Fig. 2.

Simulation results. Panel a shows the probability of a significant p-value as a function of the p-value threshold of each method for the null setting β _m=β _x=β _y=0 with n=100 subjects. The legend of line color and styles indicate results for the indicated methods and provide the result for the p-value threshold 0.01. The same line colors and styles are used in the other three panels. Panel b shows similar results for the non-null setting β _m=β _x=β _y=0.5 and sample size n=100. Panel c shows the observed type I error rate for the methods with p-value threshold 0.01 across all 100 null settings with β _y=0 indicating the endpoints have no association with the molecular data. Panel d shows the statistical power of the methods with adequate type I error rate control for the 400 non-null settings with β _y≠0 indicating that the endpoints are associated with at least one element of the molecular data