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Synthetic surrogates improve power for genome-wide association studies of partially missing phenotypes in population biobanks

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Abstract

Within population biobanks, incomplete measurement of certain traits limits the power for genetic discovery. Machine learning is increasingly used to impute the missing values from the available data. However, performing genome-wide association studies (GWAS) on imputed traits can introduce spurious associations, identifying genetic variants that are not associated with the original trait. Here we introduce a new method, synthetic surrogate (SynSurr) analysis, which makes GWAS on imputed phenotypes robust to imputation errors. Rather than replacing missing values, SynSurr jointly analyzes the original and imputed traits. We show that SynSurr estimates the same genetic effect as standard GWAS and improves power in proportion to the quality of the imputations. SynSurr requires a commonly made missing-at-random assumption but relaxes the requirements of existing imputation methods by not requiring correct model specification. We present extensive simulations and ablation analyses to validate SynSurr and apply it to empower the GWAS of dual-energy X-ray absorptiometry traits within the UK Biobank.

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Fig. 1: Graphical overview of the SynSurr GWAS.
Fig. 2: Unlike imputation-based estimators, SynSurr is robust to misspecification of the imputation model.
Fig. 3: SynSurr controls type I errors across missingness rates and target-surrogate correlations.
Fig. 4: Power of SynSurr across several missing rates, target-surrogate correlations and SNP heritabilities.
Fig. 5: Comparing SynSurr and standard GWAS regarding the number and significance of GWS associations for body composition traits.
Fig. 6: External validation via overlap of GWS variants for body composition with associations from the GWAS Catalog.

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Data availability

This work used genotypes and phenotypes from the UKB. Summary statistics from the DEXA trait analysis will be deposited with the GWAS Catalog, and are available upon reasonable request in the interim.

Code availability

SurrogateRegression v.0.6.0.1 is available as an R54 package on the Comprehensive R Archive Network: https://CRAN.R-project.org/package=SurrogateRegression (ref. 56). The replication code for the analyses presented in this paper is available on GitHub at https://github.com/jianhuig/SyntheticSurrogateAnalysis (ref. 57).

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Acknowledgements

This work was supported by National Institutes of Health grant nos. R35-CA197449 and F31-HL140822 to Z.R.M.; nos. R35-CA197449, U19-CA203654, R01-HL163560, U01-HG012064 and U01-HG009088 to X.L.; and a Natural Sciences and Engineering Research Council of Canada grant no. RGPIN-2021-03734 and a Connaught New Researcher Award to J. Gronsbell. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

Author information

Author notes

  1. These authors jointly supervised this work: **hong Lin, Jessica Gronsbell.

Authors and Affiliations

  1. Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA

    Zachary R. McCaw & **hong Lin

  2. Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada

    Jianhui Gao & Jessica Gronsbell

  3. Department of Statistics, Harvard University, Cambridge, MA, USA

    **hong Lin

  4. Department of Computer Science, University of Toronto, Toronto, Ontario, Canada

    Jessica Gronsbell

  5. Department of Family & Community Medicine, University of Toronto, Toronto, Ontario, Canada

    Jessica Gronsbell

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Contributions

Z.R.M., X.L. and J. Gronsbell designed the study and the experiments. Z.R.M. implemented the software with input from X.L. Z.R.M., J. Gao and J. Gronsbell performed the simulations. J. Gao conducted the analyses of the UKB data. Z.R.M. performed the overlap analysis. Z.R.M. and J. Gronsbell wrote the first draft of the manuscript; all coauthors provided intellectual revisions.

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Correspondence to Zachary R. McCaw or Jessica Gronsbell.

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Z.R.M. is currently an employee of insitro, but he was not at the time of this work; his employer had no role in this study. The other authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Robustness and precision of SynSurr with an uninformative and informative synthetic surrogate.

In all cases, the number of subjects with observed phenotypes was n = 103. The number of subjects with missing phenotypes was varied to achieve the indicated level of missingness. The standard estimator utilizes the observed values of Y only. In panel A, the synthetic surrogate has correlation ρ = 0.00 with the target phenotype, and is in fact independent of the target phenotype. Use of the SynSurr estimator with this uninformative surrogate results in no loss of efficiency relative to the standard analysis. In panel B, the synthetic surrogate has correlation ρ = 0.75 with the target phenotype. SynSurr becomes more efficient as the number of subjects with missing target outcomes increases.The center of the box plot is the median, the upper and lower bounds of the box are the 75th and 25th percentiles, and the whiskers extend from the minimum to the maximum. The number of simulation replicates is 5 × 103.

Extended Data Fig. 2 Signal recovery of SynSurr relative to the oracle GWAS for height and FEV1.

A slope of 1.0 (red line) indicates that the estimated effect sizes are consistent with the oracle effect sizes. Note that although the slope deviates from 1.0 at 90% missigness, the slope approaches 1.0 as missingness declines. The following figure, which assesses signal recovery for standard GWAS, provides a point of comparison for the R2 values.

Extended Data Fig. 3 Signal recovery of imputation-based approaches and SynSurr relative to the oracle GWAS for height with 50% missingness.

A slope of 1.0 (red line) indicates that the estimated effect sizes are consistent with the oracle effect sizes, whereas a slope deviating from 1.0 suggests the presence of bias. The estimated slope of the data is shown by the blue line. In (a) the surrogates and imputations were generated from a random forest model, whereas in (b) they were generated from a linear regression. In (c), the surrogates and imputations were permuted such that they were uncorrelated with the target outcome. In (d), the surrogates and imputations were negated such that the correlation changed direction but not magnitude.

Extended Data Fig. 4 Predicted vs. observed values of body composition phenotypes within the model-building and GWAS data sets.

A random forest was trained to predict each of the 6 body composition phenotypes, obtained via DEXA scan, using 4,584 subjects allocated to the model-building data set. The GWAS dataset consists of 29,577 unrelated subjects with body compositions measured via DEXA. Model inputs included age, sex, height, body weight, body mass index, and 5 impedance measures (whole body, left arm, right arm, left leg and right leg). The estimated slope of the data is shown by the blue line.

Extended Data Fig. 5 Distribution of predicted body masses comparing subjects with and without DEXA measurements.

The violin plot shows the kernel density estimation of the distribution of the data, with the tips of the violin indicating the maximum and minimum observed values among subjects. Sample sizes: n = 29, 577 independent subjects with DEXA measurements; n = 317, 921 subjects without DEXA measurements.

Extended Data Fig. 6 SynSurr remains unbiased and properly controls the type I error when the same data are utilized for model training and for GWAS.

The number of subjects with observed phenotypes was n = 103, while the number with missing phenotypes was varied to achieve the indicated level of missingness. The model that generated the synthetic surrogate was either trained in the GWAS data set or in an independent data set of size n = 103. Upper shows the distribution of effect sizes across 20 × 103. The true genetic effect size is βG = 0.1. The center of the box plot is the median, the upper and lower bounds of the box are the 75th and 25th percentiles, and the whiskers extend from the 5th to the 95th percentile. Lower shows the average χ2 statistic under H0: βG = 0 across 50 × 103 simulation replicates, for which the expected value is 1.0. Error bars are 95% confidence intervals for the mean. Panel A (left) considers a ‘misspecified’ (k = 2) model that can only capture quadratic dependence of Y on X, while Panel B (right) considers a ‘correctly specified’ model (k = 3) that can capture the cubic dependence. As seen, the validity of SynSurr is not contingent on correct specification of the surrogate model.

Extended Data Fig. 7 Survey of assumptions surrounding missing phenotypic data in GWAS.

The methods sections of all studies contributing summary statistics to the GWAS catalog between May 1st and November 1st, 2023, were manually reviewed. Among 47 studies, 24 did not address missing phenotypic data. Of the 23 remaining, 21 made an assumption of missing at random (MAR) or missing completely at random (MCAR).

Extended Data Table 1 Type I error and power of SynSurr across several missing rates and synthetic surrogates
Full size table
Extended Data Table 2 Comparison of SynSurr with proxy and MTAG GWAS for height
Full size table
Extended Data Table 3 Comparison of GWS SNPs discovered by SynSurr with Standard GWAS for the UKB DEXA phenotypes
Full size table

Supplementary information

Supplementary Information

Supplementary Figs. 1–22, Tables 1–22, Methods, Simulations, Genotype quality control and Survey of missing data in the GWAS.

Reporting Summary

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Supplementary Data 1

Accession numbers for the GWAS Catalog overlap analysis.

Supplementary Data 2

DEXA body composition phenotype gene set enrichment analysis.

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McCaw, Z.R., Gao, J., Lin, X. et al. Synthetic surrogates improve power for genome-wide association studies of partially missing phenotypes in population biobanks. Nat Genet (2024). https://doi.org/10.1038/s41588-024-01793-9

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