## 3 Results  
### Linkage Disequilibrium Score Regression (LDSC) and K-Means Clustering  
Figure 1 shows the genetic correlation matrix between psychiatric disorders, cardiometabolic and sleep traits. A total of 20 genetic correlations between psychiatric disorders and cardiometabolic traits (Table 1) and 11 between psychiatric disorders and sleep traits (Table 2) were significant after multiple testing correction. Significant correlations between cardiometabolic and sleep traits, or between psychiatric disorders, are reported in Table S2. We observed significant positive correlations between BMI or CRP levels and MDD, ADHD or PTSD. Conversely, BMI and CRP levels were negatively correlated with increased predisposition to SCZ, OCD and AN (Table 1). T2D was positively associated with increased predisposition to MDD, PTSD and ADHD, and negatively associated with predisposition to AN and OCD. Finally, CAD was positively associated with MDD, PTSD and ADHD (Table 1). As regards to sleep traits, BD, MDD, ADHD, and PTSD showed positive genetic correlation with insomnia with \(r_{g}\) ranging from 0.11 to 0.48 (Table 2). Several psychiatric disorders were associated with sleep duration, though in different directions: BD and SCZ \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Psychiatric Trait** & **Cardiometabolic Trait** & \(r_{g}\) & **se** & **Z** & \(p\) & **adj**\(p\)** \\ \hline SCZ & BMI & \(-0.10\) & 0.01 & \(-7.07\) & \(1.6\times 10^{-12}\) & \(1.9\times 10^{-10}\) \\ SCZ & CRP & \(-0.06\) & 0.02 & \(-3.75\) & \(0.002\) & \(0.02\) \\ MDD & BMI & 0.11 & 0.02 & 6.55 & \(5.6\times 10^{-11}\) & \(6.8\times 10^{-9}\) \\ MDD & CAD & 0.21 & 0.02 & 10.33 & \(5.1\times 10^{-25}\) & \(6.1\times 10^{-23}\) \\ MDD & CRP & 0.11 & 0.02 & 5.50 & \(3.8\times 10^{-8}\) & \(4.6\times 10^{-6}\) \\ MDD & T2D & 0.14 & 0.02 & 6.58 & \(4.8\times 10^{-11}\) & \(5.8\times 10^{-9}\) \\ PTSD & BMI & 0.32 & 0.04 & 7.77 & \(8.1\times 10^{-15}\) & \(9.7\times 10^{-13}\) \\ PTSD & CAD & 0.30 & 0.05 & 6.06 & \(6.5\times 10^{-7}\) & \(7.7\times 10^{-5}\) \\ PTSD & CRP & 0.21 & 0.04 & 4.98 & \(1.4\times 10^{-9}\) & \(1.7\times 10^{-7}\) \\ PTSD & T2D & 0.25 & 0.05 & 5.21 & \(1.9\times 10^{-7}\) & \(2.2\times 10^{-5}\) \\ AN & BMI & \(-0.31\) & 0.02 & \(-13.52\) & \(1.3\times 10^{-41}\) & \(1.5\times 10^{-39}\) \\ AN & CRP & \(-0.28\) & 0.03 & \(-9.28\) & \(1.7\times 10^{-20}\) & \(2.1\times 10^{-18}\) \\ AN & T2D & \(-0.20\) & 0.03 & \(-7.37\) & \(1.8\times 10^{-13}\) & \(2.1\times 10^{-11}\) \\ ADHD & BMI & 0.35 & 0.02 & 14.65 & \(1.4\times 10^{-48}\) & \(1.7\times 10^{-46}\) \\ ADHD & CAD & 0.27 & 0.03 & 9.86 & \(1.4\times 10^{-16}\) & \(1.6\times 10^{-14}\) \\ ADHD & CRP & 0.30 & 0.04 & 8.27 & \(5.9\times 10^{-23}\) & \(7.1\times 10^{-21}\) \\ ADHD & T2D & 0.32 & 0.03 & 12.16 & \(5.0\times 10^{-34}\) & \(6.0\times 10^{-32}\) \\ OCD & BMI & \(-0.29\) & 0.04 & \(-6.97\) & \(3.2\times 10^{-12}\) & \(3.8\times 10^{-10}\) \\ OCD & CRP & \(-0.22\) & 0.04 & \(-5.39\) & \(6.9\times 10^{-8}\) & \(8.3\times 10^{-6}\) \\ OCD & T2D & \(-0.17\) & 0.04 & \(-3.81\) & 0.0001 & 0.02 \\ \hline \hline \end{tabular} Abbreviations: ADHD, attention deficit/hyperactivity disorder; AN, anorexia nervosa; ASD, autism spectrum disorders; BD, bipolar disorder; BMI, body mass index; CAD, coronary artery disease; CRP, C-reactive protein; MDD, major depressive disorder; OCD, obsessive-compulsive disorder; SCZ, schizophrenia; se, standard error; PTSD, post-traumatic stress disorder; T2D, type 2 diabetes. The adj \(p\) column reports \(p\)-values adjusted according to Bonferroni based on the number of conducted tests (n = 120).  
\end{table} 
Table 1: Significant genetic correlations between psychiatric and cardiometabolic traits. Figure 1: Genetic correlation matrix of psychiatric disorders, cardiometabolic and sleep traits. The size of each circle corresponds to the strength of the relationship between pairs of traits based on the computed \(r_{g}\). The color of the circle indicates a positive (blue) or negative (red) correlation.