Figure 2 presents the Manhattan and QQ plots of p values for the GxE parameter estimate from the GWGEI models (b3 in Eq. (2)). Manhattan plots efficiently summarize the vast amount of information from GWAS results because they indicate the chromosomal location (the x-axis) and the magnitude of the p value (the y-axis). Together with a QQ plot, the Manhattan plot enables an assessment of the significance and meaning of results from hundreds of thousands of regression models. For a trait like human height (see, e.g., Weedon et al. 2008), with sufficient sample size the Manhattan plot contains many loci with p values that exceed genome-wide significance, and the SNPs will tend to cluster together in similar regions across the genome. Similarly, the QQ plot will conform to the uniform distribution until the right tail, in which there is typically a notable upward departure. Neither association is evident in the plots in Fig. 2. No SNP approaches genome-wide significance; our smallest observed p value is only 5.8E–06. This is also shown in the QQ plot, in which deviation from uniform
