Statistics and Actuarial Science, Department of

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A Computational Pipeline for the Development of Multi-Marker Bio-Signature Panels and Ensemble Classifiers

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

BACKGROUND:Biomarker panels derived separately from genomic and proteomic data and with a variety of computational methods have demonstrated promising classification performance in various diseases. An open question is how to create effective proteo-genomic panels. The framework of ensemble classifiers has been applied successfully in various analytical domains to combine classifiers so that the performance of the ensemble exceeds the performance of individual classifiers. Using blood-based diagnosis of acute renal allograft rejection as a case study, we address the following question in this paper: Can acute rejection classification performance be improved by combining individual genomic and proteomic classifiers in an ensemble?RESULTS:The first part of the paper presents a computational biomarker development pipeline for genomic and proteomic data. The pipeline begins with data acquisition (e.g., from bio-samples to microarray data), quality control, statistical analysis and mining of the data, and finally various forms of validation. The pipeline ensures that the various classifiers to be combined later in an ensemble are diverse and adequate for clinical use. Five mRNA genomic and five proteomic classifiers were developed independently using single time-point blood samples from 11 acute-rejection and 22 non-rejection renal transplant patients. The second part of the paper examines five ensembles ranging in size from two to 10 individual classifiers. Performance of ensembles is characterized by area under the curve (AUC), sensitivity, and specificity, as derived from the probability of acute rejection for individual classifiers in the ensemble in combination with one of two aggregation methods: (1) Average Probability or (2) Vote Threshold. One ensemble demonstrated superior performance and was able to improve sensitivity and AUC beyond the best values observed for any of the individual classifiers in the ensemble, while staying within the range of observed specificity. The Vote Threshold aggregation method achieved improved sensitivity for all 5 ensembles, but typically at the cost of decreased specificity.CONCLUSION:Proteo-genomic biomarker ensemble classifiers show promise in the diagnosis of acute renal allograft rejection and can improve classification performance beyond that of individual genomic or proteomic classifiers alone. Validation of our results in an international multicenter study is currently underway.

Document type: 
Article

Generalized Classes of Starlike and Convex Functions of Order α

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1985
Abstract: 

We have introduced, in this paper, the generalized classes of starlike and convex functions of order α by using the fractional calculus. We then proved some subordination theorems, argument theorems, and various results of modified Hadamard product for functions belonging to these classes. We have also established some properties about the generalized Libera operator defined on these classes of functions.

Document type: 
Article

Contractive Mappings on a Premetric Space

Author: 
Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1985
Abstract: 

In this paper, we study the fixed point property of certain types ofcontractive mappings defined on a premetric space. The applications of these results to topological vector spaces and to metric spaces are also discussed.

Document type: 
Article

A Bounded Consistency Theorem for Strong Summabilities

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1989
Abstract: 

The study of R-type summability methods is continued in this paper byshowing that two such methods are identical on the bounded portion of the strongsummability field associated with the methods. It is shown that this “boundedconsistency” applies for many non-matrix methods as well as for regular matrix methods.

Document type: 
Article

A Weak Invariance Principle and Asymptotic Stability for Evolution Equations with Bounded Generators

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1995
Abstract: 

If V is a Lyapunov function of an equation du/dt u’ Zu in a Banach space thenasymptotic stability of an equilibrium point may be easily proved if it is known that sup(V’) < 0 onsufficiently small spheres centered at the equilibrium point. In this paper weak asymptotic stability isproved for a bounded infinitesimal generator Z under a weaker assumption V’ < 0 (which aloneimplies ordinary stability only) if some observability condition, involving Z and the Frechet derivativeof V’, is satisfied. The proof is based on an extension of LaSalle’s invariance principle, which yieldsconvergence in a weak topology and uses a strongly continuous Lyapunov funcdon. The theory isillustrated with an example of an integro-differential equation of interest in the theory of chemicalprocesses. In this case strong asymptotic stability is deduced from the weak one and explicit sufficientconditions for stability are given. In the case of a normal infinitesimal generator Z in a Hilbertspace, strong asymptotic stability is proved under the following assumptions Z* + Z is weaklynegative definite and Ker Z 0 }. The proof is based on spectral theory.

Document type: 
Article
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On Approximation of Functions and Their Derivatives by Quasi-Hermite Interpolation

Author: 
Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
1996
Abstract: 

In this paper, we consider the simultaneous approximation of the derivatives of thefunctions by the corresponding derivatives of qua.si-Hcrmite interpolation based on the zeros of (1z2)p,(z) (where p,(x)is a Lcgcndrc polynomial). The corresponding approximation degrees are given.It is shown that this matrix of nodes is almost optimal

Document type: 
Article

Modelling Desert Dune Fields Based on Discrete Dynamics

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2002
Abstract: 

A mathematical formulation is developed to model the dynamics of sand dunes. The physical processes display strong non-linearity that has been taken into account in the model. When assessing the success of such a model in capturing physical features we monitor morphology, dune growth, dune migration and spatial patterns within a dune field. Following recent advances, the proposed model is based on a discrete lattice dynamics approach with new features taken into account which reflect physically observed mechanisms.

Document type: 
Article

Systems Mapping: How to Improve the Genetic Mapping of Complex Traits Through Design Principles of Biological Systems

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2011
Abstract: 

Background: Every phenotypic trait can be viewed as a “system” in which a group of interconnected componentsfunction synergistically to yield a unified whole. Once a system’s components and their interactions have beendelineated according to biological principles, we can manipulate and engineer functionally relevant components toproduce a desirable system phenotype.Results: We describe a conceptual framework for mapping quantitative trait loci (QTLs) that control complex traitsby treating trait formation as a dynamic system. This framework, called systems mapping, incorporates a system ofdifferential equations that quantifies how alterations of different components lead to the global change of traitdevelopment and function through genes, and provides a quantitative and testable platform for assessing theinterplay between gene action and development. We applied systems mapping to analyze biomass growth data ina mapping population of soybeans and identified specific loci that are responsible for the dynamics of biomasspartitioning to leaves, stem, and roots.Conclusions: We show that systems mapping implemented by design principles of biological systems is quiteversatile for deciphering the genetic machineries for size-shape, structural-functional, sink-source and pleiotropicrelationships underlying plant physiology and development. Systems mapping should enable geneticists to shedlight on the genetic complexity of any biological system in plants and other organisms and predict itsphysiological and pathological states.

Document type: 
Article

Canadian Physiotherapists' Views on Certification, Specialisation, Extended Role Practice, and Entry-Level Training in Rheumatology

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2009
Abstract: 

Background: Since the last decade there has been a gradual change of boundaries of health professionsin providing arthritis care. In Canada, some facilities have begun to adopt new arthritis care models, someof which involve physiotherapists (PT) working in extended roles. However, little is known about PTs'interests in these new roles. The primary objective of this survey was to determine the interests amongorthopaedic physiotherapists (PTs) in being a certified arthritis therapist, a PT specialized in arthritis, oran extended scope practitioner in rheumatology, and to explore the associated factors, including thecoverage of arthritis content in the entry-level physiotherapy training.Methods: Six hundred PTs practicing in orthopaedics in Canada were randomly selected to receive apostal survey. The questionnaire covered areas related to clinical practice, perceptions of rheumatologytraining received, and attitudes toward PT roles in arthritis care. Logistic regression models weredeveloped to explore the associations between PTs' interests in pursuing each of the three extendedscope practice designations and the personal/professional/attitudinal variables.Results: We received 286 questionnaires (response rate = 47.7%); 258 contained usable data. Theaverage length of time in practice was 15.4 years (SD = 10.4). About 1 in 4 PTs agreed that they wereinterested in assuming advanced practice roles (being a certified arthritis therapist = 28.9%, being a PTspecialized in rheumatology = 23.3%, being a PT practitioner = 20.9%). Having a caseload of ≥ 40% inarthritis, having a positive attitude toward advanced practice roles in arthritis care and toward the formalcredentialing process, and recognizing the difference between certification and specialisation wereassociated with an interest in pursing advanced practice roles.Conclusion: Orthopaedic PTs in Canada indicated a fair level of interest in pursuing certification,specialisation and extended scope practice roles in arthritis care. Future research should focus on theeffectiveness and cost-effectiveness of the emerging health service delivery models involving certified,specialized or extended scope practice PTs in the management of arthritis.

Document type: 
Article

Assessment of Health-Related Quality of Life in Arthritis: Conceptualization and Development of Five Item Banks using Item Response Theory

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2006
Abstract: 

Background: Modern psychometric methods based on item response theory (IRT) can be used to developadaptive measures of health-related quality of life (HRQL). Adaptive assessment requires an item bank for eachdomain of HRQL. The purpose of this study was to develop item banks for five domains of HRQL relevant toarthritis.Methods: About 1,400 items were drawn from published questionnaires or developed from focus groups andindividual interviews and classified into 19 domains of HRQL. We selected the following 5 domains relevant toarthritis and related conditions: Daily Activities, Walking, Handling Objects, Pain or Discomfort, and Feelings.Based on conceptual criteria and pilot testing, 219 items were selected for further testing. A questionnaire wasmailed to patients from two hospital-based clinics and a stratified random community sample. Dimensionality ofthe domains was assessed through factor analysis. Items were analyzed with the Generalized Partial Credit Modelas implemented in Parscale. We used graphical methods and a chi-square test to assess item fit. Differential itemfunctioning was investigated using logistic regression.Results: Data were obtained from 888 individuals with arthritis. The five domains were sufficientlyunidimensional for an IRT-based analysis. Thirty-one items were deleted due to lack of fit or differential itemfunctioning. Daily Activities had the narrowest range for the item location parameter (-2.24 to 0.55) and HandlingObjects had the widest range (-1.70 to 2.27). The mean (median) slope parameter for the items ranged from 1.15(1.07) in Feelings to 1.73 (1.75) in Walking. The final item banks are comprised of 31–45 items each.Conclusion: We have developed IRT-based item banks to measure HRQL in 5 domains relevant to arthritis. Theitems in the final item banks provide adequate psychometric information for a wide range of functional levels ineach domain.

Document type: 
Article