Guidelines for Evaluating the Comparability of Down-Sampled GWAS Summary Statistics.

LD Score genetic correlations and heritability estimates for the seven indicator phenotypes of the single-factor models of EXT and EXT-minus-23andMe (see Step 1). The left panel displays the analysis of the original study with 23andMe data, the middle panel displays the down-sampled analysis excluding 23andMe data, and the right panel displays the difference in estimates computed by subtracting the values in the middle panel from those in the left panel. The lower and upper triangles display pairwise genetic correlation (rg) estimates and standard errors, respectively. The diagonals display the observed-scale heritability (h2; see Table 1 for standard errors). These results are also reported in Table S1. ADHD attention-deficit/hyperactivity disorder; ALCP problematic alcohol use; CANN lifetime cannabis use; FSEX age at first sexual intercourse (reverse coded); NSEX number of sexual partners; RISK risk tolerance; SMOK lifetime tobacco initiation

Path diagram of a single-factor model with seven indicator phenotypes, of which SMOK and CANN are down-sampled, as estimated with Genomic SEM. These results are also reported in Table S2. Neither the factor loadings nor residual variances were statistically different from the original estimates (a path diagram of the original estimates was therefore omitted). The same figure displaying the results of the original study is available here: https://www.nature.com/articles/s41593-021-00908-3/figures/1. EXT-minus-23andMe genetic externalizing factor; ADHD attention-deficit/hyperactivity disorder; ALCP problematic alcohol use; CANN lifetime cannabis use; FSEX age at first sexual intercourse (reverse coded); NSEX number of sexual partners; RISK risk tolerance; SMOK lifetime tobacco initiation; AIC Akaike Information Criterion; CFI comparative fit index; SRMR standardized root mean square residual

Scatterplot of genetic correlations (rg) and marginal density plots between EXT (y-axis) or EXT-minus-23andMe (x-axis) with 77 other phenotypes. Each point corresponds to the genetic correlation coefficient with its 95% confidence intervals (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{g}\pm 1.96\times SE$$\end{document}rg±1.96×SE) estimated with bivariate LD Score regression. Table S5 reports the estimates, their standard errors, and confidence intervals. The Spearman rank correlation reported in the figure is rounded from r = 0.9995. No particular shape, such as a normal distribution, is expected for the marginal density because the figure displays an arbitrary selection of traits

Comparison of the down-sampled polygenic score (PGS) analyses in Add Health (29 phenotypes) and the Collaborative Study on the Genetics of Alcoholism (COGA; 26 phenotypes). Panel A displays the standardized difference between the coefficient estimates (i.e., a Z-statistic) of the down-sampled PGS for EXT-minus-23andMe versus the PGS for EXT from the original study. Absolute values were evaluated so that a negative standardized difference refers to an attenuation towards zero in the down-sampled analysis. Panel B displays the same measure but as a histogram. Four coefficient estimates were significantly (at the 5% level) attenuated in the down-sampled analysis: lifetime smoking initiation (Add Health and COGA; P = 3.18 × 10–5 and 4.17 × 10–5, respectively), the phenotypic externalizing factor (Add Health; P = 0.046), and lifetime cannabis use (Add Health, P = 0.03). None of the coefficients were significantly larger in the down-sampled analysis. Panel C displays a scatter plot of the absolute value of the coefficient estimates divided by their respective standard errors (i.e., a Z-statistic). These results are also reported in Table S6