In Add Health and COGA, the phenotypic externalizing factor corresponding to the seven discovery phenotypes (see above) was regressed on the genome-wide EXT polygenic scores in a within-family model (Supplementary Table 33). Parameter estimates from the within-family model (βWF Add Health = 0.12, 95% CI: 0.04–0.20; βWF COGA = 0.14, 95% CI: 0.08–0.20) were smaller compared to OLS models without family-specific intercepts (βAdd Health = 0.20, 95% CI, 0.16 to 0.24; βCOGA = 0.16, 95% CI, 0.12 to 0.20), but remained statistically significant (Add Health two-sided P = 4.89×10−3; COGA two-sided test P = 1.87×10−6). As a formal test of attenuation, we evaluated the standardized difference between βWF and β (i.e., a Z-statistic assumed to be normally distributed, see Supplementary Information section 5.2.6) and found that it was −1.988 (two-sided P = 0.047) and −0.704 (two-sided P = 0.481) for the PRS-CS polygenic score in Add Health and COGA, respectively. Thus, we conclude that there was some, but not extreme, attenuation when predicting the phenotypic externalizing factor within families. Also, the association of the quasi-replication polygenic score constructed with the
