As discussed earlier, a nonlinear relation between X1 and Y can lead to bias in estimating the cross-over point. As a preliminary analysis, we regressed Y on the linear, quadratic, and cubic trends of X1 for each of the two groups. Using hierarchical testing, the quadratic and cubic trends had F-ratios of 0.13 and 0.02, respectively, for the DRD4 low-risk group, and F-ratios of 0.83 and 0.01, respectively, for the DRD4 high-risk group. These results suggest the absence of nonlinearities that might bias estimation of the cross-over point under a linear specification.
