Age at menarche and risk of metabolic syndrome.

Age at menarche and risk of metabolic syndrome.</p

Metabolic parameters of study participants by age at menarche.

Metabolic parameters of study participants by age at menarche.</p

Baseline characteristics of study participants by age at menarche.

Baseline characteristics of study participants by age at menarche.</p

Age at menarche and risk of diabetes mellitus.

Age at menarche and risk of diabetes mellitus.</p

Image1_Investigation of heteroscedasticity in polygenic risk scores across 15 quantitative traits.pdf

The polygenic risk score (PRS) could be used to stratify individuals with high risk of diseases and predict complex trait of individual in a population. Previous studies developed a PRS-based prediction model using linear regression and evaluated the predictive performance of the model using the R2 value. One of the key assumptions of linear regression is that the variance of the residual should be constant at each level of the predictor variables, called homoscedasticity. However, some studies show that PRS models exhibit heteroscedasticity between PRS and traits. This study analyzes whether heteroscedasticity exists in PRS models of diverse disease-related traits and, if any, it affects the accuracy of PRS-based prediction in 354,761 Europeans from the UK Biobank. We constructed PRSs for 15 quantitative traits using LDpred2 and estimated the existence of heteroscedasticity between PRSs and 15 traits using three different tests of the Breusch-Pagan (BP) test, score test, and F test. Thirteen out of fifteen traits show significant heteroscedasticity. Further replication using new PRSs from the PGS catalog and independent samples (N = 23,620) from the UK Biobank confirmed the heteroscedasticity in ten traits. As a result, ten out of fifteen quantitative traits show statistically significant heteroscedasticity between the PRS and each trait. There was a greater variance of residuals as PRS increased, and the prediction accuracy at each level of PRS tended to decrease as the variance of residuals increased. In conclusion, heteroscedasticity was frequently observed in the PRS-based prediction models of quantitative traits, and the accuracy of the predictive model may differ according to PRS values. Therefore, prediction models using the PRS should be constructed by considering heteroscedasticity.</p

Table1_Investigation of heteroscedasticity in polygenic risk scores across 15 quantitative traits.xlsx

The polygenic risk score (PRS) could be used to stratify individuals with high risk of diseases and predict complex trait of individual in a population. Previous studies developed a PRS-based prediction model using linear regression and evaluated the predictive performance of the model using the R2 value. One of the key assumptions of linear regression is that the variance of the residual should be constant at each level of the predictor variables, called homoscedasticity. However, some studies show that PRS models exhibit heteroscedasticity between PRS and traits. This study analyzes whether heteroscedasticity exists in PRS models of diverse disease-related traits and, if any, it affects the accuracy of PRS-based prediction in 354,761 Europeans from the UK Biobank. We constructed PRSs for 15 quantitative traits using LDpred2 and estimated the existence of heteroscedasticity between PRSs and 15 traits using three different tests of the Breusch-Pagan (BP) test, score test, and F test. Thirteen out of fifteen traits show significant heteroscedasticity. Further replication using new PRSs from the PGS catalog and independent samples (N = 23,620) from the UK Biobank confirmed the heteroscedasticity in ten traits. As a result, ten out of fifteen quantitative traits show statistically significant heteroscedasticity between the PRS and each trait. There was a greater variance of residuals as PRS increased, and the prediction accuracy at each level of PRS tended to decrease as the variance of residuals increased. In conclusion, heteroscedasticity was frequently observed in the PRS-based prediction models of quantitative traits, and the accuracy of the predictive model may differ according to PRS values. Therefore, prediction models using the PRS should be constructed by considering heteroscedasticity.</p

High birefringent reactive discotic liquid crystals based on asymmetrical triphenylene with phenyl-acetylene moieties

<p>Triphenylene (TP)-based liquid crystals, a category of discotic liquid crystals (DLCs), are easy to synthesise, thermally stable and can undergo self-assembly. A new DLC compound, 2,7,10-tris[4-(6-acryloyloxyhexyloxy)benzoate]-3,6,11-tris[(4-hexylphenyl)ethynyl]-triphenylene, was obtained with a 49% yield using catechol as a starting material and features acetylene groups on its TP core. This material can form films with high birefringence through its cross-linkable acrylate ends. Here, we synthesised this new compound and characterised it using nuclear magnetic resonance spectroscopy, mass spectrometry and elemental analysis. The thermal behaviour was also investigated using differential scanning calorimetry and polarised optical microscopy. This new asymmetric TP-based DLC compound exhibited a nematic liquid-crystalline phase between −20 and 170°C and formed an optical anisotropic film with a high birefringence (Δ<i>n</i> = 0.21–0.25).</p

Additional file 1 of Identification of asthma-related genes using asthmatic blood eQTLs of Korean patients

Additional file 1: Table S1. Results of cis-eQTLs in 433 Korean patients with asthma