Figure 1

Power and Significance levels for NPBAT, the Improved Score Test and the Likelihood Ratio Test (LRT). This plot compares the power and type-1 error rate of the NPBAT method using E _x based on the sample mean of the cases, the controls and both the cases and controls. The power and significance levels of this method is compared to the improved score test and a standard linear regression. Note that the spike or drop in all the plots occurs where $Y_{\text{offset}}\approx \bar{Y}$, the sample mean of the secondary phenotype for the cases since the secondary phenotype is not available for the controls in this scenario. The power of the NPBAT approach is maximized when E _x is based on the genotype of the controls and Y_offset is significantly different than the phenotypic mean of the cases. When E _x is based on the genotype of the cases, the power of the NPBAT approach is similar to the improved score test and the regression. Note that the power of NPBAT approach when E _x is based on the genotype of both the cases and the controls is best for high values of heritability.