## Introduction

Many human anthropometric traits are highly heritable. Twin studies have estimated that genetic factors contribute to 40–80% of the observed variability of body mass index (BMI)1,2,3,4,5 and up to 80% of height6, 7. Findings from the largest genome-wide association studies (GWAS) on BMI8 and height9, including over 250,000 samples, revealed 97 and 697 single nucleotide polymorphisms (SNPs) explaining cumulatively only 2.7 and 20% of the variance of the respective phenotypes. Using genotyping arrays enriched for coding regions (exome-chip) large meta-analysis GWAS for height and BMI discovered several rare coding single nucleotide variants (SNVs) associated with these traits. Still, these SNVs have thus far explained only a very small variation in these traits (e.g., 0.51% explained height variance10). Nevertheless, random effect models accounting for imperfect imputation estimate that the total additive effect of all SNVs explain 56 and 27% of height and BMI variability, respectively11. While there is a growing consensus that predominantly SNVs contribute to the heritability, the impact of the structural architecture of the genome (copy number variants, complex rearrangements, etc.) is understudied and not negligible12. It has been shown that rare and large copy number variants (CNVs), such as the 600 kb breakpoint 4–5 (BP4–BP5) 16p11.2 rearrangement13, 14, can exert substantial impact on BMI, but little effort has been made towards assessing the genome-wide impact of CNVs on complex traits. To our knowledge, only one genome-wide CNV-association study (on schizophrenia) has been performed in large adult population samples15. The aim of our study is to establish a genome-wide catalog of CNVs and to identify CNVs associated with height, weight, waist-to-hip ratio ﻿(WHR) and BMI. To this end, we apply the same CNV calling16 and association pipeline to 25 studies of the Genetic Investigation of Anthropometric Traits (GIANT) Consortium combined with the UK Biobank and perform a genome-wide association meta-analysis study in up to 191,161 unrelated European adults. These analyses show that overall CNV burden is linked to shorter stature and higher WHR. The genome-wide scans reveal rare variations in several genomic regions (1q21.1, 7q11.23, 3q29, 16p11.2, FIBIN/BBOX1, and MC4R) to be associated with anthropometric measures. Some of these loci have variable frequencies across cohorts and explain or overlap previous SNP or rare variant associations. These results highlight the important contribution of rare CNVs to complex human traits.

## Results

### Summary of the methods

All the 25 GIANT cohorts were genotyped on Illumina arrays, whereas the UK Biobank used the Affymetrix Axiom chip. Only unrelated adult samples of European origin were included. As PennCNV was initially designed for data generated on Illumina arrays, we took extra care with the signal normalization and pre-processing of the UK Biobank data (see “Methods”). Each cohort applied our standardised CNV pipeline to call CNVs16 and to test associations between probabilistic CNV dosages (a continuous value between −1 (deletion) and 1 (duplication)) at each probe on the genotyping chip and our target anthropometric traits. In brief, our pipeline combines pennCNV calls, CNV- and sample parameters to yield a more accurate probabilistic CNV call, especially in the case of rare or low confidence CNVs. The number of probes varied between ~680,000 and 2,500,000 across the 26 cohorts. We then imputed the summary statistics to the Illumina 1M Duo V3 probe set in order to have a common set of probes for the meta-analysis. Based on an in-house cohort we conservatively estimated the number of effective tests17 to be ~29,400, resulting in a P-value threshold of 1.7 × 10−6 to control family-wise error rate (see “Methods”). We performed a CNV burden and a genome-wide CNV association meta-analysis for BMI, weight, height, and waist–hip ratio. The genome-wide CNV association scan was performed considering a mirror effect model (assuming opposite and equal sized effect of deletions and duplications at any given locus) and the genome-wide significant signals were further tested for deletion-only and duplication-only effects. As secondary analysis, we also tested U-shaped (assuming the same effect of deletions and duplications), deletion-only, duplication-only models genome-wide. All reported CNV effect sizes (unless specified otherwise) represent the impact of one additional copy relative to the population average. For burden analysis all four abovementioned models (mirror, U-shaped, deletion, duplication) were tested. Depending on the trait, the sample sizes varied between 161,244 and 191,161.

### Total CNV burden

The increased burden of rare CNVs has already been observed for persons with short stature18, higher BMI19, and also schizophrenia15. Indirectly, increased deletion burden is also reflected in longer regions with loss-of-heterozygosity, which has shown to associate with stature and cognition20. In this study we confirm the link between CNV burden, measured as the total number of copy variant probes, and height and BMI and we also found an effect on the waist–hip ratio (Supplementary Table 1). Individuals with an additional 1 Mb of copy-altered interval tend to have 0.144 kg/m2 higher BMI (P = 2.9 × 10−3). The effect of CNV burden was much stronger on waist–hip ratio and height, for which increased CNV burden (be it duplication or deletion) was associated with a 0.001 higher WHR (P = 6.9 × 10−5) and 0.132 cm shorter stature (P = 4.5 × 10−7). For both traits the impact was dominated by the burden of deletions rather than duplications (0.003 WHR unit (P = 6 × 10−5) and 0.41 cm (P = 2.5 × 10−10) per Mb deletion, respectively). We did not observe any CNV burden effect on human weight.

### Genome-wide scan

The analyses on these four anthropometric traits revealed seven independent CNV regions associated with one or several traits with P value below the genome-wide significance threshold (1.7 × 10−6, see “Methods”) (Table 1, Fig. 1). Two of them correspond to the well known BP2–BP3 and BP4–BP5 CNVs in the 16p11.2 region associated with BMI and neurodevelopment. Three further CNVs (1q21.1, 3q29, and 7q11.23) overlap recurrent syndromic CNV regions, associated with variable neurodevelopmental traits, schizophrenia and developmental delay. One CNV (near MC4R) overlaps with SNPs associated with BMI in GWAS and is part of a larger deletion reported to be associated with obesity21. And finally one deletion, encompassing BBOX1 and FIBIN genes (the latter harboring rare, height-lowering coding variants10), seems to be particularly frequent in the Finnish population (0.89% vs 0.02% in the non-Finnish cohorts). In the following we provide a detailed description of the impact of each of these CNVs (both deletions and duplications). We tested U-shaped, deletion-only, duplication-only models, but these did not yield further significant associations (Supplementary Table 2).

### New insights on the 16p11.2 region

The 16p11.2 region is well known for several distinct recurrent CNVs, two of them associated with anthropometric traits. The 220 kb BP2–BP3 deletion was associated with severe early-onset obesity and developmental delay22. The 600 kb BP4–BP5 rearrangement was first known for its impact on autism but it has also been proven to have effects on BMI and head circumference13, 14. Both have been recently reported as associated with lower IQ and schizophrenia15. First, we replicated the known effects of the 220 kb deletion (β =  + 3.07 kg/m2, P = 5.3 × 10−8) and the mirror effect of the 600 kb rearrangement (mirror effect: β = −3.66 kg/m2, P = 1.4 × 10−12; deletion: β = 6.15 kg/m2, P = 4.5 × 10−14; duplication: β = −1.81 kg/m2, P = 1.2 × 10−2) on BMI. In addition, we found that while the 220 kb deletion increases BMI through increasing weight (by 10.35 kg, P = 5 × 10−9), the 600 kb deletion does so by both decreasing height (by 5.21 cm, P = 1.1 × 10−14) and increasing weight (6.57 kg, P = 5.3 × 10−5) (Supplementary Figs. 14). Furthermore, our analysis revealed that the 600 kb rearrangement also impacts waist–hip ratio (β = −0.04, P = 2.3 × 10−7) (Supplementary Figs. 3C4C). Neither analyzing deletions and duplications separately, nor their absolute effect showed stronger signal for the 16p11.2 220 kb rearrangement than the mirror effect association. On the contrary, the observed effect from the 600 kb seems almost exclusively driven by the deletion, which demonstrated a stronger signal than the duplications or the pooled results (Supplementary Table 2). The list of the Online Mendelian Inheritance in Man (OMIM) diseases corresponding to the genes present in these two CNVs is available in Supplementary Table 3. The top associations between these CNVs and 27 tested traits in the UK Biobank are listed in Supplementary Tables 47.

We could not narrow down the BMI association signal to the previously proposed SH2B1 (lowest P = 7.7 × 10−8) as it covers other genes, including SPNS1 and LAT (lowest P = 5.3 × 10−8) (Fig. 2). Fine-mapping of the signal using variable breakpoints would be necessary, which are extremely rare due to the regional architecture shaped by segmental duplications and non-allelic homologous recombinations (Supplementary Fig. 2).

Results from previous GWAS revealed BMI-associated SNPs near SH2B1 located in the 220 kb rearrangement and height-associated SNPs near FLJ25404 located in the 600 kb rearrangement highlighting the importance of both common and rare variants in these regions (Supplementary Table 8). Next, we tested whether the previously published three independent BMI-associated SNPs at this locus (rs3888190, rs2650492, and rs4787491) could be explained by the CNV associations in the 16p11.2 region using the UK Biobank data for which both SNPs and CNV calls were available. Our analysis showed that the original BMI-SNP association P values increased substantially (from 2.28 × 10−8, 6.45 × 10−5, 8.67 × 10−6 to 2.94 × 10−4, 3.80 × 10−3, 1.56 × 10−2, respectively) when the most BMI-associated CNV probe was included in the multivariate model. In the meantime the BMI-CNV association signals remained unchanged. Similarly, the height-FLJ25404 (rs11642612) association P value increased more than 100-fold from P = 1.5 × 10−5 to P = 4.35 × 10−3 when including the 16p11.2 CNV probe with strongest height association, indicating that the previously observed SNP-height association may be (at least partially) explained by the 16p11.2 CNV-height association.

Cis eQTL analysis for height- and BMI-associated SNPs located in the 600 kb rearrangement showed a potential effect of these SNPs modulating the expression levels (in whole-blood) of CORO1A (rs11150581, rs11642612) and INO80E (rs11150581, rs11642612, rs2278557, rs6565173, rs9925915) genes (Supplementary Table 9).

### 1q21.1 distal rearrangement

A CNV region on chromosome 1 (145–145.9 Mb, Supplementary Figs. 5 and 6) was associated with both height (β = 3.46 cm, P = 3.8 × 10−10) and weight (β = 6.66 kg, P = 1.7 × 10−6). This rearrangement corresponds to the distal part of the 1q21.1 recurrent CNV (OMIM deletion: #612474; OMIM duplication: #612475). As for the 16p11.2 600 kb CNV, this CNV is known to have a mirror effect on head circumference and to be a potential cause of autism and schizophrenia15, 23. An effect on height has been reported for the deletion, with 25–50% of the carriers having short stature24. In contrast, duplication carriers tend to be in the upper percentiles of height but the effect is less clear. Supporting the effect on height, a common variant in this region, near the FMO5 gene (rs6658763) was associated with height in previous GWAS9 (Supplementary Table 8). This SNP was not significantly associated with height in the UK Biobank (P = 0.14), and thus, no conditional analysis was performed. However, the SNP seems to be independent of the CNV (Deletion: r 2 = 0, Dʹ = 0.005−Duplication r 2 = 0, Dʹ = 0.022 in the UK Biobank). As for the 16p11.2 600 kb rearrangement, the observed effects seem to be mainly due to the deletions (Supplementary Table 2). The list of the OMIM diseases corresponding to the genes present in the CNV is available in Supplementary Table 3. The top associations between this CNV and 27 tested traits in the UK Biobank are listed in Supplementary Tables 10 and 11.

### A CNV overlapping FIBIN and BBOX1

A 220 kb CNV (chr11: 26.97–27.19 Mb, Supplementary Figs. 7 and 8) was associated with height (β = 2.43 cm, P = 1.5 × 10−6). While the duplication frequency is low in all cohorts (0.008–0.016%), the deletion frequency is much higher in the Finnish population than in the others (0.89% vs 0.016%). This region has added interest, because a case-report described an Iranian short-statured girl with homozygous deletion of this region25. Separate analysis of the deletions and duplications showed a highly significant effect from the deletions (β = 2.56 cm, P = 8.2 × 10−8). The involvement of the FIBIN gene for height was also confirmed by the GIANT-exome study on height10 including 381,625 individuals. This study revealed a strong association between the rare (0.3% in ExAC) missense variant rs138273386, located in the FIBIN gene, and height (P = 5.79 × 10−12) (Supplementary Table 12). The top associations between this CNV and 27 tested traits in the UK Biobank are listed in Supplementary Tables 13 and 14.

### CNV in the MC4R region

Single nucleotide coding mutations in the MC4R gene cause severe obesity, and common variants near the gene are associated with BMI8, 26, 27. Our analysis revealed a rare (frequency 0.018% (del), 0.004% (dup)), 300 kb long CNV (55.81–56.05 Mb, Supplementary Figs. 9 and 10) associated with BMI (β = −5.06 kg/m2, P = 2 × 10−7) and weight (β = −15.94 kg, P = 1.4 × 10−8). Follow-up analysis demonstrated that the observed signal is exclusively due to deletions (Supplementary Table 2). This CNV encompasses the BMI-associated lead SNP (rs6567160)8, 28 (Fig. 3, Supplementary Table 8), but we observed virtually identical BMI-association P values for the SNP and the CNV in univariate and multivariate analysis. Hence, the two associations are most probably independent, further evidenced by the low LD between them (r 2 = 0.0014, D′= 0.31 in the UK Biobank). While rare height-increasing MC4R variants27 have been previously reported, we found no height-effect of any CNV probes in this regions. Previous evidence for CNVs affecting BMI in the MC4R gene is scarce—there is only one case report of a 9-year-old obese boy carrying a larger (2.6 Mb) deletion encompassing the MC4R gene21. The top associations between this CNV and 27 tested traits in the UK Biobank are listed in Supplementary Tables 15 and 16.

### 7q11.23 rearrangement

The only WHR-specific genome-wide significant association implicated a CNV in the 7q11.23 region (72.6–73.58 Mb, Supplementary Figs. 11 and 12). Duplication carriers tend to have a higher waist-hip ratio (β = 0.11, P = 1.5 × 10−6). Separate analysis of deletions and duplications and absolute effect association did not show any stronger association, nevertheless, the effect of the duplication is slightly larger than that of the deletion (Supplementary Table 2). This CNV was recently found to be associated with schizophrenia in a large case–control study15. It also overlaps with a 1.55–1.84 Mb long region known as the Williams–Beuren (WB) syndrome critical region (WBSCR)29, 30. WB syndrome31, 32 is responsible for several complications: cardiovascular disease, neurologic abnormalities, attention deficit hyperactivity disorder, cognitive impairment, distinctive behavioral, and social traits. Due to selection bias, our prevalence estimation for the duplication (0.005%) and the deletion (0.005%) is somewhat lower than what is estimated for the WBSCR in the literature (0.005–0.013% for the duplication33, 34 and 0.008–0.013% for the deletion35). The top associations between this CNV and 27 tested traits in the UK Biobank are listed in Supplementary Tables 17 and 18.

### 3q29 rearrangement

We discovered two CNVs in the 3q29 region, one 256 kb long (197.6–197.9 Mb), affecting weight (β = 22.55 kg, P = 1.6 × 10−6, deletion frequency = 0.004%, duplications frequency = 0.005%) and one 212 kb long (198.2–198.4 Mb) affecting height (β = 13.3 cm, P = 2.3 × 10−8, deletion frequency = 0.007%, duplications frequency = 0.007%) (Supplementary Figs. 13 and 14). Running the meta-analysis separately on the UKBB and the other cohorts, it appears that the signal comes mainly from the UK Biobank, however, without evidence for strong heterogeneity (Cochran P > 0.05). The proportional effects on height and weight are concordant with the fact that no association has been found with BMI or WHR. Children with this 3q29 deletion suffer from feeding problems, which may result in reduced adult weight36. A recurrent syndromic CNVs encompassing the two segments has recently been reported to be associated with schizophrenia15. On the anthropometric aspect, case reports from the literature are in agreement with our findings regarding the deletion impact on both weight and height24, 37, 38. Concerning the duplication, the phenotype spectrum is wider and the literature mainly reports obese/overweight cases, which is in agreement with our weight estimates. The reported effect on height is less pronounced. Our (median) deletion frequency (0.004 and 0.007%, for the two segments respectively) is slightly over the reported value in a control population (0.003%)36. Finally, upon closer inspection of the region (Supplementary Fig. 14) we observed that the centromeric part of the CNV is implicated in weight regulation, while the telomeric end impacts height (implicated genes are listed in the legend of Table 1). Deletion and duplication frequencies were too low to be able to reliably establish the effects of deletions and duplications separately. The top associations between this CNV and 27 tested traits in the UK Biobank are listed in Supplementary Tables 1922.

### CNVs with variable frequency across geographic locations

Our meta-analysis revealed two population-specific CNVs. The first one is the CNV overlapping FIBIN and BBOX1, for which Finnish population cohorts have much higher deletion frequency. The second one, near MC4R, is specific for UK population cohorts. In both cases we compared potential confounding factors, such as probe densities, call rates, and CNV quality, but none of these could explain the frequency differences (Supplementary Figs. 8 and 10). Note that the frequency of the MC4R CNV both in the UK Biobank (0.028% (del), 0.005% (dup)) and in other UK cohorts genotyped on Illumina arrays (0.018% (del), 0.009% (dup)) is consistently higher than the frequency in non-UK samples (0.006% (del), 0.005% (dup)). Thus, the observed frequency difference is, at least in part, not due to array effect.

## Discussion

Our genome-wide CNV association meta-analysis on four anthropometric traits in ~190,000 unrelated adults showed a non-negligible CNV burden effect on BMI, height, and WHR. Furthermore, we identified seven CNVs significantly associated with at least one trait and three additional CNV regions have a close to genome-wide significant effect on one of the four traits (Supplementary Table 23). The analysis also gave new insights into the two 16p11.2 rearrangements13, 14, 22.

As a proof of concept, we looked at CNVs known to be associated with BMI or obesity39, 40. Only one CNV (22q11.21) outside the 16p11.2 region was confirmed (Supplementary Fig. 15, Supplementary Tables 24 and 25). This difference might in part be explained by insufficient power or by the fact that, contrary to most previously published CNV studies13, 15, 39, 41, our samples come from general populations. In addition, some of the previously reported CNVs might have been population-specific or simply spurious42.

CNV burden analysis confirmed the already observed effect on BMI19 and height18, and showed an important effect on fat distribution (WHR). These observed signals are dominated by the deletions (up to five-fold larger effects), while the duplication effects are minor, except for WHR. The overall CNV burden has seemingly opposite effects on height and BMI, compatible with having no significant CNV burden effect on weight.

Overall, the genome-wide P values showed good adherence to the null distribution (Supplementary Fig. 16). For well-powered GWAS studies on heritable traits (e.g., height9 and menarche43) high genomic control lambda value rather reflects true polygenic signals than uncorrected population stratification44. This was the case for our study too: while we observed inflated genomic lambda coefficients (λ = 1.16 (height), λ = 1.12 (weight), λ = 1.08 (BMI) and λ = 1.05 (WHR)), upon applying LD score regression44 in the UK Biobank sample the intercept terms revealed no unaccounted population stratification (λ LD = 0.971(height), λ LD = 1.005(weight), λ LD = 0.993 (BMI), λ LD = 0.942 (WHR)).

Among the seven significant CNVs, two might be ancestry-specific, one Finnish and one British. It is not surprising, as these two populations have contributed the most samples to our meta-analysis. These results show the need for collecting large population cohorts of the same origin since the frequency of many CNVs may vary across populations. Therefore, we believe that in the future, collecting larger, genotyped population-based cohorts from other countries and ethnicities could be an efficient way to discover novel trait-associated CNVs with larger effects.

Although we would have had higher power to detect associations with common CNVs, all of the anthropometric trait-associated CNVs identified in this study are rare (0.01–0.07%). This may be explained by the massive shift of CNV frequency spectrum compared to that of SNVs: based on CNV calls from >191,000 samples we observed that more than 92.4% of the CNVs are present in <1 in 1000 samples and 99.4% of them are rare (<1%). We are unsure whether the reason for the very low number of common CNVs is due to the detection technology or whether it reflects the nature of the underlying genomic events. Given the low frequency of most of the discovered CNVs and the neighboring genome structure, the majority of them may result from de novo and recent rearrangements. The total explained variance for all these rearrangements is 0.09% for BMI, 0.10% for weight, 0.14% for height, and 0.04% for waist–hip ratio.

Our conditional analysis showed that CNV probes in the 16p11.2 region explain a substantial fraction of the association between all previously published SNPs near SH2B1 and BMI and, similarly, the association between the SNP near FLJ25404 and height. None of the remaining associated CNVs showed evidence for tagging common SNPs, nor do they explain known height/BMI-SNP associations. Note, however, that our CNV data are much noisier than SNP calls and thus the measured CNVs are poorer proxies for the true CNV status, which biases the conditional analysis towards the null (no tagging). Still, most of the obtained results are in line with the proposed theory that the majority of the discovered disease-associated common SNPs are not synthetic associations due to rare variant tagging45.

Our study, besides reporting the association with anthropometric traits, can serve as an atlas of CNV maps based on a large general population of European ancestry46, 47 (https://cnvcatalogue.bbmri.nl/ and underlying data in Supplementary Data 1). Similarly to large compendia of sequenced population individuals (e.g., EXaC48) for whole exome-/genome-sequence analysis for rare diseases, our inventory of CNV frequencies could help estimating their pathogenicity in the rare disease setting.

So far, many anthropometric GWASs have focused on BMI or height, but less on weight. In our analysis we found that studying the effect of CNVs on height and weight separately can carry important additional information beyond what we can learn from looking only at BMI. All the CNVs found to be associated with BMI were also associated either with height or weight, but the opposite does not hold. CNVs affecting height and weight in the same direction (e.g., 1q21.1) have less impact on BMI.

Our study has several weaknesses, which we tried to mitigate. Despite the fact that a plethora of software has been developed to detect CNVs from SNP array platforms, these genotyping chips were not initially designed for this purpose. This drawback reduces statistical power in our analysis by introducing false positive and false negative CNV calls. Importantly, there is no particular reason to believe that CNV calling artefacts appear specifically for samples enriched for low/high trait values. Thus, we believe that false CNV calls do not translate to false positive findings, but of course can substantially reduce statistical power. We did not perform independent (e.g., qPCR) experiments to confirm these CNV findings, but provided several lines of evidences to support our claims: (i) most of our reported CNVs have been reported before with similar frequency and breakpoints; (ii) many of our CNVs fall into regions already associated with obesity; (iii) QQ-plots for all traits show excellent adherence to the null for the bulk of the CNV probes (Supplementary Fig. 16); (iv) our top CNVs show little or no heterogeneity across studies; (v) cohorts used 15 different genotyping arrays eliminating array-specific artefacts. Crucially, these genotyping platforms are more reliable than low-coverage sequencing to infer CNVs and thus remain the most cost-efficient to perform such large CNV-association studies. Another limitation is selection bias: As shown in the results, many of the anthropometric trait-associated CNVs we discovered are syndromic and were already observed in patients with specific genomic disorders (including traits like e.g., developmental delay41, schizophrenia15, etc.). In such situations we cannot distinguish whether the effect of those are mere consequence of the primary syndromes or trigger molecular mechanisms that act independently on anthropometric traits. Note, however, that this criticism is valid for any GWAS. The anthropometric effects of most of the syndromic CNVs are often poorly reported due to the small number of cases. We found evidence that 1q21.1 duplication carriers fall to the ~80th population height percentile49, equivalent to ~4 cm of height increase, close to our observed effect of 3.46 cm. Carriers of the 22q11.2 deletion have on average 3 kg/m2 higher BMI by the age of 2050, which is comparable to our estimated effect of 4 kg/m2. Moreover, our pheWAS analysis on 27 traits in the UK Biobank did not identify any non-anthropometric trait to be stronger associated with the discovered CNVs. Furthermore, we could not identify any trend between effects on anthropometric traits and schizophrenia (Supplementary Table 26), indicating that the anthropometric associations we observed cannot be secondary to schizophrenia. These lines of evidence indicate that most of the discovered CNVs affect anthropometric traits either primarily or in a disease-independent fashion. Importantly, the samples we analyzed come from population-based cohorts, healthier than the general population51. Selection bias, thus, removes many carriers of CNVs with larger effects52, implying that the effects seen in our study are potentially smaller than the real ones. A further limitation is the variability in the frequency of such rare CNVs across populations. This phenomenon may render some of these discoveries difficult to replicate across populations, as not only similarly large replication studies would be necessary, but also populations in which the CNV frequency is high enough to yield sufficient statistical power. The final weakness to mention is that—to reduce cohort analyst burden—although we adjusted the analyzed traits for gender, but did not perform sex-specific analysis, which will be the central focus of a future study.

CNV studies in general population cohorts have been neglected in the past due to data availability issues. We have shown that such studies are feasible through a careful re-analysis of existing genotyping data. Our study has identified several height- and obesity-associated rare CNVs with substantial effect. We hope that our study will open new avenues for research to understand the impact of CNVs on human health on an unprecedented scale. The pipeline used for this meta-analysis could be applied with any other type of quantitative trait, and, with some modification, to any binary trait. Given the considerable overlap between CNVs associated with anthropometric traits, developmental delay and schizophrenia, in the future it would be insightful to switch point of view and apply a pheWAS approach in large, phenotype-rich cohorts such as the UK BioBank, allowing deeper interpretation of candidate CNVs.

## Methods

### Cohorts

We conducted the meta-analysis for BMI (N UKBB = 119,873, N GIANT = 71,288), weight (N UKBB = 119,767, N GIANT = 55,416), height (N UKBB = 116,259, N GIANT = 65,706) and waist-hip ratio (N UKBB = 119,867, N GIANT = 41,377) (Supplementary Table 27). All GIANT samples were genotyped on Illumina platforms and the UK BioBank was genotyped on Affymetrix Axiom. Participants of each cohort have signed the informed consent form of the respective study. In addition to the ethical committee approval of each individual study, this meta-analysis effort was also approved by the steering committee of the GIANT Consortium and the ethical review board of the UK Biobank (applications #17085, #16389, #9072). Only unrelated adults (genetic relatedness < 0.1) of European ancestry were included in the study.

### CNV calling

For the Affymetrix Axiom chip, additional preprocessing was necessary: Raw probeset intensity values were quantile-normalized. Briefly, intensities were sorted numerically across each chromosome with missing values being allocated an overall median value to facilitate normalization. The mean intensity across each genotyping batch was then calculated for each sorted position. Mean intensities were then substituted in place of the equivalently ranked raw intensities whilst ignoring missing values. Each transformed intensity value was then log2 transformed for processing in PennCNV-Affy. Mean values of all intensities across each chromosome were checked to ensure that they were the same within each genotyping batch of the UK Biobank. PennCNV-Affy was used to infer genotype clusters, generate Log R Ratio (LRR) and B-Allele Frequencies (BAF). All other cohorts used Illumina arrays, so LRR and BAF values were readily available.

We devised a pipeline that takes as input normalized BAF and LRR for each probe and sample (using the PennCNV software53), assigns probabilistic CNV calls16 and runs association with each trait. The pipeline created a “population B allele frequency” (PFB) file for each cohort based on 200 randomly selected final reports. Adjacent CNVs with small gaps (gap shorter than 20% of the total length) were merged using the default PennCNV parameters. Finally, samples with more than 200 CNVs were excluded from further analysis.

For each CNV probe the pipeline computed a quality score (QS)16. The QS, based on the PennCNV quality metrics, estimates (Supplementary Table 28) the probability for a pennCNV call to be a true positive CNV call. It is a continuous value between −1 and 1, representing the product of the relative copy number (+1 for duplication, −1 for deletion) and the probability of the call being true, i.e., it is the expected copy number dosage relative to the copy neutral (2 copy) state. The QS is computed for each probe j and sample i (QS i,j ) and used as genotype value for CNV-trait association assuming a mirror effect of deletions and duplications. Since the QS accounts for various CNV characteristics (length, number of probes, etc.) we did not apply any filtering on these scores, which was shown to be the most powerful strategy for association16. However, probes with low imputation quality (see below) are filtered out in each cohort.

### CNV associations with anthropometric traits

We focussed on the following anthropometric traits: BMI, weight, height and waist–hip ratio. BMI (kg/m2), weight (kg), and waist–hip ratio were adjusted for sex, age, age2 and the first five principal components of the genotype data when available. Height (in meters) was adjusted for sex, age and the first five principal components of the genotype data when available. The resulting trait residuals were then inverse normal quantile transformed.

As CNV boundaries vary across individuals, all associations were performed at the probe level. For this, CNV calls and quality measures were translated to probe level. For each probe in each cohort, association summary statistics are computed and collected for meta-analysis. The summary statistics for each probe are the mean QS, the sum of squared QS s, the sum of the phenotype–genotype products, the phenotype means and the sum of the squared phenotype values. These quantities are sufficient to compute regression coefficients as if we had access to each individual cohort data, which is, for rare variant associations, advantageous compared to standard inverse-variance meta-analysis.

### Summary statistics imputation

As we collected different SNP arrays with variable probe content we imputed summary statistics to the Illumina 1M probes as reference probe set. For each Illumina 1M probe not present in the summary statistic probe list for a study we imputed its summary statistics based on the closest neighboring probes on each side within a 5 kb window. The imputation weights are set to be inversely proportional to the distance between the target probe and the neighboring probes.

### CNV imputation quality

Analogously to genotype imputation, we used the MACH $${\hat r^{\rm{2}}}$$ measure54 to estimate the quality of the CNVs estimation using the QS. This measure is the ratio of the variance of the Bernoulli distributed probabilistic CNV (taking value 1 with probability |QS i,j |, 0 otherwise) averaged over the samples to the empirical variance of an expected dosage across all samples

$$\hat r^2_j = \frac{{\mathop {\sum }\nolimits_i \left| {{\rm{Q}}{{\rm{S}}_{i,j}}} \right| - {\rm{QS}}_{i,j}^2}}{{\mathop {\sum }\nolimits_i {{\left( {\left| {{\rm{Q}}{{\rm{S}}_{i,j}}} \right| - \overline {{\rm{Q}}{{\rm{S}}_{\cdot,j}}} } \right)}^2}}}$$

where QS i,j represents the QS for individual i and probe j, and $$\overline {{\rm{Q}}{{\rm{S}}_{\cdot,j}}}$$ is the average QS i,j for probe j across the samples. For each cohort, only probes with $$\hat r^2_j \ge 0.1$$ were kept for the meta-analysis. Imputation qualities were also meta-analyzed using sample-size weighting.

### Pipeline

Our published pipeline16 based on bash, perl and R has been implemented to run all pre-meta-analysis steps. In brief, this pipeline formats the genotype files to run CNV calls using PennCNV, it cleans and merges the raw CNV calls, it computes a QS for each CNV and it finally calculates the summary statistics at the probe level. All participating cohorts ran the exact same pipeline and shared summary statistics with us. An example configuration file can be found in the Supplementary Note 1.

### Meta-analysis

We ran fixed effects meta-analysis as described by RAREMETAL55. We directly computed the meta β Meta and seMeta for a given CNV probe from the summary statistics from the multiple cohorts:

$${\beta _{{\rm{Meta}}}} = \frac{{\mathop {\sum }\nolimits_{c}} p{g_{\rm{c}}}}{{\mathop {\sum }\nolimits_{c} g_{c}^2 - {N_{c}}{\rm{*}}{{\overline {{g_{c}}} }^2}}}$$
$${\rm{s}}{{\rm{e}}_{{\rm{Meta}}}} = \sqrt {\frac{1}{{\mathop {\sum }\nolimits_{c} g_{c}^2 - {N_{c}}{\rm{*}}{{\overline {{g_{c}}} }^2}}}}$$

where $$g_{c}^2$$ is the sum of the squared CNV dosage for all individuals in cohort c, pg c is the sum of the products of phenotype × CNV dosage values for all individuals in cohort c, $$\overline {{g_{c}}}$$ is the average CNV dosage in cohort c, and N c is the sample size of cohort c. An overall Z score can be estimated as: Z Meta = β Meta/seMeta. Eventually P values are computed for each probe as: P value = 2 ϕ(−|Z Meta|). All reported results in the paper are based on the full study population, unless stated otherwise (e.g., conditional analysis).

In order to decrease the number of tests and to avoid spurious associations we kept only probes that were CNV in at least four cohorts and had a frequency of at least 0.01%. Beside, using a 1 Mb sliding window over the entire genome, we merged probes with exactly the same summary statistics (frequency, effect size, SE), i.e., highly likely having the same profile across all individuals, within that window.

### Number of effective tests

Based on an in-house cohort (HYPERGENES, N = 2930) we estimated the number of effective tests for the probes that were not discarded at the previous step (N total = 399,665). We computed the QS for this cohort and kept only the probes for which the QS was not zero (N non-zero). For each chromosome we used a 1 Mb window to calculate the number of effective tests locally. The number of effective tests corresponds to the number of probes explaining 99.5% of the variance in the window17. The results for each window and chromosome were then summed to obtain an overall N eff number of effective tests for the non-zero probes. This indicated the strength of dependence between CNV probes, f=N eff /N non-zero. We obtained a ratio of f = 8.23 and applied this scaling constant to the 242,022 probes tested in our meta-analysis study, yielding 29,407 independent tests and subsequently a 1.7 × 10−6 genome-wide significant threshold. To ensure robustness, we repeated the same analysis for each of the 33 batches of the UK Biobank samples and obtained a slightly less stringent ratio (median f = 13.83, CI95% = [8.20, 20.17]), but we preferred to use the more conservative threshold of 1.7 × 10−6.

### CNV burden analysis

For each sample we calculated the total number of (imputed) CNV probes showing deviation from the copy neutral state. To account for uncertainty in the calls and to avoid arbitrary thresholding, we used the absolute QS of each probe (for the U-shaped model) and summed them up for the whole genome. For the other models (deletion-, duplication-only) we used the respective modifications (minus deletion QS, duplication QS). We then ran a linear regression between the total burden score and the various traits and meta-analyzed the results from the 26 cohorts.

### Candidate CNV regions

In order to validate our methodology, we decided to first look at regions already associated with BMI, weight or height. Regions have been defined based on proximity of GWAS SNP8, 9, CNVs report39, genes from OMIM repository15 and from a very recent systematic review of known genes implicated in genetic syndromes with obesity (Table 1 of Kaur et al.40). Regarding the candidate CNVs/genes or the OMIM regions, all high quality (r 2 > 0.5) probes falling into the regions were selected. For each GWAS SNP we selected all the probes with association results in a ±500 kb region around the SNP position. The CNV report cataloged 84 BMI and obesity-associated CNVs from research published since 2008 via PubMed search (see Supplementary Table 2 of the publication by Petersen et al.39). Out of the 84 CNVs, we had good quality probes for 48 of them that we subsequently tested. Out of the 79 OMIM regions for weight and BMI, 37 had good quality probes (r 2 > 0.5). The 96 Kaur et al. genes40 represent 65 regions, out of which 57 are on autosomes and 32 of those contained probes within 10 kb with good imputation quality (r 2 > 0.5). In every candidate region we computed the minimal P value and multiplied it with the number of effective tests for that region to obtain one (corrected) P value per region. We then computed quantile–quantile plot to visually inspect potential inflation and computed the fold-enrichment of regions with low P values (P < 0.05).

### GWAS and eQTL lookup

In order to further interpret our findings, we checked whether height-associated coding variants10 were located within our height-associated CNVs. Genes whose expression is modulated by both trait-associated SNPs and CNVs are good gene candidates and can help narrowing down the critical region. To identify such genes, we asked whether known height/BMI-associated SNPs8, 9 act also as cis eQTLs in blood56 for the genes located within height/BMI-associated CNVs.

### Data availability

All association results are available in Supplementary Data 1 and can also be browsed at https://cnvcatalogue.bbmri.nl