A model selection approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis - PubMed (original) (raw)

A model selection approach for the identification of quantitative trait loci in experimental crosses, allowing epistasis

Ani Manichaikul et al. Genetics. 2009 Mar.

Erratum in

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.

PubMed Disclaimer

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 S

ugiyama

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 S

ugiyama

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 S

mith

R

ichards

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 S

mith

R

ichards

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

Cited by

References

    1. Akaike, H., 1969. Fitting autoregressive models for prediction. Ann. Inst. Stat. Math. 21 243–247.
    1. Baierl, A., M. Bogdan, F. Frommlet and A. Futschik, 2006. On locating multiple interacting quantitative trait loci in intercross designs. Genetics 173 1693–1703. - PMC - PubMed
    1. Ball, R. D., 2001. Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion. Genetics 159 1351–1364. - PMC - PubMed
    1. Boer, M. P., C. J. Ter Braak and R. C. Jansen, 2002. A penalized likelihood method for mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics 162 951–960. - PMC - PubMed
    1. Bogdan, M., J. K. Ghosh and R. W. Doerge, 2004. Modifying the Schwarz Bayesian information criterion to locate multiple interacting quantitative trait loci. Genetics 167 989–999. - PMC - PubMed

Publication types

MeSH terms

Grants and funding

LinkOut - more resources