Interval Mapping Of Quantitative Trait Loci With Interaction Effects

In bio-Statistics,A variety of statistical methods can be applied to locating quantitativetrait loci(QTL). The QTL problem with multiple interacting is more often thanthat is without interacting. The trait of this problem is that the the number of QTL issmall, and the sample size is not large, and the number of loci is much more than thatof the true QTL. This is actually the variable selection problem in statistics.In previous work, a modified Bayesian Information Criteria and forward selectionmethod is applied to locating multiple interacting QTL. In this article, we suggestthat we use an path algorithm based on L1 regularization for generalized linear modelinstead of forward selection algorithm. This algorithm based on L1 norm is with iterationactually. It repeat the procedure of predict-correct step based on generalized linearmodel until the result is stable.Also, we replace the original BIC with the eBIC(Extended Bayesian InformationCriteria), because the original BIC has a tendency to include some extraneous covariates.The eBIC, which adds a penalty item in the definition of the original BIC, hasa tendency to exclude much more covariates than the original BIC. It is particularlyuseful for this QTL mapping problem. And the condition for consistency and identifiabilityof eBIC is weak, too.In the mean time, we applied our statistic technique based on the ranks of thedependent variables.The new method not only has better properties theoretically, but also performmuch better in stimulation studies and, especially when the sample size is not large.Besides, we use FDR(False Discover Rate) and PSR(Positive Selection Ratio)as the statistic standard to measure the efficiency and power of different methods,comparing with others who only use FDR. And we discuss the results later.