The effect of X-linked dosage compensation on complex trait variation

Quantitative genetics theory predicts that X-chromosome dosage compensation (DC) will have a detectable effect on the amount of genetic and therefore phenotypic trait variances at associated loci in males and females. Here, we systematically examine the role of DC in humans in 20 complex traits in a sample of more than 450,000 individuals from the UK Biobank and 1600 gene expression traits from a sample of 2000 individuals as well as across-tissue gene expression from the GTEx resource. We find approximately twice as much X-linked genetic variation across the UK Biobank traits in males (mean h2SNP = 0.63%) compared to females (mean h2SNP = 0.30%), confirming the predicted DC effect. Our DC estimates for complex traits and gene expression are consistent with a small proportion of genes escaping X-inactivation in a trait- and tissue-dependent manner. Finally, we highlight examples of biologically relevant X-linked heterogeneity between the sexes that bias DC estimates if unaccounted for.


Introduction
In eutherian mammals, including humans, females inherit two copies of the X chromosome and males only one. Ohno's hypothesis posits that the dosage difference between the X chromosome and autosomes is resolved by doubling the expression of X-linked genes in both males and females, and to balance allele dosages differences in X-linked genes between the sexes, mechanisms have evolved to randomly inactivate one of the X chromosomes in females during embryogenesis, where female cells will express the maternal or paternal X chromosome approximately 50 percent of the time (Lyon, 1961;Ohno, 1967). X chromosome inactivation (XCI) is controlled by an approximately 1Mb region on the long arm of the X chromosome called the X inactivation centre. Initiation of the XCI process involves a step to ensure that at least two copies of the X inactivation centre are present in the female cell (Rastan and Robertson, 1985), and then the expression of the non-coding RNA X inactivation-specific transcript (XIST) from the X inactivation centre of the future inactive X chromosome (Brown et al., 1991;Penny et al., 1996;Panning, Dausman and Jaenisch, 1997). Rapid accumulation of XIST RNA is shown to start around the 8-cell human embryo development stage (van den Berg et al., 2009) and most of female-to-male X-linked expression levels are equalized prior to embryo implantation (Petropoulos et al., 2016;Moreira de Mello et al., 2017). While exact dynamics of the human pre-embryonic XCI remain to be fully understood (Keniry and Blewitt, 2018), this process eventually resolves to the random transcriptional silencing of the one X chromosomes in female somatic cells. Random XCI remains maintained in mitotically derived cell lineages through a combination of epigenetic modifications including histone modifications and DNA methylation (Csankovszki, Nagy and Jaenisch, 2001;Lucchesi, Kelly and Panning, 2005) and leads to diverse patterns of mosaicism. However, approximately 15 to 23 percent of X-linked genes are shown to escape XCI (Carrel and Willard, 2005;Balaton and Brown, 2016;. Studies have previously used sex-bias in DNA methylation (Lister et al., 2013;Cotton et al., 2015;Schultz et al., 2015) and gene expression (Johnston et al., 2008;Zhang et al., 2011) as an indication of XCI, where an inactivated X-linked gene in the non-pseudoautosomal region (non-PAR) of the X chromosome is expected to show no difference in expression between the sexes, while a non-PAR X-linked gene that escapes XCI is expected to have higher expression in females compared to males. Indeed, genes that show significant differences in expression between the sexes are enriched in escape genes, with the non-PAR region of the X chromosome enriched for genes with female-biased expression, and the PAR region enriched for genes with male-biased expression (Tukiainen, A.-C. Villani, et al., 2017). The sex-bias in gene expression and its magnitude varies across tissues and even between the single cells, indicating variability in escape from XCI (Carrel and Willard, 1999;. Sex is an important predictor for many quantitative traits, such as height, or the risk, incidence, prevalence, severity, and age-at-onset of disease (Ober, Loisel and Gilad, 2008). In addition to mean differences, males and females may also differ with respect to the trait variance (Lynch and Walsh, 1998). In this study, we focus on one aspect of Ohno's hypothesis, where dosage compensation (DC) between the sexes is achieved by XCI. Theoretically, DC at loci affecting complex traits has a predictable effect on differences in genetic and therefore phenotypic trait variances in males and females and on the resemblance between male-male, male-female and female-female relatives (Bulmer, 1980;Lynch and Walsh, 1998;Kent, Dyer and Blangero, 2005). In particular, for X-linked complex trait loci, FDC is predicted to lead to twice as much variation in males compared to females and, conversely, escape from XCI is predicted to lead to twice the variance in females. Additionally, lack of DC can also contribute to mean differences in the trait of interest (Kent, Dyer and Blangero, 2005). Studies examining the relationship between X-linked SNPs and gene expression variation (Castagné et al., 2011;Brumpton and Ferreira, 2016) and variation in complex traits (Zhang et al., 2015) have noted that a larger proportion of SNPs are associated with these traits in males compared to females, indicating that these SNPs explain a larger proportion of variance in males compared to females. By comparing theoretical expectations from standard DC models to empirical data, we can systematically examine the effect of X-inactivation or escape from XCI on complex trait variation.
In this study, we leverage information on 20 complex phenotypes in the UK Biobank (N=208,419 males and N=247,186 females), 1,649 gene expression traits in whole-blood (N=1,084 males and N=1,046 females), and a mean of 808 gene expression traits across 22 tissue-types in GTEx (mean N=142 males and mean N=85 females) to compare the predicted effect of random X-inactivation in females to the empirical data. We perform a sex-stratified X-chromosome-wide association analysis (XWAS) for all traits to estimate male-female (M/F) ratio of the heritability attributable to the X chromosome in high-order UK Biobank traits and to compare M/F effect estimates of associated SNPs for both phenotypic and gene expression traits. Our results are consistent with expectations from full DC, and show a negligible effect of escape from XCI on complex trait variation.

Evidence for dosage compensation in complex traits
We first performed a sex-stratified genome-wide association analysis for 20 quantitative traits in the UK Biobank (UKB) (for trait information see Supplementary Table 1), and estimated ratios of male to female SNP-heritabilities (h 2 SNP ) on the X chromosome and the autosomes from summary statistics (Supplementary Material). Depending on the amount of DC on the X chromosome in females, this ratio is expected to take a value between 0.5 (no DC) and 2 (full DC). We refer to this as the DC ratio (DCR). For 19 out of 20 traits, the DCR estimates on the X chromosome (non-PAR) were significantly different from the expectation for no DC (DCR=0.5), and consistent with evidence for DC between sexes on the X chromosome and its detectable effect on phenotypic trait variation (Figure 1A, black). We validated our DCR summary statistics approach by calculating DCR from the estimates of h 2 SNP in males and females derived from GCTA-GREML (Yang, Lee, et al., 2011) on individual-level data from up to 100,000 unrelated individuals (Supplementary Table 2). From the GCTA-GREML analysis, we found the X-linked genetic variance of the complex traits to be low in general, but detectable in this large sample with the mean X-chromosome h 2 SNP estimates of 0.62% (SD=0.34%) and 0.30% (SD=0.20%) across the 20 UK Biobank traits in males and females, respectively. These h 2 SNP estimates were significant for all 20 traits in males and for 18 traits in females (the X-chromosome h 2 SNP estimates for the skin and hair colour traits did not significantly differ from zero in the female-specific analysis) (Supplementary Table 2). For these 18 traits, we observe a strong overall correlation between DCR estimates obtained with the two methods (Pearson correlation, r=0.78) (Supplementary Figure 1).
From the analysis based on summary statistics, the mean DCR for the X chromosome across 20 traits was 2.22 (SD=1.14), consistent with the expected value of 2 for full DC. In contrast, the estimates of the ratios of autosomal SNP-heritability varied from 0.66 to 1.17 with mean 0.95, in agreement with a limited difference in h 2 SNP between the sexes in autosomal loci (Supplementary Table 3). We observed DCR on the X chromosome significantly different from expected values under both hypotheses (full and no DC) for nine traits (Figure 1A, black). While for standing height (height), forced expiratory volume in 1 second (FEV1), diastolic blood pressure (DBP), fluid intelligence (FI) and educational attainment (EA) the DCR estimates ranged between 0.5 and 2, indicating partial DC, values larger than 2 (body fat percentage (Fat%), basal metabolic rate (BMR), haemoglobin concentration (Hgb) and haematocrit percentage (Hcrit)) could not be explained under either of the DC models. We therefore sought an alternative explanation for these observations. When estimating the DCR, we assumed that the genetic correlation (r g ) between males and females is equal to one, and that any difference in the genetic variance is due to differences in dosage (i.e. number of active copies) of the X-linked genes. We estimated autosomal (r gA ) and X-linked (r gX ) genetic correlations in our sample using the GWAS summary statistics (see Methods and Materials). The evidence for autosomal genetic heterogeneity in complex trait is limited (Yang et al., 2015;Rawlik, Canela-Xandri and Tenesa, 2016) and our estimates of r gA between sexes are similar to published results (mean r gA =0.92, SD=0.06 across 20 traits, Supplementary Table 3). However, we found lower genetic correlation across the 20 traits on the X chromosome (r gX =0.80, SD=0.14) (Supplementary Table 3). The smallest r gX estimates correspond to Hcrit (r gX =0.51, SE=0.05), Fat% (r gX =0.57, SE=0.05), red blood cell count (RBC) (r gX =0.64, SE=0.07) and Hgb (r gX =0.65, SE=0.04). These relatively low r gX estimates may indicate local differences in genetic variance between males and females on the X chromosome that is independent of DC, which may explain the observed extreme DCR for these traits. We therefore explored biological heterogeneity as an explanation for these observations.

Biological heterogeneity on the X chromosome
To investigate sex-specific genetic architectures on the X chromosome, we tested for heterogeneity in male and female SNP effects under the null hypothesis of no difference (see Methods and Materials). A total of 6 traits (Hcrit, Fat%, RBC, Hgb, height and heel bone mineral density T-score (hBMD)) showed evidence for heterogeneity, with four distinct heterogeneity signals. SNPs with significant differences in effect estimates between the sexes (P Het <5.0x10 -8 ) were then LD-clumped to define four regions of heterogeneity, two of which overlap due to the complex LD structure in the centromere region (Figure 2, Supplementary  Table 4).
Sex-related differences between males and females are most likely to arise due to naturally differing sex hormone levels. We therefore examined the evidence for hormonal regulation in these regions. We observed a highly significant trait association in males and lack of association in females in heterogeneity region 1 (Xp22.31) for 5 traits: Fat%, Hgb, Hcrit, RBC and hBMD (Figure 2). Notably, this region near the FAM9A/FAM9B genes, has been shown to be significantly associated male-specific traits such as testosterone levels (Ohlsson et al., 2011), male pattern baldness (Pickrell et al., 2016;Pirastu et al., 2017) and age at voice drop (Pickrell et al., 2016). Moreover, the FAM9A/FAM9B genes are shown to be expressed exclusively in testis in hybridization experiments (Martinez-Garay et al., 2002). Indeed, in the GTEx data (see URLs), we found that FAM9A is highly expressed in testis only, with lower levels of expression of FAM9B in both uterus and testis, supporting the male-specific architecture for this locus and suggesting the androgenic pathway. Androgens play essential erythropoiesis promoting- (Shahani et al., 2009), fat-reducing-(De Pergola, 2000 and anti-osteoporotic- (Clarke and Khosla, 2009) roles. Thus, we presume that a pleiotropic effect of the region 1 on erythropoiesis associated traits (Hgb, Hcrit and RBC), Fat% and hBMD may be mediated by androgen levels.
The NROB1 gene in the region 2 (Xp21.2), which encodes the DAX1 protein, was a candidate gene for male-specific genetic control for height in this region (Figure 2). DAX1 is essential for regulation of hormone production and loss of DAX1 function leads to adrenal insufficiency and hypogonadotropic hypogonadism (Jadhav, Harris and Jameson, 2011). Moreover, Xp21.2 region in known as a dosage-sensitive sex reversal region, where its duplication or deletion is associated with male-female or female-male sex reversal (Bardoni et al., 1994;Smyk et al., 2007;Dangle et al., 2017).
The top signal in region 4 was located in another well-known androgen-associated locus (Xq12) near the androgen receptor (AR) gene (Figure 2). The significant heterogeneity in this region between males and females for Fat% supports the male-specific fat-reducing effect of androgens. Notably, we observed the sex-specific heterogeneity in regions 1 and 4 for Fat% but not for BMI, suggesting that, although highly correlated, these traits differ in aetiology.
For hematopoietic traits (significant heterogeneity for Hgb and Hcrit, and nominal although not significant evidence for heterogeneity for RBC) the main heterogeneity signal was identified in Xp11.21 (region 3) (Figure 2). This region is shown to be associated with blood zinc concentrations (near KLF8, ZXDA and ZXDB encoding Zn-finger proteins (Evans et al., 2013)) and male-pattern baldness (Pickrell et al., 2016). Zinc has been shown to modulate serum testosterone levels in men (Prasad et al., 1996) and is associated with haemoglobin concentrations in epidemiological studies (Houghton et al., 2016). However, we find that the 5' end of the region 3 is adjacent to the ALAS2 gene, encoding a protein involved in heme synthesis and thus erythropoiesis (OMIM *301300). Mutations in this gene cause sideroblastic anaemia with X-linked recessive inheritance (OMIM #300751). Thus, the evidence for the androgen-dependent effect of this region on hematopoietic traits remains inconclusive.
Overall, at least three of the four regions of detected heterogeneity on the X chromosome show evidence of male-specific and/or androgen-related effects on the traits, and thus may not reflect an effect of DC, but rather biological differences between the sexes which are mediated by sex hormones. We therefore re-estimated DCR for Hcrit, Fat%, RBC, Hgb, height and hBMD after excluding these regions of heterogeneity (Supplementary Table 5, Figure 1A). While there was no significant change in DCR for height, we found a significant decrease in DCR and an increase in genetic correlation for the remaining five traits. After reestimating DCR for the 6 traits our mean estimate of DCR across all 20 UK biobank traits changed from 2.22 (SD=1.14) to 1.87 (SD=0.51). These observations are consistent with the hypothesis that a disproportionate amount of male-specific genetic variance in these regions is at least partially hormonally influenced.

Genetic effects of associated loci indicate limited escape from XCI in complex traits
In addition to testing for differences in overall X-linked variance between the sexes, we can estimate a dosage compensation parameter d such that ߚ ൌ ݀ ߚ (see Supplementary Methods and Material) for genome-wide significant trait-associated SNPs. We did this by regressing the male-specific effect estimates onto the effects of the same markers estimated in female-specific analysis, weighted by the inverse of the variance of male-specific effect estimates. We define this regression slope as DC coefficient (DCC), which is expected to take on values between 1 (no DC or escape from XCI) and 2 (full DC).
We applied the conditional and joint association analysis (GCTA-COJO) (Yang et al., 2012) to the summary statistics from the male-, female-and combined discovery analysis to select jointly significant trait-associated SNPs (hereafter, lead SNPs) for each of the 20 UKB traits. This identified 153 (male discovery) and 62 (female discovery) lead SNPs on the non-PAR X chromosome at a genome-wide significance level (GWS) (P<5.0x10 -8 ) across the tested phenotypic traits (Supplementary Table 6 -8). That is, more than twice the number of non-PAR lead SNPs was identified in males compared to females, indicating that a larger proportion of per-locus and therefore total genetic variance is explained in males compared to females. In contrast, in the PAR, we only identified two lead loci in males, while eight of them were detected in female discovery analysis (Supplementary Table 6-9). In the combined male-female discovery analysis 261 non-PAR and 16 PAR SNPs satisfy our GWS threshold in the COJO-analysis (Supplementary Table 9). The increased number of lead SNPs in comparison to the sex-stratified analysis indicates concordance of effects from sexspecific analyses. The proportion of sex-specific genetic variance explained by the lead SNPs in the combined set is presented in Supplementary Figure 2.
We estimated DCC to be 2.13 (SE=0.08) and 1.46 (SE=0.08) for the male and female non-PAR discovery analyses, respectively, using the lead SNPs across the analysed complex traits (Supplementary Figure 3). DCC for the markers identified in the combined analysis was 1.85 (SE=0.04) ( Figure 1B). The observation from the combined analysis indicates only limited overall effect of escape from XCI on the variance or mean of the traits in our analysis. For the PAR, although the number of significant associations was small, the effects size estimates from sex-specific analyses were similar (Supplementary Figure 4), consistent with theoretical expectations.
The ratio of the M/F per-allele effect sizes for individual SNPs, which approximates the dosage compensation parameter, indicated the evidence for escape from XCI only for a few candidate variants. For instance, SNP rs113303918 in the intron of the FHL1 gene is significantly associated with WHR in female and the combined analyses (P female =6.6x10 -12 and P combined =9.8x10 -14 , respectively), while being only marginally significant in malespecific analysis P male =4.5x10 -5 ) and the per-allele effect sizes on WHR are similar in both sexes (effect size ratio=0.93, SE=0.26). Similarly, the effect size ratio of SNP rs35318931 (P female =2.7x10 -17 , P male =6.7x10 -4 , P combined =2.8x10 -15 ), a possible missense variant in the SRPX gene, is 0.63 (SE=0.20) consistent with escape from XCI for WHR. Assuming that these SNPs are the causal variants, the observed effect size estimates may indicate potential escape from XCI for FHL1 and SRPX. Interestingly, for height (effect size ratio=2.12, SE=0.35; P height, combined =1.9x10 -37 ) and BMR (effect size ratio=3.26, SE=1.21; P BMR, combined =6.6x10 -12 ) the results for the SNP rs35318931 in the SRPX gene were indicative of DC. Consistent with these observations, SRPX is annotated with "Variable" XCI status in (Cotton et al., 2013;Tukiainen, A.-C. Villani, et al., 2017). For FHL1, although, annotated as "Inactive" in (Tukiainen, A.-C. Villani, et al., 2017), findings from two earlier studies (Carrel and Willard, 2005;Cotton et al., 2013), show that XCI is incomplete. Moreover, heterogeneous XCI of FHL1 is detected in single cells and across tissues (Tukiainen, A.-C. Villani, et al., 2017).
Previously, a locus near the ITM2A gene (SNP rs1751138, bp 78,657,806) was proposed as a potential XCI-escaping locus associated with height (Tukiainen et al., 2014). In our sexstratified and combined analyses from a sample size an order of magnitude larger, the lead marker for height was a nearby SNP rs1736534 located approximately 100 bp upstream of the previously reported rs1751138. The estimated M/F effect size ratio for the both variants was 1.75 (SE=0.11) (ߚ height, male =-0.086, SE=0.004 and ߚ height, female =-0.049, SE=0.002), providing evidence against extensive escape of ITM2A from XCI.
About one-third of the identified lead SNPs were physically located within X-linked gene regions. For these SNPs, we assigned the XCI status according to the reported XCI status of the corresponding genes (Tukiainen, A.-C. Villani, et al., 2017) and compared the effect size ratios between "Escape/Variable" and "Inactive" genes. The results remained similar between two groups of genes (Supplementary Figure 5). A notable disadvantage of this approach is that the physical location of a SNP within a gene region does not necessarily indicate a causal variant for a complex trait. In contrast, an expression quantitative loci (eQTL) analysis avoids this, as there is no ambiguity between mapped SNPs and genes, and thus the annotation of XCI status.

eQTL analysis indicates negligible escape from XCI in gene expression
We extended our DCC analysis to lower-order gene expression traits and performed a sexstratified cis-eQTL analysis for 1,639 X-chromosome gene expression probes (28 of them in PAR) measured in whole blood. For each probe, we identified the top associated Xchromosome SNP with MAF>0.01 that satisfied the Bonferroni significance threshold of P<1.6x10 -10 (i.e. 0.05/(1,639 x 190,245)) in the discovery sex (hereafter called eQTL), and extracted the same eQTL in the other sex and calculated DCC for M/F eQTL effect size estimates. We observed DCC of 1.95 (SE=0.04) for 51 eQTLs (48 unique SNPs) in the female discovery analysis, and DCC of 2.07 (SE=0.04) for 74 eQTLs (68 unique SNPs) in the male discovery analysis (Supplementary Figure 6), consistent with expectations from FDC and in agreement with our observations in high-order complex traits. We did not identify eQTLs for probes in PAR. Partitioning the non-PAR eQTLs based on reported XCI status of the corresponding genes (Tukiainen, A.-C. Villani, et al., 2017) did not alter our results (Figure 3). In particular, for eQTLs annotated to escape XCI, DCC estimates were approximately two, consistent with FDC. Interestingly, for 6 eQTLs identified in the male discovery analysis and annotated to escape XCI (USP9X, EIF2S3, CA5B, TRAPPC2, AP1S2, and OFD1) we observed higher expression in females compared to males (P<3.1x10 -3 , i.e. 0.05/16), as expected for genes that escape from XCI, but found significant differences between the eQTL effect estimates of the top associated SNP on gene expression after correction for mean differences in expression between the sexes (genotype-by-sex interaction P<3.1x10 -3 ), which is consistent with FDC. This suggests that sexual dimorphism in these genes may not be due to escape from XCI (Supplementary Figure 7). Full details of the eQTLs in blood can be found in Supplementary Tables 11 and 12. We validated our results in 22 tissue samples from GTEx (v6p release) for which within tissue sample size was greater than N=50 in both males and females (Supplementary Table  10). We estimated DCC for at least three eQTLs (i.e. transcript-SNP pairs) that satisfied the within tissue Bonferroni significance threshold in the discovery sex in each of the 22 tissuetypes. No eQTLs were identified for probes in PAR. A mean of 28 (SD=18) eQTLs were identified in the male discovery analysis across the 22 tissues. We observed a mean DCC of 1.94 (SD=0.16) across 22 tissues in the male discovery analysis, with the 95 percent confidence intervals for 20 tissues overlapping 2 (Figure 4). Heart (atrial appendage) tissue was an outlier, with DCC of 2.50 (SE=0.19). In contrast, a mean of 5 (SD=0.82) eQTLs were identified in females across the 7 tissues. A mean DCC of 1.59 (SD=0.13) across 7 tissues was observed in the female discovery analysis, with only the 95 percent confidence interval for thyroid tissue overlapping 2. We verified that the difference in estimated DCCs is not due to differences in sample size between males and females by down-sampling males so that the proportions match that of females within each of the 7 tissues and calculating mean DCC across 100 replicates (Figure 4). We did not observe enrichment for escape/variable eQTLs identified in the male or female discovery analyses by hypergeometric test (Supplementary Table 11). These results were consistent when the top eQTLs were chosen among all tissues in the discovery sex and compared to the same eQTL from the same tissue in the other sex (Supplementary Figure 8). Finally, we compared our results to those from a sex-stratified autosomal cis-eQTL analysis in 36,267 autosomal gene expression probes in whole blood. A similar number of eQTLs with P<10 -10 were identified in males and females (3,116 in the male discovery vs. 3,165 in the female discovery), indicating that an approximately equal proportion of autosomal genetic variance per locus is explained in each of the sexes. As expected, DCC in the male and female discovery was 1.00 (SE=2.3x10 -3 ) and 0.94 (SE=2.3x10 -3 ), respectively, indicating that the autosomal eQTL effect sizes are approximately equal in males and females (Supplementary Figure 9). Full details of the eQTLs across tissues can be found in Supplementary Table 13.

Summary-data based Mendelian randomisation
As noted above, there may be some ambiguity in mapping the associated variants to the genes based on its physical location, since the true causal variants may be masked by the local LDstructure or may exert the regulatory action on both near and distantly located genes (Smemo et al., 2014;Zhu et al., 2016). To investigate this we aimed to integrate the GWAS data from the complex trait analysis and the eQTL data from the whole blood analysis in the CAGE dataset to prioritize genes whose expression levels are associated with complex phenotypes because of pleiotropy, so that the XCI status would be assigned to the relevant "causal" gene. The combined summary data-based Mendelian randomisation (SMR) analysis (Zhu et al., 2016) identified 18 genes (tagged by 20 probes) to be significantly (P SMR <3.0x10 -5 (0.05/1,639) and P HEIDI >0.05) associated with 14 complex phenotypes (total of 37 associations) in the combined analysis (Supplementary Table 14). For males, associations between 13 genes (15 probes) and 11 traits satisfy our significance thresholds (total of 23 associations) ( Supplementary Table 15), while for females we only identify 4 significant pleiotropic associations between 3 genes (3 probes) and 4 traits (Supplementary Table 16). The effects of the genetic variants on the trait, whose effects on the phenotype were identified to be potentially mediated by gene expression in sex-specific and combined analyses are shown in Supplementary Figure 10. The estimated DCC for these variants is similar to the results estimated with all jointly significant SNPs from COJO analysis ( Figure 1B,  Supplementary Figure 3).
Our SMR analysis linked many SNPs located in the intergenic regions to the expression of a number of genes, however, also a number of the SNPs physically located within a gene were determined to be associated with expression of another gene (e.g. a SNP in TMEM255A was an eQTL for ZBTB33 whose expression is associated with traits skin and hair colour). This also included previous signals in escape genes being assigned to inactive genes (e.g. the SNPs physically located in the annotated escape gene SMC1A was associated with the expression of the inactive HSD17B10 for BMI, BMR, Fat% and EA in the combined SMR analysis). Now the expression of only 2 genes (MAGEE1 and PRKX) annotated with "Variable" or "Escape" (respectively) from XCI showed evidence for pleiotropic association with a phenotypic trait (hand grip strength (Grip) and white blood cells (WBC), respectively) due to a shared genetic determinant (MAGEE1: P SMR,combined =2.1x10 -6 , PRKX: P SMR,combined =8.7x10 -6 , Supplementary Figure 10, Supplementary Table 14). The estimated effect size ratio (2.84, SE=0.85) for the variant rs757314 (mediated by MAGEE1 expression levels) on hand grip strength was not consistent with the escape from X-inactivation (the expected ratio for an escape gene is 1). For the rs6641619 (associated with PRKX expression and WBC), we estimate the effect size ratio of 1.33 (SE=0.44), which is indicative of partial escape from X-inactivation.
Variants near ITM2A were shown to be associated with height (Tukiainen et al., 2014) and with height, BMR, Grip, WHR and FEV1 in the current study. In the combined SMR analysis we also observed evidence for pleiotropic association (P SMR <3.0x10 -5 ) of the ITM2A (tagged by ILMN_2076600) expression with 7 traits: height, BMR, Grip, WHR, FEV1, DBP and RBC (genetic instrument rs10126553). However, only for the DBP and RBC, this association passes the test for heterogeneity (HEIDI), aimed to distinguish pleiotropy/causality from linkage. For the remaining traits, P HEIDI varied from 6.5x10 -3 for WHR to 8.0x10 -16 for height, suggesting heterogeneity in gene expression effect on the trait estimated at different eSNPs that are in LD with the top-associated eSNP. That is, we cannot reject the null hypothesis that the gene-trait association is due to a single genetic variant. SMR analysis in trans regions on the X chromosome identified additional association between the expression of the ITM2A gene and height and BMR, which was mediated by a trans-eQTL located 2.2Mb upstream ITM2A (rs112933714). The mean M/F effect size ratio for the genetic instrument rs10126553 (P eQTL,combined =1.5x10 -76 ) across these 7 traits (not filtered on P HEIDI value) was 1.83 (SD=0.25) ( Supplementary Table 17), and 2.30 (SD=0.65) for the trans acting variant rs112933714 across two traits with significant trans-eQTLs (Supplementary Table 18), in agreement with reported "Inactive" status of the ITM2A gene.

Discussion
The theoretically predicted effect of random X-inactivation in female cells is two-fold reduced amount of additive genetic variance in females compared to males, whereas escape from XCI would increase genetic variance in females and contribute to sexual dimorphism. Having analysed phenotypes with varying degree of polygenicity, we found only limited effect of escape from X-inactivation on complex trait variation both in moderately (gene expression) and highly polygenic traits (phenotypic traits in the UKB). The two strategies that we use to estimate DC are the overall ratio of M/F X-linked heritabilities (i.e. the dosage compensation ratio) and the comparison of the individual effects of the trait-associated variants (i.e. the effect size ratio and dosage compensation coefficient). These are parameterisations of the same effect, the former based upon the variance contributed by all X-linked trait loci and the latter based upon per-allele effect sizes of trait-associated loci. Previous studies demonstrate that ~1% of phenotypic variance of the phenotypic traits, such as height and BMI, is attributable to the X chromosome (Yang, Manolio, et al., 2011;Tukiainen et al., 2014). However, the attempts to disentangle the relationships of additive genetic variance between the sexes in high-order traits were limited in power due to moderate sample sizes and/or computational challenges (Yang, Manolio, et al., 2011;Tukiainen et al., 2014). Here, a large the sample of > 205,000 males and >245,000 females allowed us to identify a statistically significant contribution of the X chromosome to the total trait heritability for 18 of the 20 studied complex traits in both sexes and for all traits in malespecific analysis, so we could make further inferences about DCR in complex traits. While we observed good overall evidence for DC across the phenotypic traits, a number of outliers were present in our analysis. First, we observed unexpectedly high ratios of male to female genetic variance for some of the traits. The male-specific genetic control for some genome regions appear to be sex-hormone dependent and thus are not informative on DC. Additionally, while the region comprising a testosterone-associated locus (near FAM9A/FAM9B genes) had the strongest evidence of heterogeneity, its removal had modest effect on DCR, while the exclusion of the genomic region near the centromere had the strongest effect. In addition to possible androgen-specific influence of this region, the tight LD structure could contribute disproportionately to sex-specific genetic variance. Second, we observe DCR supporting possible escape from XCI rather than full DC in brain related traits, such as educational attainment and fluid intelligence, and also diastolic blood pressure. Consistently, brain tissues have the highest X chromosome to autosome expression ratio, followed by heart (Nguyen and Disteche, 2005;Xiong et al., 2010), in agreement with an enhanced X-chromosome role in cognitive functions. Thus, the effect of DC may be tissuespecific.
We also found consistent evidence for DC when examining individual trait-associated markers. Interestingly, our results for height associated loci near ITM2A, a gene known to be involved in cartilage development, differ from reported evidence for lack of DC (Tukiainen et al., 2014) and only a few loci associated with WHR were candidates to be putative "escapees". It should be noted, however, that for WHR genetic correlation on both autosomes and the X chromosome is markedly low, which may reflect the sex-specific genetic control for this trait.
In contrast to the complex phenotypic traits, gene expression has a notably different genetic architecture with as much as 65% of the expression variance for a gene explained by a single SNP alone, thus potentially violating the (polygenic) modelling assumptions for a DCR analysis, and thus was not included as part of this study. However, we were able to leverage information from eQTLs to show that DCC estimates in gene expression are consistent with expectations from FDC and in agreement with our observations in high-order complex traits and previous eQTL studies (Castagné et al., 2011;Brumpton and Ferreira, 2016). These results were broadly consistent across multiple tissue-types, where a larger number of eQTLs were identified in males compared to females and, in the male discovery analysis, DCC is approximately 2. Across both the high-order and gene expression traits, we observed DCC estimates larger than 2 in the male discovery analysis and smaller than 2 in the female discovery analyses. This may be attributed to a combination of partial escape from XCI and "winner's curse" of the XWAS analysis. For example, any loci that partially escapes XCI in females would be preferentially selected in the female discovery analysis due to increased statistical power of detection, and thus bias the DCC estimates towards 1. Further, DCC estimates may be influence by "winner's curse", where the per-allele effect estimates in the discovery sex is biased upwards compared to the corresponding estimates in the other sex.
While identification of new associations between X-linked SNPs and complex traits was not the aim of our study, our results show these are readily found and that they cumulatively contribute to trait variation. For example, we find pleiotropic association between expression levels of the HSD17B10 gene, which encodes a mitochondrial enzyme involved in oxidation of neuroactive steroids, fatty acids as well as sex hormones and its deficiency is implicated in neurodegenerative disorders (S. Y.  with obesity-related traits (Fat% and BMI) and educational attainment. Consistently, similar putative causal relationships were recently identified for the autosomal gene HSD17B12, where its increased expression of this gene was associated with decreased BMI across 22 tissues (Yengo et al., 2018). Therefore, comprehensive surveys of sex-stratified X chromosome wide association studies for disease and other traits are likely to be rewarding, and may provide insight into new biology and sexual dimorphism. Moreover, since our method for estimating the amount of DC only requires summary statistics from association analyses, the availability of sex-stratified results from XWAS studies can further be informative on the effect and dosage of X-linked variation across a range of complex traits. supported by the Sylvia & Charles Viertel Charitable Foundation. The content is solely the responsibility of the authors and does not necessarily represent the official views of the grant funding bodies. This study makes use of data from GTEx Consortium data from dbGaP (accession phs000424.v6.p1). Complex trait analysis has been conducted using the UK Biobank Resource under project 12514. We thank Prof. Naomi R. Wray for her helpful comments and suggestions for the manuscript.

Declaration of Interests
We declare that we have no competing interests.  Table 4) and presented in colour (Excluding region 1=green; excluding region 2=yellow; excluding region 3 or 4=red; excluding region 1 and 3 or 4=blue). The mean DC ratio is estimated after accounting for heterogeneity. B) Male and female per-allele effect estimates (in standard deviation units) (+/-SE) are compared for the GWS SNPs identified in the combined discovery analysis (N=251). The SNPs located in the regions of heterogeneity for the six traits mentioned above are excluded. The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. The black line represents DCC. Height = standing height, FEV1 = forced expiratory volume in 1second, Smoking = smoking status, Grip = hand grip strength (right), BMI = body mass index, Fat% = body fat percentage, BMR = basal metabolic rate, WHR = waist to hip ratio, DBP = diastolic blood pressure, hBMD = heel bone mineral density T-score, FI = fluid intelligence score, Neuroticism = neuroticism score, EA = educational attainment, Skin = skin colour, Hair = hair colour, WBC = white blood cell (leukocyte) count, Platelet = platelet count, RBC = red blood cell (erythrocyte) count, Hgb = haemoglobin concentration, Hcrit = Haematocrit percentage.  Table 4). In each region the P Het values are plotted (grey dots) for all traits with significant heterogeneity in that region. The top SNPs for each trait are shown in blue. The genes discussed in the text are highlighted in red. In region 3, only the ALAS2 gene and genes with X-chromosome position >56 Mb are shown for simplicity (the omitted 15 genes are: ITIH6, MAGED2, TRO, PFKFB1, APEX2, PAGE2B, PAGE2, FAM104B, MTRNR2L10, PAGE5, PAGE3, MAGEH1, USP51, FOXR2, RRAGB). The red dashed line represents the significance threshold (P Het = 5.0x10 -8 ). The green dashed lined represent the boundaries of the regions. P Het = heterogeneity P-value, hBMD = heel bone mineral density T-score, Height = standing height, Hgb = haemoglobin concentration, Hcrit = Haematocrit percentage, RBC = red blood cell (erythrocyte) count, Fat% = body fat percentage.

Supplementary Figure 3.
Comparison of the male-and female-specific per-allele effect estimates (+/-SE) for the lead SNPs (non-PAR) identified in the B) male discovery set (N=143) or C) female discovery set (N=62). The SNPs located in the regions of heterogeneity are excluded. The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. The black line represents DCC.

Supplementary Figure 4.
Comparison of per-allele effects from sex-specific analyses (+/-SE) of lead SNPs in PAR as identified in a A) combined discovery set (N=16), B) male discovery set (N=2) or C) female discovery set (N=8). The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. DCC was not estimated due to low number of lead SNPs in PAR. Figure 5. Effects size ratios for the lead SNPs across analysed complex traits are compared between "Escape/Variable" and "Inactive" groups, which include SNPs physically located within a gene region with previously reported XCI status (Tukiainen, A.-C. Villani, et al., 2017). We exclude variants in the regions of heterogeneity as well as 2 variants with the absolute ratio values > 10 (male discovery sample). Figure 6. Comparison of per-allele effects from sex-specific analyses (+/-SE) for X-chromosome cis-eQTLs in CAGE whole blood. DCC of 1.95 (SE=0.04) is observed for 51 eQTLs (P<1.6x10 -10 ) in the female discovery analysis, and DCC of 2.07 (SE=0.04) for 74 eQTLs (P<1.6x10 -10 ) in the male discovery analysis. The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. The black line represents DCC. Figure 7. A total of 6 eQTLs identified in the male discovery cis-eQTL analysis in CAGE whole blood are annotated to escape XCI. These genes show higher expression in females compared to males (P<3.1x10 -3 , i.e. 0.05/16), as expected for genes that escape from XCI, but also significant differences between the effect estimate of the top associated SNP on gene expression after correction for mean differences in expression between the sexes (genotype-by-sex interaction P<3.1x10 -3 ), which is consistent with FDC. This suggests that sexual dimorphism in these genes may not be due to escape from XCI. Orange corresponds to females. Blue corresponds to males. Figure 8. The per-allele effect estimates of top eQTLs across all 22 tissues in GTEx in the discovery sex is compared to the corresponding eQTL in the other sex from the matching tissue. DCC of 1.96 (SE=0.05) is observed for 175 eQTLs in the male discovery analysis, and 1.51 (SE=0.05) for 23 eQTLs in the female discovery analysis. The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. The black line represents DCC. Figure 9. Comparison of per-allele effects from sex-specific analyses (+/-SE) for autosomal cis-eQTLs identified in CAGE whole blood. DCC is expected to be equal in males and females. DCC of 1.00 (SE=2.3x10 -3 ) is observed for 3,116 eQTLs with P<10 -10 in the male discovery analysis, and 0.94 (SE=2.3x10 -3 ) for 3,165 eQTLs with P<10 -10 in the female discovery analysis. The green dashed line represents the y=2x line. The black line represents DCC. Figure 10. Comparison of per-allele effects from sex-specific analyses (+/-SE) of the SNPs associated with complex traits through gene expression, as identified in a A) combined male-female SMR analysis (N=37), and sex-stratified SMR analyses (B, N=23; C, N=4). The SNPs are coloured according to the reported inactivation status of the genes that showed evidence of pleiotropic association with phenotypic traits (SMR genes, red "Escape/Variable", black = "Inactive", grey = "Unknown"). The results are presented in the Supplementary Tables 12-14. The green and red dashed lines indicate the expectations under full DC and escape from X-inactivation, respectively. The black line represents DCC. Supplementary Tables 7-9, 11-18 are provided as Excel spreadsheets.

Supplementary Table 5.
Estimates of dosage compensation (DC) and genetic correlation (r g ) after excluding regions of heterogeneity. The DC and r g are marked as follows: 0 -including all SNPs, 1-excluding the SNPs in the region 1; 2-excluding the SNPs in the region 2; 3excluding the SNPs in the region 3; 4-excluding the SNPs in the region 4; 13-excluding the SNPs in the region 1 and region 3; 14-excluding the SNPs in the region 1 and region 4  Table 6. Number of lead SNPs identified in sex-stratified and combined analyses (GCTA-COJO). The number of SNPs retained after exclusion of markers located in the regions of male-female heterogeneity for six traits is indicated parentheses.

Genotype coding
The summary statistics reported in this study were generated with a combination of BOLT-LMM v2.3 (Loh et al., 2018), GCTA 1.94 (Yang, Lee, et al., 2011), and PLINK 1.90 (Purcell et al., 2007), all of which have default settings for the treatment of X-chromosome SNPs. For analyses performed using PLINK, we used the default parameters which codes males as {0,1}, and thus gives the appropriate per-allele effect estimates. For BOLT-LMM and GCTA, the male genotypes were analysed as diploid using a {0,2} coding. This distinction makes no impact on the strength of association (i.e. P-values), however, we multiply the effect estimates and the corresponding standard errors from the diploid male-specific analysis by 2, allowing us to report our results as per-allele effect estimates. In all cases, females were coded as {0,1,2}.
Data UK Biobank data. Sex-stratified association analyses of 20 complex was performed using the phenotype data on N m =208,419 males and N f =247,186 females of European-ancestry and UKB Version 3 release of imputed genotype data (6,871 SNPs in pseudoautosomal region (PAR) and 253,842 SNPs in non-pseudoautosomal region (non-PAR) that satisfied our quality control criteria and had minor allele frequency, MAF>0.01). The phenotypes were adjusted for appropriate covariates and converted to sex-specific Z-scores prior to analysis (See Supplementary Table 1 and Supplementary Methods and Material for full details).
CAGE gene expression data. Gene expression and X-chromosome genotype data were available in a subset of N=2,130 individuals of verified European ancestry (N m =1,084 males, N f =1,046 females) from the Consortium for the Architecture of Gene Expression (CAGE) (Lloyd-jones et al., 2017). A total of 36,267 autosomal and 1,639 X-chromosome gene expression probes (28 in the PAR) in whole-blood were available for analysis following quality control. Gene expression levels were adjusted for PEER factors (Stegle et al., 2010(Stegle et al., , 2012 that were not associated with sex (P sex >0.05) in order to preserve the effect of sex on expression and where available, measured covariates such as age, cell counts, and batch effects. A total of 1,066,905 HapMap3 SNPs imputed to 1000 Genomes Phase 1 Version 3 reference panel (Altshuler et al., 2012) and 190,245 non-PAR X-chromosome SNPs (minor allele frequency, MAF>0.01) imputed to the Haplotype Reference Consortium (HRC, release 1.1) (McCarthy et al., 2016) were available for analysis.
GTEx gene expression data. We used the fully-processed, normalised and filtered RNA-seq data from the Genotype Tissue Expression project (GTEx v6p release). X-chromosome imputed SNP data was obtained from dbGap (Accession phs000424.v6.p1). We restricted our analyses to 22 tissue samples for which within tissue sample size was greater than N=50 in both males and females (Supplementary Table 10). A total of 1,121 transcripts (31 in the PAR) were expressed in at least one tissue, with a mean of 808 transcripts expressed across all 22 tissues (Supplementary Table 10) and a total of 127,808 imputed SNPs in the non-PAR of the X chromosome (MAF>0.05).

Statistical analysis
Sex-stratified XWAS. Summary statistics were generated for 20 complex traits in the UK Biobank using BOLT-LMM v2.3 (Loh et al., 2018) for the X-chromosome SNPs with MAF>0.01 in both sexes and using 561,572 HapMap3 SNPs (autosomal and Xchromosomal, pairwise R 2 <0.9) as "model SNPs" to estimate genetic relationship matrix (GRM) and correct for confounding.

Combined analyses.
For complex traits, the results from the sex-stratified association testing were meta-analysed using the inverse-variance weighted method to obtain combined results (performed in R). For combined analysis of gene expression traits, individual data from males and female were pooled together. We assumed full DC for all loci for these analyses.
Significant SNP-trait associations. GCTA-COJO (Yang et al., 2012) was used to identify sets of jointly significant SNPs associated with a trait at genome-wide significance (GWS) threshold P<5.0x10 -8 . We use genotypes of a random sample of 100,000 unrelated UKB females of European ancestry as a linkage disequilibrium (LD) reference and increase a distance of assumed complete linkage equilibrium between markers (window size) to 50Mb due to higher levels of LD on the X chromosome.
Estimation of dosage compensation ratio and genetic correlation from summary statistics. Following (Lee et al., 2018), we calculated the DC ratio for 20 complex traits from the summary statistics of the sex-stratified X-chromosome analysis using the following equation: The corresponding standard error is estimated as: is the variance of the mean test statistic across the X chromosome, which is approximately equal to ‫ܯ/2(‬ eff )[1 + 2(߯̂ଶ− 1)].
‫ܯ‬ eff is the effective number of SNPs, which for the X chromosome is approximately equal to 1,300 (Lee et al., 2018). The DC ratio of 2 indicates the evidence for full DC, while the value of 0.5 implies complete escape from inactivation (no DC).
We also we obtained an estimator for the male-female genetic correlation on the X chromosome (non-PAR region) or autosomes using the following equation, where, as before, ߯ ଶ and ߯ ଶ are the mean chi-square estimates from association analysis and ߯ ଶ is the cross-product of the Z-statistics from the male and female analyses.
We calculate standard errors using a block jackknife method. We assign SNPs across the X chromosome to blocks (B=1000) and for each block k we calculate an estimate of the genetic which follows a χ 2 -distribution with one degree of freedom under the null hypothesis of no difference in estimates under full DC assumption. We set a P-value threshold of P<5.0x10 -8 to identify the markers with significant difference in estimated effects and further apply LDclumping (R 2 threshold 0.05) to identify regions of heterogeneity. The coordinates of protein coding genes in these regions were extracted with BioMart tool (See URLs), using the genome assembly GRCh37.p13 from Genome Reference Consortium.
Estimation of the SNP-heritability. We estimated the proportion of variance explained by X-chromosome SNPs in males and females separately using GREML and a genome and in a combined cis-SMR analysis, respectively. SMR analysis in trans regions was performed with combined data and 74 probes with trans-eQTLs P eQTL <5.0x10 -8 were included. A reference for LD estimation was a random sample of 100,000 unrelated UKB females of European ancestry. Trait-gene associations were identified using a significance level of P SMR <3.0x10 −5 (i.e 0.05/1,639) for SMR analysis. These associations were then tested for evidence of linkage, rather than pleiotropy/causality, using the HEIDI test, which tests for heterogeneity in the effect estimates of the exposure on the outcome at SNPs in LD with the top associated eSNP under the null hypothesis of no heterogeneity. Gene-trait associations with P HEIDI >0.05 were selected.
Estimating the effect size ratio and dosage compensation coefficient (DCC). We refer to the effect size ratio as the ratio of M/F per-allele effect estimates for a single trait-SNP association. The corresponding standard errors are estimated as, are the corresponding standard errors, respectively. To compare the per-allele effect estimates across all conditionally independent trait-associated SNPs (complex trait analysis) and top eQTLs (gene expression analysis) identified in the discovery datasets, we calculated an effect size regression coefficient (DCC) by regressing the per-allele effect estimates in males onto females weighted by inverse of the variance of male-specific estimates, and extracting the slope estimate and corresponding standard error. The estimates from sex-stratified XWAS, rather than joint effect estimates from the GCTA-COJO analysis were used for estimating DCC in the UKB traits. DCC is expected to take on values between 1 and 2, where DCC of 1 indicates that, on average, the effect sizes in males and females are equal (i.e. no DC or escape from XCI), and DCC of 2 indicates that, on average, the effect sizes in males are twice that of females (i.e. full DC).

X-chromosome gene inactivation status.
To determine X-chromosome inactivation status, we downloaded annotation from the "Reported XCI status" column in Supplementary Table  13 of (Tukiainen, A.-C. Villani, et al., 2017) and mapped gene expression probes to XCI status using the gene name. A total of 683 X-linked transcripts were available, where transcripts were classified as either "Escape" (82 transcripts), "Variable" (89 transcripts), "Inactive" (392 transcripts) or "Unknown" (120 transcripts). For each SNP in UKB dataset we determine if it is physically located within a gene to infer the presumable gene and its inactivation status for independent GWS SNPs.

Full detail of Methods and Materials can be found in the Supplementary Methods and Material.
missing, and keeping the markers which meet our quality control criteria in the set of unrelated European individuals (HWE test P<10 -6 and missing call rate <5%). The heterozygous calls in non-PAR region of the X chromosome male genotypes were set to missing. To avoid deflation of heritability estimates on the X chromosome we only analyse the markers with MAF>0.01 in our full sample of European participants. We estimate allele frequencies (AF) of the X-chromosome markers for both sexes and keep the common set of 6,871 PAR and 253,842 non-PAR SNPs.

Phenotype selection.
A total of 20 complex traits were selected for the analysis in the UKB. All analyses as well as phenotype adjustment were performed on a sex-specific basis. The phenotypes were adjusted for covariates and the residuals were transformed to sex-specific zscores (mean=0, variance=1) with the phenotype measure values over 6 standard deviations (SD) away from the mean previously removed from the analysis. For individuals with repeated measures of the phenotype, we estimated the mean value of the observed measures after outlier removal procedure for each assessment visit and used mean age across the visits as a covariate. For each trait the UK Biobank variable identifiers, available sample sizes and covariates are presented in Supplementary Table 1a, as well as the minimum, maximum and mean values of the raw phenotype measures and the standard deviations of the phenotype after adjustment for trait-specific covariates. The discrete phenotypes (educational attainment, smoking status, skin and hair colours) were treated as quantitative (see Supplementary Table 1b for description of the categories) in our association analysis.

Consortium for the Architecture of Gene Expression (CAGE) data
Gene expression and X-chromosome genotype data. Gene expression and X-chromosome genotype data were available in a subset of N=2,130 individuals (N=1,084 males, N=1,046 females) from the Consortium for the Architecture of Gene Expression (CAGE), a study examining the genetic architecture of gene expression in a mixture of pedigree and unrelated individuals (Lloyd-jones et al., 2017). This subset of individuals comes from three cohorts with genotype data on the X chromosome (Powell et al., 2012(Powell et al., , 2013Kim et al., 2014;Leitsalu et al., 2015), and are of European ancestry, as identified by principal component analysis with the HapMap3 populations. Further details are provided in (Lloyd-jones et al., 2017).
Quality control of gene expression data. RNA was collected from whole-blood samples in each cohort and gene expression levels quantified using the Illumina Whole-Genome Expression BeadChips (HT12 v.3 and HT12 v.4). A total of 38,624 gene expression probes were common to all cohorts. Gene expression quality control and normalisation was performed in each cohort separately before concatenation. This included variance stabilisation and quantile normalisation to standardise the distribution of expression levels across samples. To remove hidden and known experimental confounders, gene expression levels were then adjusted for a mean of 39/50 PEER factors (Stegle et al., 2010(Stegle et al., , 2012 across the three cohorts that were not associated with sex (P sex >0.05) in order to preserve the effect of sex on expression and where available, measured covariates such as age, cell counts, and batch effects. Residuals for each cohort were then standardised to z-scores and concatenated across cohorts. The concatenated gene expression dataset was further adjusted for 18/50 PEER factors that were not associated with sex (P sex >0.05) and standardised to z-scores. A total of 36,267 autosomal and 1,639 X-chromosome gene expression probes (corresponding to 26,384 and 1,138 unique genes, respectively) that unambiguously mapped to the genome formed our final gene expression dataset. This included a total of 28 PAR X-chromosome gene expression probes.
Quality control and imputation of genotype data. Genotype data was acquired using different genotyping platforms for each cohort, with quality control performed within each cohort before concatenation. Details for autosomal quality control and imputation are provided in (Lloyd-jones et al., 2017). Briefly, autosomal SNPs were imputed to the 1000 Genomes Phase 1 Version 3 reference panel (Altshuler et al., 2012) within each cohort and concatenated resulting in 7,763,174 SNPs passing quality control, which included filtering SNPs for minor allele frequency (MAF) <0.01, HWE test P<10 −6 , and imputation info score <0.3. This set of imputed autosomal SNPs was further filtered to 1,066,905 HapMap3 SNPs that were common to all three cohorts. This set of imputed autosomal SNPs formed our final dataset.
For each cohort, we used the Sanger Imputation Server (https://imputation.sanger.ac.uk/) to impute SNPs on the non-PAR of the X chromosome to the Haplotype Reference Consortium (HRC, release 1.1) (McCarthy et al., 2016), using the EAGLE2+PBWT pre-phasing and imputation pipeline (Durbin, 2014;Loh et al., 2016). Preimputation checks included ensuring all alleles are on the forward strand, and coordinates and reference alleles are on the GRCh37 assembly. Pre-imputation quality control included filtering X-chromosome genotyped SNPs for MAF<0.01, HWE test P<10 −6 within females, SNP missingness call rate >2%, and genotyped SNPs that are not in the HRC reference panel. A total of 1,228,034 X-chromosome SNPs were available following imputation in each cohort. Post-imputation quality control within cohort included filtering imputed Xchromosome SNPs for MAF<0.01, HWE test P<10 −6 within females, imputation info score <0.3, and multiallelic SNPs. A total of 306,589 imputed X-chromosome SNPs were common to all cohorts and formed the concatenated dataset. We performed further quality control of the concatenated dataset by filtering imputed X-chromosome SNPs for missingness call rate >2%. A total of 190,506 imputed X-chromosome SNPs remained. Additional post-imputation quality control on the concatenated dataset included a comparison of allele frequencies between males and females, which led to the exclusion of 261 SNPs with MAF differences of >0.05 between sexes. A total of 190,245 imputed X-chromosome SNPs formed our final dataset.

Genotype Tissue Expression (GTEx) data
We used the Genotype Tissue Expression project (GTEx v6p release) dataset comprised of RNA-seq data from 39 non-diseased tissue-types for which a sex covariate was available in N=449 deceased human donors as an external validation of our X-chromosome cis-eQTL results across multiple tissue-types. The fully-processed, normalised and filtered RNA-seq GTEx v6p data were downloaded from the GTEx Portal (https://www.gtexportal.org/home/datasets) along with corresponding covariate files. Xchromosome imputed SNP data was obtained from dbGap (Accession phs000424.v6.p1). Briefly, gene expression normalisation included filtering for transcripts with at least 10 samples with RPKM >0.1 and raw read counts greater than 6, quantile normalisation within tissue, and inverse quantile normalisation for each transcript. Sample outliers were identified and excluded using a correlation-based statistic described in (Wright et al., 2014), and samples with less than 10 million mapped reads were excluded. Further details can be found in (Consortium, 2017). Quality control of the X-chromosome imputed SNP data included filtering for MAF<0.05, HWE test P<10 −6 within females, imputation info score <0.4, and multiallelic SNPs. A total of 127,808 imputed SNPs in the non-PAR of the X chromosome were included in our analysis. We restricted our analyses to 22 tissue samples for which within tissue sample size was greater than N=50 in both males and females (Supplementary Table 10). Sample sizes per tissue ranged from N=124 in colon (sigmoid) to N=361 in muscle (skeletal) with a mean of N=226 across the 22 tissues. The proportion of males and females within each tissue ranged from 34% females in heart (atrial appendage) to 44% females in adrenal gland, with a mean of 38% females across all 22 tissues. A total of 1,121 X-linked transcripts (including 31 PAR transcripts) were expressed in at least one tissue of the 22 tissues. The number of X-linked transcripts identified as expressed in each tissue ranged from 726 in pancreas to 916 in thyroid, with a mean of 808 across all 22 tissues (Supplementary Table 10.).

GWAS.
To determine the DC ratios across 20 complex traits and to compare effect sizes of genome-wide significant X-chromosome markers on those phenotypes, we analyse the results of X-chromosome wide analysis (XWAS) (both PAR and non-PAR) performed on a sexspecific basis using BOLT-LMM v2.3 (Loh et al., 2018) in the full set of UKB European males (N m =208,419) and females (N f =247,186). We include a set of HapMap3 SNPs (MAF>0.01 and pairwise R 2 <0.9 in the window of 1000 SNPs) in the mixed model to correct for the population stratification and to account for relatedness. This set of model SNPs (M=561,572) includes autosomal markers, 12,508 non-PAR and 205 PAR SNPs on the X chromosome. All other X-chromosome SNPs are fixed effects and tested for association using linear regression.
Combined analyses. The choice of the optimum meta-and combined analyses depends on the assumptions of dosage compensation and the genotype coding in males (see Supplementary information in Lee et al., 2018). While the true extent of dosage was assigned by mapping transcript gene identifiers from (Tukiainen, A.-C. Villani, et al., 2017). We tested for enrichment of escape/variable status in each tissue using a hypergeometric test. As the proportion of males and females within each tissue is highly skewed towards males, sensitivity analysis included randomly removing male samples from the analysis so that the proportions match that of females within each of the tissues. This is repeated 100 times, with DCC calculated across the 100 replicates. Finally, we identified the top eQTLs among all tissues in the discovery sex, and extracted the corresponding eQTL from the same tissue in the other sex. DCC is calculated as previously described.