Height was normally distributed in both males (N
565) and females (N
739), and males (177.7±7.5 cm) were significantly taller than females (164.4±7.1 cm). Regression analysis showed that adult height was negatively associated with age in both genders with a larger age-effect in females. Estimated height decrease per year in females was 0.239 cm (P
28.0%) and in males was 0.195 cm (P
16.6%, Figure S1
Genetic scores based on the five published studies are shown in . The allele frequencies of the 180 genome-wide significant SNPs reported by Lango Allen et al. 
in our samples were similar to the original report (Figure S2
). The correlation of effect size estimates of these SNPs between our study and the original report (Stage 1+2) was highly significant although not perfect (Pearson ρ
). The effect size estimates of 58 SNPs were in different directions (points in the 2nd and 4th quadrants in ). After removing these 58 SNPs, Pearson's ρ increased to 0.851 for the remaining 122 SNPs. However, heterogeneity test did not show significant differences in estimates of effect sizes between our study and that of Lango Allen et al. 
. Though 12 of the 180 SNPs showed nominally significant heterogeneity (P<0.05) none survived adjustment for multiple testing (a full list of these 180 SNPs are provided in the Table S1
). As expected, based on the central limit theorem, the genetic scores were normally distributed (Figure S3
). The weighted genetic score and adjusted height were significantly (P<1×10−16
) correlated (). Combining the information from the 180 reference SNPs the explained variance was 7.94%, which was at the lower bound of the range of variance explained reported by Lango Allen et al. – 10.5% (range 7.9–11.2%) 
. As reflected in , the correlation of genetic score with adjusted height was higher in females than males with a larger fraction of variance explained (10.09% vs 5.87% in females and males respectively). The unweighted genetic scores explained a lower fraction (5.45%) of the overall variance.
Genetic scores based on different reference studies.
Effect size estimates of the 180 height SNPs were correlated between our study and the reference study by Lango Allele et al.
Correlation between height and weighted genetic scores in males and females.
The weighted genetic scores constructed using the SNPs and effect size estimates reported by the three Nature Genetics studies 
explained 3~4% of the height variance in our study sample. The study by Gudbjartsson et al. 
included an African American cohort (n
1,148) and the variance explained by the genetic scores built on the effect sizes estimated from this group was significantly smaller (P<0.001) than the scores based on the effect sizes estimated from other groups of European descent (Icelandic, Dutch or the Europeans Americans), which may reflect effect size differences among diverse populations.
In addition to testing height as a quantitative variable, Lettre et al. 
evaluated their identified SNPs in a height ‘case-control’ sample (the USHT tall-short panel with subjects selected from tails of the height distribution) and reported allelic effects using odds ratios (ORs). Our effect size estimates correlated well with the log transformed ORs (Pearson ρ
0.639) and the genetic scores weighted by these log transformed ORs explained even higher variance (4.62%) than the genetic scores weighted by the beta value estimates ().
In addition, we estimated the variance explained by the panel of 54 SNPs analyzed by Aulchenko et al. 
, which were identified by the three aforementioned GWAS 
. The weighted and unweighted genetic scores based on these 54 SNPs explained slightly larger variances than the scores based on any of the individual studies (). This study also reported genotypic effect sizes, which enabled us to construct weighted genotype scores without the assumption of allelic additivity, though the variance explained by this genotypic score was similar to that obtained by weighted genetic scores assuming additive allelic effects.
The reported height-associated SNPs that overlapped across studies may capture more genuine effects than those obtained from a single study. Therefore, we tested whether the variance explained can be increased by including multiple genetic scores as multi-dimensional predictors. By including the scores with largest variance explained from each study, the explained variance was increased to 10.21%.
We also performed genome-wide association analysis in order to replicate previous findings. As indicated by QQ-plots (Figure S4
), both GC and MG appropriately controlled type I error rates. The genome-wide single-locus test statistics were inflated compared to the null distribution with an estimated inflation factor λ
1.41. As expected this estimate was the highest among all metabolic traits we studied (unpublished data) since the inflation factor is larger for traits with higher heritability and substantial inflation is likely attributable to the large number of SNPs associated with height 
The P-values obtained by GC and MG were highly correlated (Pearson's ρ
0.766). Interestingly, the GC method recovered 9 previously known loci ( and Figure S5
) compared to 4 recovered by the MG approach, three of which were in the 9 GC regions. Due to our limited sample size, however, none of these loci reached genome-wide significance (P<5×10−8
). The 9 GC regions include several well known height loci, including EFEMP1, UQCC and HMGA2. Of particular interest is the UQCC locus (also known as the GDF5-UQCC region; ). This region encompasses approximately 850 kb, covering more than 20 genes, and has a relatively low recombination rate. The most significant signal was observed on SNP rs6058227 (P
); the minor allele (T) was associated with an average increase of height 1.93 cm. Re-analysis of the region conditional on rs6058227 failed to completely eliminate the signals of the other SNPs, suggesting the possibility of multiple causal variants within the region (). Similar evidence for allelic heterogeneity was also reported by Lango Allen et al., and the presence of multiple functional variants could be a potential source of missing heritability 
Nine replicated height-associated loci identified by GC approach.
LocusZoom plot of the GDF5-UQCC region before (A) and after (B) conditioning.