Technical Report 2010-005

Assessing Orthogonality and Statical Properties of Linear Regression Methods for Interval Mapping with Partial Information

Carl Nettelblad, Örjan Carlborg, and José M. lvarez-Castro

March 2010


Background: Mapping quantitative trait loci (QTL) has become a widely used tool in genetical research. In such experiments, it is desired to obtain orthogonal estimates of genetic effects for a number of reasons concerning both the biological meaning of the estimated locations and effects, and making the statistical analysis clearer and more robust. The currently used statistical methods, however, are not optimized for orthogonality, especially in cases involving interval mapping between markers and/or in incomplete datasets. This is an adverse limitation for the application of such methods for QTL scans involving model selection over putative complex gene networks.

Results: We describe how deviations from orthogonality arise in currently used methods. We demonstrate one option for obtaining orthogonal estimates of genetic effects using multiple imputations per individual in an otherwise unchanged regression context. Our proposed IRIM method avoids inflated values for explainable variance and genetic effect variables, while showing a clear preference for marker locations in a fine mapping context. Despite possible shortcomings, similar results to linear regression are demonstrated for our proposed approach (IRIM) in an experimental dataset.

Conclusions: Imputation-based methods can be used to enhance the statistical dissectability of effects, as well as computational performance. We exemplify how Haley-Knott regression is not only distorting the explainable variance, but also point out how the estimated phenotype values between classes, and the resulting effects, become dependent. This illustrates the need for a more radical departure in the approach chosen in order to achieve orthogonality.

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