Novel Methods for Multivariate Ordinal Data applied to Genetic Diplotypes, Genomic Pathways, Risk Profiles, and Pattern Similarity

Introduction: Conventional statistical methods for multivariate data (e.g., discriminant/regression) are based on the (generalized) linear model, i.e., the data are interpreted as points in a Euclidian space of independent dimensions. The dimensionality of the data is then reduced by assuming the components to be related by a specific function of known type (linear, exponential, etc.), which allows the distance of each point from a hyperspace to be determined. While mathematically elegant, these approaches may have shortcomings when applied to real world applications where the relative importance, the functional relationship, and the correlation among the variables tend to be unknown. Still, in many applications, each variable can be assumed to have at least an “orientation”, i.e., it can reasonably assumed that, if all other conditions are held constant, an increase in this variable is either “good” or “bad”. The direction of this orientation can be known or unknown. In genetics, for instance, having more “abnormal” alleles may increase the risk (or magnitude) of a disease phenotype. In genomics, the expression of several related genes may indicate disease activity. When screening for security risks, more indicators for atypical behavior may constitute raise more concern, in face or voice recognition, more indicators being similar may increase the likelihood of a person being identified. Methods: In 1998, we developed a nonparametric method for analyzing multivariate ordinal data to assess the overall risk of HIV infection based on different types of behavior or the overall protective effect of barrier methods against HIV infection. By using u-statistics, rather than the marginal likelihood, we were able to increase the computational efficiency of this approach by several orders of magnitude. Results: We applied this approach to assessing immunogenicity of a vaccination strategy in cancer patients. While discussing the pitfalls of the conventional methods for linking quantitative traits to haplotypes, we realized that this approach could be easily modified into to a statistically valid alternative to a previously proposed approaches. We have now begun to use the same methodology to correlate activity of anti-inflammatory drugs along genomic pathways with disease severity of psoriasis based on several clinical and histological characteristics. Conclusion: Multivariate ordinal data are frequently observed to assess semiquantitative characteristics, such as risk profiles (genetic, genomic, or security) or similarity of pattern (faces, voices, behaviors). The conventional methods require empirical validation, because the functions and weights chosen cannot be justified on theoretical grounds. The proposed statistical method for analyzing profiles of ordinal variables, is intrinsically valid. Since no additional assumptions need to be made, the often time-consuming empirical validation can be skipped.ranking; nonparametric; robust; scoring; multivariate

Towards Novel Nonparametric Statistical Methods and Bioinformatics Tools for Clinical and Translational Sciences

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge.Biostatistics Bioinformatics NIH NCRR ROADMAP

New Statistical Paradigms Leading to Web-Based Tools for Clinical/Translational Science

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge

Novel Methods for Multivariate Ordinal Data applied to Genetic Diplotypes, Genomic Pathways, Risk Profiles, and Pattern Similarity

Introduction: Conventional statistical methods for multivariate data (e.g., discriminant/regression) are based on the (generalized) linear model, i.e., the data are interpreted as points in a Euclidian space of independent dimensions. The dimensionality of the data is then reduced by assuming the components to be related by a specific function of known type (linear, exponential, etc.), which allows the distance of each point from a hyperspace to be determined. While mathematically elegant, these approaches may have shortcomings when applied to real world applications where the relative importance, the functional relationship, and the correlation among the variables tend to be unknown. Still, in many applications, each variable can be assumed to have at least an “orientation”, i.e., it can reasonably assumed that, if all other conditions are held constant, an increase in this variable is either “good” or “bad”. The direction of this orientation can be known or unknown. In genetics, for instance, having more “abnormal” alleles may increase the risk (or magnitude) of a disease phenotype. In genomics, the expression of several related genes may indicate disease activity. When screening for security risks, more indicators for atypical behavior may constitute raise more concern, in face or voice recognition, more indicators being similar may increase the likelihood of a person being identified. Methods: In 1998, we developed a nonparametric method for analyzing multivariate ordinal data to assess the overall risk of HIV infection based on different types of behavior or the overall protective effect of barrier methods against HIV infection. By using u-statistics, rather than the marginal likelihood, we were able to increase the computational efficiency of this approach by several orders of magnitude. Results: We applied this approach to assessing immunogenicity of a vaccination strategy in cancer patients. While discussing the pitfalls of the conventional methods for linking quantitative traits to haplotypes, we realized that this approach could be easily modified into to a statistically valid alternative to a previously proposed approaches. We have now begun to use the same methodology to correlate activity of anti-inflammatory drugs along genomic pathways with disease severity of psoriasis based on several clinical and histological characteristics. Conclusion: Multivariate ordinal data are frequently observed to assess semiquantitative characteristics, such as risk profiles (genetic, genomic, or security) or similarity of pattern (faces, voices, behaviors). The conventional methods require empirical validation, because the functions and weights chosen cannot be justified on theoretical grounds. The proposed statistical method for analyzing profiles of ordinal variables, is intrinsically valid. Since no additional assumptions need to be made, the often time-consuming empirical validation can be skipped

Towards Novel Nonparametric Statistical Methods and Bioinformatics Tools for Clinical and Translational Sciences

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge

Novel Methods for Multivariate Ordinal Data applied to Genetic Diplotypes, Genomic Pathways, Risk Profiles, and Pattern Similarity

Introduction: Conventional statistical methods for multivariate data (e.g., discriminant/regression) are based on the (generalized) linear model, i.e., the data are interpreted as points in a Euclidian space of independent dimensions. The dimensionality of the data is then reduced by assuming the components to be related by a specific function of known type (linear, exponential, etc.), which allows the distance of each point from a hyperspace to be determined. While mathematically elegant, these approaches may have shortcomings when applied to real world applications where the relative importance, the functional relationship, and the correlation among the variables tend to be unknown. Still, in many applications, each variable can be assumed to have at least an “orientation”, i.e., it can reasonably assumed that, if all other conditions are held constant, an increase in this variable is either “good” or “bad”. The direction of this orientation can be known or unknown. In genetics, for instance, having more “abnormal” alleles may increase the risk (or magnitude) of a disease phenotype. In genomics, the expression of several related genes may indicate disease activity. When screening for security risks, more indicators for atypical behavior may constitute raise more concern, in face or voice recognition, more indicators being similar may increase the likelihood of a person being identified. Methods: In 1998, we developed a nonparametric method for analyzing multivariate ordinal data to assess the overall risk of HIV infection based on different types of behavior or the overall protective effect of barrier methods against HIV infection. By using u-statistics, rather than the marginal likelihood, we were able to increase the computational efficiency of this approach by several orders of magnitude. Results: We applied this approach to assessing immunogenicity of a vaccination strategy in cancer patients. While discussing the pitfalls of the conventional methods for linking quantitative traits to haplotypes, we realized that this approach could be easily modified into to a statistically valid alternative to a previously proposed approaches. We have now begun to use the same methodology to correlate activity of anti-inflammatory drugs along genomic pathways with disease severity of psoriasis based on several clinical and histological characteristics. Conclusion: Multivariate ordinal data are frequently observed to assess semiquantitative characteristics, such as risk profiles (genetic, genomic, or security) or similarity of pattern (faces, voices, behaviors). The conventional methods require empirical validation, because the functions and weights chosen cannot be justified on theoretical grounds. The proposed statistical method for analyzing profiles of ordinal variables, is intrinsically valid. Since no additional assumptions need to be made, the often time-consuming empirical validation can be skipped

"Harshlighting" small blemishes on microarrays

BACKGROUND: Microscopists are familiar with many blemishes that fluorescence images can have due to dust and debris, glass flaws, uneven distribution of fluids or surface coatings, etc. Microarray scans show similar artefacts, which affect the analysis, particularly when one tries to detect subtle changes. However, most blemishes are hard to find by the unaided eye, particularly in high-density oligonucleotide arrays (HDONAs). RESULTS: We present a method that harnesses the statistical power provided by having several HDONAs available, which are obtained under similar conditions except for the experimental factor. This method "harshlights" blemishes and renders them evident. We find empirically that about 25% of our chips are blemished, and we analyze the impact of masking them on screening for differentially expressed genes. CONCLUSION: Experiments attempting to assess subtle expression changes should be carefully screened for blemishes on the chips. The proposed method provides investigators with a novel robust approach to improve the sensitivity of microarray analyses. By utilizing topological information to identify and mask blemishes prior to model based analyses, the method prevents artefacts from confounding the process of background correction, normalization, and summarization

U-Scores for Multivariate Data In Sports

In many sport competitions athletes, teams, or countries are evaluated based on several variables. The strong assumptions underlying traditional ‘linear weight’ scoring systems (that the relative importance, interactions and linearizing transformations of the variables are known) can often not be justified on theoretical grounds, and empirical ‘validation’ of weights, interactions and transformations, is problematic when a ‘gold standard’ is lacking. With μ-scores (u-scores for multivariate data) one can integrate information even if the variables have different scales and unknown interactions or if the events counted are not directly comparable, as long as the variables have an ‘orientation’. Using baseball as an example, we discuss how measures based on μ-scores can complement the existing measures for ‘performance’ (which may depend on the situation) by providing the first multivariate measures for ‘ability’ (which should be independent of the situation). Recently, μ-scores have been extended to situations where count variables are graded by importance or relevance, such as medals in the Olympics (Wittkowski 2003) or Tour-de-France jerseys (Cherchye and Vermeulen 2006, 2007). Here, we present extensions to ‘censored’ variables (life-time achievements of active athletes), penalties (counting a win more than two ties) and hierarchically structured variables (Nordic, alpine, outdoor, and indoor Olympic events). The methods presented are not restricted to sports. Other applications of the method include medicine (adverse events), finance (risk analysis), social choice theory (voting), and economy (long-term profit)

In Vitro and In Vivo Evidence that Thrombospondin-1 (TSP-1) Contributes to Stirring- and Shear-Dependent Activation of Platelet-Derived TGF-β1

Thrombospondin 1 (TSP-1), which is contained in platelet α-granules and released with activation, has been shown to activate latent TGF-β1 in vitro, but its in vivo role is unclear as TSP-1-null (Thbs1−/−) mice have a much less severe phenotype than TGF-β1-null (Tgfb1−/−) mice. We recently demonstrated that stirring and/or shear could activate latent TGF-β1 released from platelets and have now studied these methods of TGF-β1 activation in samples from Thbs1−/− mice, which have higher platelet counts and higher levels of total TGF-β1 in their serum than wild type mice. After either two hours of stirring or shear, Thbs1−/− samples demonstrated less TGF-β1 activation (31% and 54% lower levels of active TGF-β1 in serum and platelet releasates, respectively). TGF-β1 activation in Thbs1−/− mice samples was normalized by adding recombinant human TSP-1 (rhTSP-1). Exposure of platelet releasates to shear for one hour led to near depletion of TSP-1, but this could be prevented by preincubating samples with thiol-reactive agents. Moreover, replenishing rhTSP-1 to human platelet releasates after one hour of stirring enhanced TGF-β1 activation. In vivo TGF-β1 activation in carotid artery thrombi was also partially impaired in Thbs1−/− mice. These data indicate that TSP-1 contributes to shear-dependent TGF-β1 activation, thus providing a potential explanation for the inconsistent in vitro data previously reported as well as for the differences in phenotypes of Thbs1−/− and Tgfb1−/− mice

Phenotyping Genetic Diseases Using an Extension of μ-Scores for Multivariate Data

As the field of genomics matures, more complex genotypes and phenotypes are being studied. Fanconi anemia (FA), for example, is an inherited chromosome instability syndrome with a complex array of variable disease phenotypes including congenital malformations, hematological manifestations, and cancer. To better understand specific aspects of the genetic etiology of FA and other rare diseases with complex phenotypes, it is often necessary to reduce the dimensions of the disease phenotype information. Towards this end, we extend a novel non-parametric approach to include information about a hierarchical structure among disease phenotypes. The proposed extension increases information content of the phenotype scores obtained and, thereby, the power of genotype-phenotype relationships studies