Table 3  Mean, standard deviation, and root mean squared error of the genome scan peak in simulations using our method and that of Yap et al. (2009)
Yap (nonpara)Yap (autoreg)EE (Wald)EE (residual)
CovariancenMeanSDrmseMeanSDrmseMeanSDrmseMeanSDrmse
Σ110032.89.99.933.27.77.833.010.410.532.89.099.1
40031.52.82.831.83.23.232.12.92.932.12.92.9
Σ210032.67.67.635.315.716.032.77.77.733.112.012.0
40031.72.62.632.05.45.432.12.42.432.23.73.7
Σ310033.222.222.246.527.431.040.626.527.939.325.326.3
40032.311.911.943.626.428.933.110.810.933.110.710.8
  • The true QTL is at 32 cM. The columns labeled “Yap (nonpara)” and “Yap (autoreg)” are derived from Tables 1 and 2 of Yap et al. (2009). They refer to the results of using the likeihood-based methods of Yap et al. (2009) with an estimated regularized covariance and autocorrelated covariance, respectively. The columns labeled “EE (Wald)” and “EE (residual)” refer to our estimating equations approach with the Wald statistic and the residual error statistic, respectively. Yap et al. (2009) performed 100 simulation replicates, whereas we used 10,000 replicates, which gave stable estimates. For each method we report the mean position of the genome scan maximum (“mean”) over simulation replicates, the standard deviation (“SD”), and the root mean squared error (“rmse”). Note that Yap et al. (2009) reported standard error, which we converted to standard deviation as the latter is independent of the number of simulation replicates. The simulations were performed with three error structures corresponding to an autocorrelated covariance (Σ1), an equicorrelated covariance (Σ2), and an unstructured covariance (Σ3).