Fareed M, Afzal M. Single nucleotide polymorphism in genome-wide association of human population: A tool for broad spectrum service. Egypt J Med Human Genet. 2013; 14(2):123–34.

Article
Google Scholar

Visscher PM, Wray NR, Zhang Q, Sklar P, McCarthy MI, Brown MA, Yang J. 10 years of gwas discovery: biology, function, and translation. Am J Hum Genet. 2017; 101(1):5–22.

Article
CAS
PubMed
PubMed Central
Google Scholar

Visscher PM, Brown MA, McCarthy MI, Yang J. Five years of gwas discovery. Am J Hum Genet. 2012; 90(1):7–24.

Article
CAS
PubMed
PubMed Central
Google Scholar

De R, Bush W, Moore J. Bioinformatics challenges in genome-wide association studies (gwas). Methods Mol Biol (Clifton, NJ). 2014; 1168:63–81.

Article
Google Scholar

Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MA, Bender D, Maller J, Sklar P, De Bakker PI, Daly MJ, et al. Plink: a tool set for whole-genome association and population-based linkage analyses. Am J Hum Genet. 2007; 81(3):559–75.

Article
CAS
PubMed
PubMed Central
Google Scholar

Evangelou E, Ioannidis JP. Meta-analysis methods for genome-wide association studies and beyond. Nat Rev Genet. 2013; 14(6):379–89.

Article
CAS
PubMed
Google Scholar

Willer CJ, Li Y, Abecasis GR. Metal: fast and efficient meta-analysis of genomewide association scans. Bioinformatics. 2010; 26(17):2190–1.

Article
CAS
PubMed
PubMed Central
Google Scholar

Mägi R, Morris AP. Gwama: software for genome-wide association meta-analysis. BMC Bioinformatics. 2010; 11(1):288.

Article
PubMed
PubMed Central
Google Scholar

Lunetta KL. Methods for meta-analysis of genetic data. Curr Protoc Human Genet. 2013; 77(1):1–24.

Google Scholar

Cantor RM, Lange K, Sinsheimer JS. Prioritizing gwas results: a review of statistical methods and recommendations for their application. Am J Hum Genet. 2010; 86(1):6–22.

Article
CAS
PubMed
PubMed Central
Google Scholar

de Vlaming R, Okbay A, Rietveld CA, Johannesson M, Magnusson PK, Uitterlinden AG, van Rooij FJ, Hofman A, Groenen PJ, Thurik AR, et al.Meta-gwas accuracy and power (metagap) calculator shows that hiding heritability is partially due to imperfect genetic correlations across studies. PLoS Genet. 2017; 13(1):e1006495.

Article
PubMed
PubMed Central
Google Scholar

Gentry C. Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing: 2009. p. 169–78.

Cramer R, Damgård IB, Nielsen JB. Secure Multiparty Computation and Secret Sharing. Cambridge: Cambridge University Press; 2015.

Book
Google Scholar

McMahan B, Moore E, Ramage D, Hampson S, y Arcas BA. Communication-efficient learning of deep networks from decentralized data. In: Artificial Intelligence and Statistics. Fort Lauderdale: PMLR: 2017. p. 1273–82.

Google Scholar

Konečnỳ J, McMahan HB, Yu FX, Richtárik P, Suresh AT, Bacon D. Federated learning: Strategies for improving communication efficiency. arXiv preprint arXiv:1610.05492. 2016. https://arxiv.org/abs/1610.05492.

Shamir A. How to share a secret. Commun ACM. 1979; 22(11):612–3.

Article
Google Scholar

Kamm L, Bogdanov D, Laur S, Vilo J. A new way to protect privacy in large-scale genome-wide association studies. Bioinformatics. 2013; 29(7):886–93.

Article
CAS
PubMed
PubMed Central
Google Scholar

Cho H, Wu DJ, Berger B. Secure genome-wide association analysis using multiparty computation. Nat Biotechnol. 2018; 36(6):547–51.

Article
CAS
PubMed
PubMed Central
Google Scholar

Shi H, Jiang C, Dai W, Jiang X, Tang Y, Ohno-Machado L, Wang S. Secure multi-party computation grid logistic regression (smac-glore). BMC Med Inf Dec Making. 2016; 16(3):89.

Article
Google Scholar

Constable SD, Tang Y, Wang S, Jiang X, Chapin S. Privacy-preserving gwas analysis on federated genomic datasets. BMC Med Inf Dec Making. 2015; 15:1–9.

Google Scholar

Alexandru AB, Pappas GJ. Secure multi-party computation for cloud-based control. In: Privacy in Dynamical Systems. Singapore: Springer: 2020. p. 179–207.

Google Scholar

Lu W-J, Yamada Y, Sakuma J. Privacy-preserving genome-wide association studies on cloud environment using fully homomorphic encryption. BMC Med Inf Dec Making. 2015; 15:1–8.

Article
Google Scholar

Morshed T, Alhadidi D, Mohammed N. Parallel linear regression on encrypted data. In: 2018 16th Annual Conference on Privacy, Security and Trust (PST). Los Alamitos: IEEE Computer Society: 2018. p. 1–5.

Google Scholar

Kim M, Song Y, Wang S, Xia Y, Jiang X, et al. Secure logistic regression based on homomorphic encryption: Design and evaluation. JMIR Med Inf. 2018; 6(2):8805.

Google Scholar

Sadat MN, Al Aziz MM, Mohammed N, Chen F, Jiang X, Wang S. Safety: secure gwas in federated environment through a hybrid solution. IEEE/ACM Trans Comput Biol Bioinforma. 2018; 16(1):93–102.

Article
Google Scholar

Chialva D, Dooms A. Conditionals in homomorphic encryption and machine learning applications. arXiv preprint arXiv:1810.12380. 2018. https://arxiv.org/abs/1810.12380.

Wang S, Jiang X, Wu Y, Cui L, Cheng S, Ohno-Machado L. Expectation propagation logistic regression (explorer): distributed privacy-preserving online model learning. J Biomed Inf. 2013; 46(3):480–96.

Article
Google Scholar

Wu Y, Jiang X, Kim J, Ohno-Machado L. Grid binary logistic regression (glore): building shared models without sharing data. J Am Med Inf Assoc. 2012; 19(5):758–64.

Article
Google Scholar

Jiang W, Li P, Wang S, Wu Y, Xue M, Ohno-Machado L, Jiang X. Webglore: a web service for grid logistic regression. Bioinformatics. 2013; 29(24):3238–40.

Article
CAS
PubMed
PubMed Central
Google Scholar

Nasirigerdeh R, Torkzadehmahani R, Matschinske J, Baumbach J, Rueckert D, Kaissis G. HyFed: A Hybrid Federated Framework for Privacy-preserving Machine Learning. arXiv preprint arXiv:2105.10545. 2021. https://arxiv.org/abs/2105.10545.

Hastie T, Tibshirani R, Friedman J. The Elements of Statistical Learning. Cambridge: Springer; 2009.

Book
Google Scholar

McHugh ML. The chi-square test of independence. Biochemia Med Biochemia Med. 2013; 23(2):143–9.

Article
CAS
Google Scholar

Völzke H, Alte D, Schmidt CO, Radke D, Lorbeer R, Friedrich N, Aumann N, Lau K, Piontek M, Born G, et al. Cohort profile: the study of health in pomerania. Int J Epidemiol. 2011; 40(2):294–307.

Article
PubMed
Google Scholar

Weiss FU, Schurmann C, Guenther A, Ernst F, Teumer A, Mayerle J, Simon P, Völzke H, Radke D, Greinacher A, et al.Fucosyltransferase 2 (fut2) non-secretor status and blood group b are associated with elevated serum lipase activity in asymptomatic subjects, and an increased risk for chronic pancreatitis: a genetic association study. Gut. 2015; 64(4):646–56.

Article
CAS
PubMed
Google Scholar

COPDGene. http://www.copdgene.org/. Accessed 30 Nov 2021.

FinnGen Documentation of R3 release. https://r3.finngen.fi/about. Accessed 30 Nov 2021.

Pillai SG, Ge D, Zhu G, Kong X, Shianna KV, Need AC, Feng S, Hersh CP, Bakke P, Gulsvik A, et al.A genome-wide association study in chronic obstructive pulmonary disease (copd): identification of two major susceptibility loci. PLoS Genet. 2009; 5(3):e1000421.

Article
PubMed
PubMed Central
Google Scholar

Pei Y-F, Tian Q, Zhang L, Deng H-W. Exploring the major sources and extent of heterogeneity in a genome-wide association meta-analysis. Ann Hum Biol. 2016; 80(2):113–22.

CAS
Google Scholar

Lyu L, Yu H, Yang Q. Threats to federated learning: A survey. arXiv preprint arXiv:2003.02133. 2020. https://arxiv.org/abs/2003.02133.

Dwork C. Differential privacy. In: International Colloquium on Automata, Languages, and Programming. Berlin: Springer: 2006. p. 1–12.

Google Scholar

Cover TM. Elements of Information Theory. New York: John Wiley & Sons; 1999.

Google Scholar

Dibert A, Csirmaz L. Infinite secret sharing–examples. J Math Cryptol. 2014; 8(2):141–68.

Article
Google Scholar

Tjell K, Wisniewski R. Privacy in Distributed Computations based on Real Number Secret Sharing. arXiv preprint arXiv:2107.00911. 2021. https://arxiv.org/abs/2107.00911.

Yang Q, Liu Y, Chen T, Tong Y. Federated machine learning: Concept and applications. ACM Trans Intell Syst Technol (TIST). 2019; 10(2):1–19.

Article
Google Scholar

Nasirigerdeh R, Torkzadehmahani R, Baumbach J, Blumenthal DB. On the privacy of federated pipelines. In: Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’21). New York: Association for Computing Machinery: 2021.

Google Scholar

Galinsky KJ, Bhatia G, Loh P-R, Georgiev S, Mukherjee S, Patterson NJ, Price AL. Fast principal-component analysis reveals convergent evolution of adh1b in europe and east asia. Am J Hum Genet. 2016; 98(3):456–472.

Article
CAS
PubMed
PubMed Central
Google Scholar

Kairouz P, McMahan HB, Avent B, Bellet A, Bennis M, Bhagoji AN, Bonawitz K, Charles Z, Cormode G, Cummings R, et al.Advances and open problems in federated learning. arXiv preprint arXiv:1912.04977. 2019. https://arxiv.org/abs/1912.04977.

Zhu L, Han S. Deep leakage from gradients. In: Federated Learning. Cham: Springer: 2020. p. 17–31.

Google Scholar

Melis L, Song C, De Cristofaro E, Shmatikov V. Exploiting unintended feature leakage in collaborative learning. In: 2019 IEEE Symposium on Security and Privacy (SP). Manhattan: IEEE: 2019. p. 691–706.

Google Scholar

Torkzadehmahani R, Nasirigerdeh R, Blumenthal DB, Kacprowski T, List M, Matschinske J, Späth J, Wenke NK, Bihari B, Frisch T, et al.Privacy-preserving Artificial Intelligence Techniques in Biomedicine. arXiv preprint arXiv:2007.11621. 2020. https://arxiv.org/abs/2007.11621.

Bonawitz K, Ivanov V, Kreuter B, Marcedone A, McMahan HB, Patel S, Ramage D, Segal A, Seth K. Practical secure aggregation for privacy-preserving machine learning. In: Proceedings of the 2017 ACM SIGSAC Conference on Computer and Communications Security. New York: Association for Computing Machinery: 2017. p. 1175–91.

Google Scholar

PLINK data formats. http://zzz.bwh.harvard.edu/plink/data.shtml. Accessed 30 Nov 2021.

HyFed API. https://github.com/tum-aimed/hyfed. Accessed 30 Nov 2021.

pandas: Python Data Analysis Library. https://pandas.pydata.org/. Accessed 30 Nov 2021.

Harris CR, Millman KJ, van der Walt SJ, Gommers R, Virtanen P, Cournapeau D, Wieser E, Taylor J, Berg S, Smith NJ, Kern R, Picus M, Hoyer S, van Kerkwijk MH, Brett M, Haldane A, del Río JF, Wiebe M, Peterson P, Gérard-Marchant P, Sheppard K, Reddy T, Weckesser W, Abbasi H, Gohlke C, Oliphant TE. Array programming with NumPy. Nature. 2020; 585(7825):357–62.

Article
CAS
PubMed
PubMed Central
Google Scholar

Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, Burovski E, Peterson P, Weckesser W, Bright J, van der Walt SJ, Brett M, Wilson J, Millman KJ, Mayorov N, Nelson ARJ, Jones E, Kern R, Larson E, Carey CJ, Polat İ, Feng Y, Moore EW, VanderPlas J, Laxalde D, Perktold J, Cimrman R, Henriksen I, Quintero EA, Harris CR, Archibald AM, Ribeiro AH, Pedregosa F, van Mulbregt P, SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nat Methods. 2020; 17:261–272.

Article
CAS
PubMed
PubMed Central
Google Scholar

Nasirigerdeh R, Torkzadehmahani R, Matschinske J, Frisch T, List M, Späth J, Weiss S, Völker U, Pitkänen E, Heider D, Wenke NK, Kaissis G, Rueckert D, Kacprowski T, Baumbach J. splink: a hybrid federated tool as a robust alternative to meta-analysis in genome-wide association studies. Zenodo. 2021. https://doi.org/10.5281/zenodo.5735472.