Mapping multiple quantitative trait loci under Bayes error control

In mapping of quantitative trait loci (QTLs), performing hypothesis tests of linkage to a phenotype of interest across an entire genome involves multiple comparisons. Furthermore, linkage among loci induces correlation among tests. Under many multiple comparison frameworks, these problems are exacerbated when mapping multiple QTLs. Traditionally, significance thresholds have been subjectively set to control the probability of detecting at least one false positive outcome, although such thresholds are known to result in excessively low power to detect true positive outcomes. Recently, false discovery rate (FDR)-controlling procedures have been developed that yield more power both by relaxing the stringency of the significance threshold and by retaining more power for a given significance threshold. However, these procedures have been shown to perform poorly for mapping QTLs, principally because they ignore recombination fractions between markers. Here, I describe a procedure that accounts for recombination fractions and extends FDR control to include simultaneous control of the false non-discovery rate, i.e. the overall error rate is controlled. This procedure is developed in the Bayesian framework using a direct posterior probability approach. Data-driven significance thresholds are determined by minimizing the expected loss. The procedure is equivalent to jointly maximizing positive and negative predictive values. In the context of mapping QTLs for experimental crosses, the procedure is applicable to mapping main effects, gene-gene interactions and gene-environment interactions.