Extended Data Fig. 7 ∣. Relationship between effective sample size and prediction accuracy.

a, This figure shows the relationship between the ratio of effective sample sizes between the full cohort (N_FC) and down-sampled (N_DS) data for each definition of depression and the ratio of their mean Chi-square (χ²) statistic from GWAS, with black line x = y for reference. Across all definitions of depression, $\frac{\overline{{\chi }_{FC}^2}-1}{\overline{{\chi }_{DS}^2}-1}$ is highly correlated with $\frac{N_{FC}}{N_{DS}}$ (Pearson r² = 0.999, P = 5.50×10⁻⁷), and $\frac{N_{FC}}{N_{DS}}$ has an effect of beta = 1.27 (s.e. = 0.02) on $\frac{\overline{{\chi }_{FC}^2}-1}{\overline{{\chi }_{DS}^2}-1}$. b, This figure shows the Nagelkerke’s r² (Nkr2) for MDD status in PGC29 cohorts predicted for PRS of different definitions of depression at N_FC, plotted against their respective empirical Nkr2 at N_FC, both at P-value threshold = 1. The Pearson correlation r² between predicted and actual NKr2 across all definitions were 0.989 (P = 4.46×10⁻⁵). c, This figure shows for each definition of depression the effective sample size N_X required for each predicted Nkr2 in out-of-sample prediction of MDD status in PGC29 cohorts. While N_x= 274,677 (indicated with orange vertical dotted line) for GPpsy to achieve a Nkr2 of 0.0172 (indicated with orange horizontal dotted line), a smaller N_x= 129,106 (indicated with pink vertical dotted line) is needed to achieve the same Nkr2 for LifetimeMDD.