pressures, dynamic capabilities and environmental management systems: Investigating the ISO 9000 – Environmental management system implementation linkage

We hypothesize a model where domestic and international institutional pressures lead to the successful implementation of ISO 9000 and can in turn lead to the successful implementation of environmental management systems such as ISO 14001 environmental certification systems or total quality environmental management (TQEM) systems. Using appropriate tests for mediation with dichotomous mediators and outcomes, we find that the model holds for a sample of 377 Chinese manufacturers in six major industrial groups in Suzhou, Dalian, and Tianjin. Our findings are consistent with the theory linking internal capabilities to heterogeneous external (in this case, institutional) pressures on organizations for environmentally proactive efforts. Our findings suggest that institutions in developing countries with significant environmental concerns such as China as well as foreign suppliers and partners to firms in these countries should encourage and support ISO 9000 implementations by local firms. These findings may influence other developing nations' adoption of quality and environmental process systems.

Parametric simultaneous robust inferences for regression coefficient under generalized linear models

In this article, the parametric robust regression approaches are proposed for making inferences about regression parameters in the setting of generalized linear models (GLMs). The proposed methods are able to test hypotheses on the regression coefficients in the misspecified GLMs. More specifically, it is demonstrated that with large samples, the normal and gamma regression models can be properly adjusted to become asymptotically valid for inferences about regression parameters under model misspecification. These adjusted regression models can provide the correct type I and II error probabilities and the correct coverage probability for continuous data, as long as the true underlying distributions have finite second moments.

A robust regression approach for spectrophotometric signal analysis

The effectiveness of a regression method strongly depends on the characteristics of the considered regression problem. As a consequence, this makes it difficult to choose a priori the most appropriate algorithm for a given dataset. This issue is faced in this work through a novel regression approach based on the fusion of an ensemble of different regressors. In order to implement the proposed robust multiple system (RMS), four different fusion strategies are explored. In this context, we propose a novel fusion strategy named selection-based strategy (SBS) that provides as output the estimate obtained by the regression algorithm (included in the ensemble) characterized by the highest expected accuracy in the region of the feature space associated with the considered model. The SBS is based not on a direct combination of the estimates yielded by all the regressors but on a selection mechanism that identifies the expected best available estimate. For such purpose, it exploits the accuracies of the regressors included in the ensemble in different portions of the input feature space. The experimental assessment of the RMS was carried out on three different datasets: a wine, an orange juice, and an apple datasets. The obtained experimental results suggest that, in general, the fusion of an ensemble of different regression algorithms leads to a regression process that is more robust and sometimes also more accurate than traditional regression methods. In particular, the proposed SBS method represents an effective solution to carry out the fusion process. Copyright © 2012 John Wiley & Sons, Ltd.