Assessment of PGS×Environment Interactions

To detect deviations in the prevalence–risk relationship across environments, we compared the shapes of the prevalence–risk curves, given that the underlying PGS have essentially a similar distribution in both environments. For each of the 151 environmental exposures, dichotomized into low and high groups, the prevalence of disease versus percentile PGS plots were generated. Next, the difference between the prevalence of the high and low curves (H-L) along the polygenic risk gradient was computed. A monotonically increasing trend of the (H-L) curve would indicate the case of decanalization, implying that as the genetic risk increases, the impact on disease increases and more so in the bad exposure environment. Conversely, a constant (H-L) curve along the risk gradient would imply that the curves are simply shifted, and there is no observed decanalization. For consistency, high in all cases was defined simply as the environment with the elevated risk overall and is not taken to imply that one or the other exposure is intrinsically high risk. This occasionally leads to counterintuitive results where the inference of canalization or decanalization is flipped (note that decanalization with respect to one exposure is canalization with respect to the other). A notable example is Townsend Deprivation Index with College Attainment, where the H exposure is low TDI since it has a very slightly elevated prevalence of CA, and hence canalization is reported in fig. 7 and supplementary figs. 4, 5, 6, 9, and 10, Supplementary Material online, yet intuitively since high TDI is the poor socioeconomic exposure, this is discussed as a case of decanalization in supplementary fig. S2, Supplementary Material online and the text.

To evaluate this phenomenon quantitatively, permutation analysis was performed by randomly selecting individuals to high or low exposure groups, keeping the sample size of the high and low groups the same as the real data in the UKB (as given in supplementary table S4, Supplementary Material online). The prevalence versus percentile plots were generated for the randomly selected individuals, and H-L curves were computed. In general, the H-L curve from random permutations should follow a nonmonotonic trend around zero. Therefore, to establish the evidence of interactions, the following conditions were required. (1) The derivative of the H-L curve be consistently either greater or lesser than 0, and the median of the derivative distribution is always higher than that generated from 100 random iterations. This ensures a significant monotonicity of the curve. (2) The absolute value of the linear slope of H-L curve (equivalent to the delta between the upper and lower tails) must be greater than that generated from 100 randomly permuted data. Once the evidence of interactions was established, its degree was defined as delta, the right versus left-tail deviation in prevalence at two SD units from the PGS mean (supplementary fig. S12, Supplementary Material online shows the departure of delta observed from delta expected for 151 exposures and all binary traits summarized, where a positive departure represents decanalization and a negative departure represent canalization. The dashed lines are at +/− 2 SD units and +/− 1.3 SD units indicating conservative and suggestive thresholds respectively). More details of this and subsequent methods are provided on our Shiny app.