Table 3.
Results of the OLS and IV regressions explaining (residualized and standardized) height
| OLS | OLS | OLS | ORIV | ORIV | PGI-RC | PGI-RC | |
|---|---|---|---|---|---|---|---|
| (UKB) | (GIANT) | (Meta-analysis) | (2-sample) | (Split-sample) | (default) | (GREML unc.) | |
| Between-family results | |||||||
| Polygenic index | 0.579*** | 0.450*** | 0.583*** | 0.652*** | 0.625*** | 0.728*** | 0.728*** |
| (0.005) | (0.005) | (0.005) | (0.006) | (0.006) | (0.006) | (0.014) | |
| First-stage estimate | 0.622*** | 0.586*** | |||||
| (0.004) | (0.004) | ||||||
| First-stage F-statistic | 27,261 | 20,792 | |||||
| Incremental R2 | 33.5% | 20.3% | 34.0% | ||||
| Family fixed effects | NO | NO | NO | NO | NO | NO | NO |
| N | 35,282 | 35,282 | 35,282 | 35,282 | 35,282 | 35,282 | 35,282 |
| Within-family results | |||||||
| Polygenic index | 0.521*** | 0.415*** | 0.537*** | 0.614*** | 0.571*** | ||
| (0.007) | (0.007) | (0.007) | (0.008) | (0.009) | |||
| First-stage estimate | 0.600*** | 0.558*** | |||||
| (0.005) | (0.005) | ||||||
| First-stage F-statistic | 15,735 | 11,150 | |||||
| Incremental R2 | 27.1% | 17.2% | 28.9% | ||||
| Family fixed effects | YES | YES | YES | YES | YES | ||
| N | 35,282 | 35,282 | 35,282 | 35,282 | 35,282 | ||
Notes: *p value < 0.10; **p value < 0.05; ***p value < 0.01 of a two-sided t test (OLS, PGI-RC) or two-sided z-test (ORIV) without adjustments for multiple comparisons. In all regressions the dependent variable is residualized height (standardized to have mean 0 and standard deviation 1), where the residuals are obtained after a regression of height on controlling for sex, year of birth, month of birth, sex interacted with year of birth, and the first 40 principal components of the genetic relationship matrix. Standard errors are robust and clustered at the family level, and in case of ORIV also at the individual level. OLS (UKB) refers to the model with the PGI constructed using the UKB non-sibling (i.e., excluding all siblings and their relatives) sample. OLS (GIANT) refers to the model with the PGI constructed using the GIANT summary statistics. OLS (Meta-analysis) uses a PGI constructed using a meta-analysis of GWAS summary statistics of the UKB non-sibling sample and the GIANT sample. ORIV (2-sample) refers to a 2SLS estimation using the PGIs from the UKB non-sibling sample and Giant as instrumental variables for each other. ORIV (Split-sample) refers to a 2SLS estimation where the summary statistics derive from a random split of the UKB sample. PGI-RC refers to the PGI repository correction, where (default) refers to the conventional application of the method, whereas (GREML unc.) refers to the case where we incorporate the uncertainty in the estimation of the SNP-based heritability.