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Assessing a Multiple QTL Search Using the Variance Component Model
Mälardalen University, School of Education, Culture and Communication.
2010 (English)In: Computational biology and chemistry (Print), ISSN 1476-9271, E-ISSN 1476-928X, Vol. 34, no 1, p. 34-41Article in journal (Refereed) Published
Abstract [en]

Development of variance component algorithms in genetics has previously mainly focused on animal breeding models or problems in human genetics with a simple data structure. We study alternative methods for constrained likelihood maximization in quantitative trait loci (QTL) analysis for large complex pedigrees. We apply a forward selection scheme to include several QTL and interaction effects, as well as polygenic effects, with up to five variance components in the model. We show that the implemented active set and primal-dual schemes result in accurate solutions and that they are robust. In terms of computational speed, a comparison of two approaches for approximating the Hessian of the log-likelihood shows that the method using an average information matrix is the method of choice for the five-dimensional problem. The active set method, with the average information method for Hessian computation, exhibits the fastest convergence with an average of 20 iterations per tested position, where the change in variance components <0.0001 was used as convergence criterion.

Place, publisher, year, edition, pages
2010. Vol. 34, no 1, p. 34-41
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:mdh:diva-4224DOI: 10.1016/j.compbiolchem.2009.12.001ISI: 000275587800004PubMedID: 20080064Scopus ID: 2-s2.0-75149131993OAI: oai:DiVA.org:mdh-4224DiVA, id: diva2:121265
Available from: 2008-04-28 Created: 2008-04-28 Last updated: 2018-10-16Bibliographically approved
In thesis
1. Numerical Algorithms for Optimization Problems in Genetical Analysis
Open this publication in new window or tab >>Numerical Algorithms for Optimization Problems in Genetical Analysis
2008 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The focus of this thesis is on numerical algorithms for efficient solution of QTL analysis problem in genetics.

Firstly, we consider QTL mapping problems where a standard least-squares model is used for computing the model fit. We develop optimization methods for the local problems in a hybrid global-local optimization scheme for determining the optimal set of QTL locations. Here, the local problems have constant bound constraints and may be non-convex and/or flat in one or more directions. We propose an enhanced quasi-Newton method and also implement several schemes for constrained optimization. The algorithms are adopted to the QTL optimization problems. We show that it is possible to use the new schemes to solve problems with up to 6 QTLs efficiently and accurately, and that the work is reduced with up to two orders magnitude compared to using only global optimization.

Secondly, we study numerical methods for QTL mapping where variance component estimation and a REML model is used. This results in a non-linear optimization problem for computing the model fit in each set of QTL locations. Here, we compare different optimization schemes and adopt them for the specifics of the problem. The results show that our version of the active set method is efficient and robust, which is not the case for methods used earlier. We also study the matrix operations performed inside the optimization loop, and develop more efficient algorithms for the REML computations. We develop a scheme for reducing the number of objective function evaluations, and we accelerate the computations of the derivatives of the log-likelihood by introducing an efficient scheme for computing the inverse of the variance-covariance matrix and other components of the derivatives of the log-likelihood.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2008
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 59
Keywords
Quantitative Trait Loci (QTL), restricted maximum likelihood (REML), variance components, average information (AI) matrix, Local optimization, Quasi-Newton method, Active Set method, Hessian approximation, BFGS update
National Category
Computational Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
urn:nbn:se:mdh:diva-650 (URN)978-91-85485-84-0 (ISBN)
Public defence
2008-06-05, Kappa, U, Högskoleplan 1, Västerås, 13:00
Opponent
Supervisors
Available from: 2008-04-28 Created: 2008-04-28

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