Score Statistics for Mapping Quantitative Trait Loci

We propose a method to detect the existence of quantitative trait loci (QTL) in a backcross population using a score test. Since the score test only uses the MLEs of parameters under the null hypothesis, it is computationally simpler than the likelihood ratio test (LRT). Moreover, because the location parameter of the QTL is unidentifiable under the null hypothesis, the distribution of the maximum of the LRT statistics, typically the statistic of choice for testing H0: no QTL, does not have the standard chi-square distribution asymptotically under the null hypothesis. From the simple structure of the score test statistics, the asymptotic null distribution can be derived for the maximum of the square of score test statistics. Numerical methods are proposed to compute the asymptotic null distribution and the critical thresholds can be obtained accordingly. We show that the maximum of the LR test statistics and the maximum of the square of score statistics are asymptotically equivalent. Therefore, the critical threshold for the score test can be used for the LR test also. A simple backcross design is used to demonstrate the application of the score test to QTL mapping.