To compare the direct effect of the PGI on various phenotypes to its population effect, we used data on siblings and trios from UKB3 (link), GS7 (link), and STR38 (link). In both UKB and GS, first-degree relatives were identified using KING with the “--related --degree 1” option72 . For parent-offspring relations, the parent was identified as the older individual in the pair. We removed 621 individuals from GS that had been previously identified by GS as being also present in UKB (Supplementary Note section 7.3).
We analyzed PGIs for EA and cognitive performance in all three samples, and height and BMI only in UKB and GS. PGIs were made using GWAS results that exclude GS, STR and all related individuals of up to third degree from UKB (Supplementary Note section 7.3), following the LDpred PGI pipeline described in Supplementary Note section 5.1.
We selected 23 phenotypes related to education, cognition, income, and health (Supplementary Table 9) available in at least one of the datasets. For each phenotype in each dataset, we first regressed the phenotype onto sex and age, age2 (link), and age3 (link), and their interactions with sex. In addition, for UKB, we included as covariates the top 40 genetic PCs provided by UKB and the genotyping array dummies3 (link). For GS and STR, we included the top 20 genetic PCs (see Supplementary Note section 5.3 for how the PCs were created). We then took the residuals from the regression of the phenotype on the covariates and normalized the residuals’ variance within each sex separately, so that the phenotypic residual variance was 1 in each sex in the combined sample of siblings and individuals with both parents genotyped. The PGIs of the phenotyped individuals were also normalized to have variance 1 in the same sample. Thus, effect estimates correspond to (partial) correlations, and their squares to proportions of phenotypic variance explained.
We give an overview of the statistical analyses performed here, with details in Supplementary Note section 7.4. In the siblings, we regressed individuals’ phenotypes onto the difference between the individual’s PGI and the mean PGI among the siblings in that individual’s family, and the mean PGI among siblings in that family. In trios, we regressed phenotypes onto the individual’s PGI and the individual’s father’s and mother’s PGIs. In both the siblings and trios, we used a linear mixed model to account for relatedness in the samples. We meta-analyzed the results from the siblings and trios, accounting for covariance between the estimates from the sibling and trio samples from the same datasets. We applied a transformation to the meta-analysis that accounts for assortative mating to estimate the population effect of the PGI and the difference between the direct and population effects.