Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2009 Mar;181(3):1077-86.
doi: 10.1534/genetics.108.094565. Epub 2008 Dec 22.

A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses, Allowing Epistasis

Affiliations
Free PMC article

A Model Selection Approach for the Identification of Quantitative Trait Loci in Experimental Crosses, Allowing Epistasis

Ani Manichaikul et al. Genetics. .
Free PMC article

Erratum in

  • Genetics. 2010 Feb;184(2):607

Abstract

The identification of quantitative trait loci (QTL) and their interactions is a crucial step toward the discovery of genes responsible for variation in experimental crosses. The problem is best viewed as one of model selection, and the most important aspect of the problem is the comparison of models of different sizes. We present a penalized likelihood approach, with penalties on QTL and pairwise interactions chosen to control false positive rates. This extends the work of Broman and Speed to allow for pairwise interactions among QTL. A conservative version of our penalized LOD score provides strict control over the rate of extraneous QTL and interactions; a more liberal criterion is more lenient on interactions but seeks to maintain control over the rate of inclusion of false loci. The key advance is that one needs only to specify a target false positive rate rather than a prior on the number of QTL and interactions. We illustrate the use of our model selection criteria as exploratory tools; simulation studies demonstrate reasonable power to detect QTL. Our liberal criterion is comparable in power to two Bayesian approaches.

Figures

F<sc>igure</sc> 1.—
Figure 1.—
Example graphical representations of QTL models. Nodes represent QTL and edges represent pairwise interactions. (A) A model containing two QTL and their interaction. (B) A model containing three QTL and two pairwise interactions. (C) A model containing three QTL and all possible pairwise interactions. (D) A model containing seven QTL, with one central locus interacting with the other six.
F<sc>igure</sc> 2.—
Figure 2.—
The final model for hypertension data in Sugiyama et al. (2001) contained a pair of QTL on chromosome 1, unlinked QTL on chromosomes 4 and 5, and a pair of interacting QTL on chromosomes 6 and 15 (solid line). We explored the possibility of additional interactions between QTL in the original model of Sugiyama et al. (2001) and also considered additional QTL on chromosomes 2, 4, and 5, with possible interactions involving these loci (dashed lines). Each new model term is annotated with its corresponding contribution to the model LOD score. For example, an interaction between model terms 1b and 5a increased the model LOD score by 0.76 compared to the original model.
F<sc>igure</sc> 3.—
Figure 3.—
Estimated error rates for intercross simulations under a model based on data from Smith Richards et al. (2002). Plots display observed distribution summaries of (A) the number of extraneous main effects, (B) the number of extraneous interactions, (C) the number of interactions associated with extraneous main effects, and (D) the probability of one or more extraneous unlinked terms as a function of the number of correct main effects, shown only when at least 30 simulation replicates had the specified number of correct main effects using a given method. Ninety-five percent confidence intervals in D are obtained by inverting an exact binomial test. Results are shown for pLODL (solid black circle), pLODH (solid red square), pLODa (solid blue triangle), Bayes (open black diamond), mBIC2 (open black circle), and mBIC1 (open red square).
F<sc>igure</sc> 4.—
Figure 4.—
Estimated power to detect true QTL in intercross simulations under a model based on data from Smith Richards et al. (2002). Plots display (A) the power to detect each individual model term, (B) the heritability of the QTL main effects and interactions, (C) the root mean squared error of the estimated positions among correctly identified QTL, and (D) the observed distribution of the number of correct main effects identified in each simulation replicate. A, C, and D show results for pLODL (solid black circle), pLODH (solid red square), pLODa (solid blue triangle), Bayes (open black diamond), mBIC2 (open black circle), and mBIC1 (open red square).

Similar articles

See all similar articles

Cited by 74 articles

See all "Cited by" articles

Publication types

LinkOut - more resources

Feedback