Locating multiple interacting quantitative trait Loci using rank-based model selection

Abstract

In previous work, a modified version of the Bayesian information criterion (mBIC) was proposed to locate multiple interacting quantitative trait loci (QTL). Simulation studies and real data analysis demonstrate good properties of the mBIC in situations where the error distribution is approximately normal. However, as with other standard techniques of QTL mapping, the performance of the mBIC strongly deteriorates when the trait distribution is heavy tailed or when the data contain a significant proportion of outliers. In the present article, we propose a suitable robust version of the mBIC that is based on ranks. We investigate the properties of the resulting method on the basis of theoretical calculations, computer simulations, and a real data analysis. Our simulation results show that for the sample sizes typically used in QTL mapping, the methods based on ranks are almost as efficient as standard techniques when the data are normal and are much better when the data come from some heavy-tailed distribution or include a proportion of outliers.

Figure 1.—

Summary of simulation setup 2. The marker locations and imputed positions are indicated by long and short vertical bars, respectively. QTL are indicated by ×'s. The exact positions and effect sizes are given in the Simulations section.

Figure 2.—

Percentage of correctly identified main and epistatic effects taken from Baierl et al. (2007) (shaded bars) and for the rank-based method (horizontal solid lines).

Figure 3.—

False discovery rates from Baierl et al. (2007) (shaded bars) and for the rank-based method (horizontal solid lines).

Figure 4.—

Distribution of MidPC1 in the set of 203 individuals from the backcross B6 population.

Figure 5.—

Distribution of CecumPC1 in the set of 203 individuals from the backcross B6 population.

Figure 6.—

Absolute values of the t-test statistics vs. absolute values of the Wilcoxon statistics, for the 11 markers used in the analysis of the CecumPC1.