Limitations of GCTA as a solution to the missing heritability problem.
Open accessAbstract
Genome-wide association studies (GWASs) seek to understand the relationship between complex phenotype(s) (e.g., height) and up to millions of single-nucleotide polymorphisms (SNPs). Early analyses of GWASs are commonly believed to have "missed" much of the additive genetic variance estimated from correlations between relatives. A more recent method, genome-wide complex trait analysis (GCTA), obtains much higher estimates of heritability using a model of random SNP effects correlated between genotypically similar individuals. GCTA has now been applied to many phenotypes from schizophrenia to scholastic achievement. However, recent studies question GCTA's estimates of heritability. Here, we show that GCTA applied to current SNP data cannot produce reliable or stable estimates of heritability. We show first that GCTA depends sensitively on all singular values of a high-dimensional genetic relatedness matrix (GRM). When the assumptions in GCTA are satisfied exactly, we show that the heritability estimates produced by GCTA will be biased and the standard errors will likely be inaccurate. When the population is stratified, we find that GRMs typically have highly skewed singular values, and we prove that the many small singular values cannot be estimated reliably. Hence, GWAS data are necessarily overfit by GCTA which, as a result, produces high estimates of heritability. We also show that GCTA's heritability estimates are sensitive to the chosen sample and to measurement errors in the phenotype. We illustrate our results using the Framingham dataset. Our analysis suggests that results obtained using GCTA, and the results' qualitative interpretations, should be interpreted with great caution.
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The study directly addresses the concern about lack of replication by replicating results across five countries and health systems.
“In addition to providing exceptional statistical power, the study directly addresses the concern of lack of replication in research findings 31,32 replicating results across 5 countries and health systems.”
From Association of Genetic and Environmental Factors With Autism in a 5-Country Cohort (2019) · cites this paper as [31]
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Association of Genetic and Environmental Factors With Autism in a 5-Country Cohort
Bai, D., Yip, B. H. K., Windham, G. C., Sourander, A., Francis, R., Yoffe, R., Glasson, E., Mahjani, B., Suominen, A., Leonard, H., et al. (2019) · JAMA Psychiatry · doi:10.1001/jamapsychiatry.2019.1411 · Cited by 683 · see citing works
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- Authors
- Krishna Kumar, S., Feldman, M. W., Rehkopf, D. H., & Tuljapurkar, S.
- Affiliations
- Department of Biology, Stanford University, Stanford, CA 94305-5020;
- Stanford University (US)
- Stanford Medicine (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2015-12-22
- Volume
- 113
- Issue
- 1
- Pages
- E61-70
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC4711841
- OpenAlex
- W2222803572
- Cited by
- 128
- References
- 49
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 7 · 2023: 5 · 2022: 12 · 2021: 29 · 2020: 6 · 2019: 24 · 2018: 12 · 2017: 11 · 2016: 18
- FWCI
- 9.39
- Type
- journal article
- Language
- en
- Update notices
- correction (2016-02-01)
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institutes of Health (AG22500)
- Center for Computational, Evolutionary and Human Genomics, Stanford University
- National Institute on Aging (K01AG047280, P01AG022500, AG22500)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Associations and Epidemiology
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic and phenotypic traits in livestock
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Genetic Mapping and Diversity in Plants and Animals
- Keywords
- GCTA, missing heritability, heritability estimation, singular values, overfitting, population stratification, measurement error, single nucleotide polymorphisms, complex traits, Framingham Heart Study
- MeSH terms
- Data Interpretation, Statistical, Genotype, Humans, Phenotype, Quantitative Trait, Heritable, Polymorphism, Single Nucleotide, Genome-Wide Association Study, Datasets as Topic
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