Polygenic risk prediction: why and when out-of-sample prediction R2 can exceed SNP-based heritability

Xiaotong Wang; Alicia Walker; Joana A. Revez; Naomi R. Wray; Abdel Abdellaoui; Conor V. Dolan; Jouke Jan Hottenga; Hamdi Mbarek; Christel M. Middeldorp; Yuri Milaneschi; Michel G. Nivard; Wouter J. Peyrot; Danielle Posthuma; Peter M. Visscher; Gonneke Willemsen; Dorret I. Boomsma; E. J.C. de Geus; Gerome Breen; Anders D. Børglum; Patrick F. Sullivan; Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium

doi:10.1016/j.ajhg.2023.06.006

Polygenic risk prediction: why and when out-of-sample prediction R² can exceed SNP-based heritability

Xiaotong Wang, Alicia Walker, Joana A. Revez, Naomi R. Wray^*, Abdel Abdellaoui, Conor V. Dolan, Jouke Jan Hottenga, Hamdi Mbarek, Christel M. Middeldorp, Yuri Milaneschi, Michel G. Nivard, Wouter J. Peyrot, Danielle Posthuma, Peter M. Visscher^*, Gonneke Willemsen, Dorret I. Boomsma, E. J.C. de Geus, Gerome Breen, Anders D. Børglum, Patrick F. SullivanMajor Depressive Disorder Working Group of the Psychiatric Genomics Consortium

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

In polygenic score (PGS) analysis, the coefficient of determination (R²) is a key statistic to evaluate efficacy. R² is the proportion of phenotypic variance explained by the PGS, calculated in a cohort that is independent of the genome-wide association study (GWAS) that provided estimates of allelic effect sizes. The SNP-based heritability (h_SNP², the proportion of total phenotypic variances attributable to all common SNPs) is the theoretical upper limit of the out-of-sample prediction R². However, in real data analyses R² has been reported to exceed h_SNP², which occurs in parallel with the observation that h_SNP² estimates tend to decline as the number of cohorts being meta-analyzed increases. Here, we quantify why and when these observations are expected. Using theory and simulation, we show that if heterogeneities in cohort-specific h_SNP² exist, or if genetic correlations between cohorts are less than one, h_SNP² estimates can decrease as the number of cohorts being meta-analyzed increases. We derive conditions when the out-of-sample prediction R² will be greater than h_SNP² and show the validity of our derivations with real data from a binary trait (major depression) and a continuous trait (educational attainment). Our research calls for a better approach to integrating information from multiple cohorts to address issues of between-cohort heterogeneity.

Original language	English
Pages (from-to)	1207-1215
Number of pages	9
Journal	American Journal of Human Genetics
Volume	110
Issue number	7
DOIs	https://doi.org/10.1016/j.ajhg.2023.06.006
Publication status	Published - 6 Jul 2023

Bibliographical note

Funding Information:
We acknowledge funding from the Australian National Health & Medical Research Council ( 1173790 , 1113400 ), Australian Research Council ( FL180100072 ), and the National Institute of Mental Health ( R01MH124871 , R01MH121545 ). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938 . For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse ( U01 MH109528 and U01 MH1095320 ). Some statistical analyses were carried out on the NL Genetic Cluster Computer ( http://www.geneticcluster.org/ ) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com .

Funding Information:
We acknowledge funding from the Australian National Health & Medical Research Council (1173790, 1113400), Australian Research Council (FL180100072), and the National Institute of Mental Health (R01MH124871, R01MH121545). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938. For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse (U01 MH109528 and U01 MH1095320). Some statistical analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org/) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com. Study motivation, N.R.W. A.M.McI.; theory, X.W. P.M.V. N.R.W.; simulations & analyses, X.W.; data preparation, A.W. J.A.R. G.N. M.J.A.; first draft, X.W. N.R.W. P.M.V.; final draft, all authors read and approved the manuscript. The authors declare no competing interests.

Publisher Copyright:
© 2023 American Society of Human Genetics

Funding

We acknowledge funding from the Australian National Health & Medical Research Council ( 1173790 , 1113400 ), Australian Research Council ( FL180100072 ), and the National Institute of Mental Health ( R01MH124871 , R01MH121545 ). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938 . For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse ( U01 MH109528 and U01 MH1095320 ). Some statistical analyses were carried out on the NL Genetic Cluster Computer ( http://www.geneticcluster.org/ ) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com . We acknowledge funding from the Australian National Health & Medical Research Council (1173790, 1113400), Australian Research Council (FL180100072), and the National Institute of Mental Health (R01MH124871, R01MH121545). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938. For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse (U01 MH109528 and U01 MH1095320). Some statistical analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org/) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com. Study motivation, N.R.W. A.M.McI.; theory, X.W. P.M.V. N.R.W.; simulations & analyses, X.W.; data preparation, A.W. J.A.R. G.N. M.J.A.; first draft, X.W. N.R.W. P.M.V.; final draft, all authors read and approved the manuscript. The authors declare no competing interests.

Funders	Funder number
National Institute of Mental Health	R01MH121545, R01MH124871, HE002938
National Institute of Mental Health
National Institute on Drug Abuse	U01 MH1095320, U01 MH109528
National Institute on Drug Abuse
Pennsylvania Game Commission
Australian Research Council	FL180100072
Australian Research Council
National Health and Medical Research Council	1113400, 1173790
National Health and Medical Research Council

Keywords

meta-analysis
out-of-sample prediction R
polygenic risk prediction
SNP-based heritability

Access to Document

10.1016/j.ajhg.2023.06.006

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Persistent link

Cite this

Wang, X., Walker, A., Revez, J. A., Wray, N. R., Abdellaoui, A., Dolan, C. V., Hottenga, J. J., Mbarek, H., Middeldorp, C. M., Milaneschi, Y., Nivard, M. G., Peyrot, W. J., Posthuma, D., Visscher, P. M., Willemsen, G., Boomsma, D. I., de Geus, E. J. C., Breen, G., Børglum, A. D., ... Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium (2023). Polygenic risk prediction: why and when out-of-sample prediction R² can exceed SNP-based heritability. American Journal of Human Genetics, 110(7), 1207-1215. https://doi.org/10.1016/j.ajhg.2023.06.006

@article{e441e583fce6466fb962bb2c9c6b6e17,

title = "Polygenic risk prediction: why and when out-of-sample prediction R2 can exceed SNP-based heritability",

abstract = "In polygenic score (PGS) analysis, the coefficient of determination (R2) is a key statistic to evaluate efficacy. R2 is the proportion of phenotypic variance explained by the PGS, calculated in a cohort that is independent of the genome-wide association study (GWAS) that provided estimates of allelic effect sizes. The SNP-based heritability (hSNP2, the proportion of total phenotypic variances attributable to all common SNPs) is the theoretical upper limit of the out-of-sample prediction R2. However, in real data analyses R2 has been reported to exceed hSNP2, which occurs in parallel with the observation that hSNP2 estimates tend to decline as the number of cohorts being meta-analyzed increases. Here, we quantify why and when these observations are expected. Using theory and simulation, we show that if heterogeneities in cohort-specific hSNP2 exist, or if genetic correlations between cohorts are less than one, hSNP2 estimates can decrease as the number of cohorts being meta-analyzed increases. We derive conditions when the out-of-sample prediction R2 will be greater than hSNP2 and show the validity of our derivations with real data from a binary trait (major depression) and a continuous trait (educational attainment). Our research calls for a better approach to integrating information from multiple cohorts to address issues of between-cohort heterogeneity.",

keywords = "meta-analysis, out-of-sample prediction R, polygenic risk prediction, SNP-based heritability",

author = "Xiaotong Wang and Alicia Walker and Revez, {Joana A.} and Guiyan Ni and Adams, {Mark J.} and McIntosh, {Andrew M.} and Wray, {Naomi R.} and Stephan Ripke and Manuel Mattheisen and Maciej Trzaskowski and Byrne, {Enda M.} and Abdel Abdellaoui and Esben Agerbo and Air, {Tracy M.} and Andlauer, {Till F.M.} and Bacanu, {Silviu Alin} and Marie B{\ae}kvad-Hansen and Beekman, {Aartjan T.F.} and Bigdeli, {Tim B.} and Binder, {Elisabeth B.} and Julien Bryois and Buttensch{\o}n, {Henriette N.} and Jonas Bybjerg-Grauholm and Na Cai and Enrique Castelao and Christensen, {Jane Hvarregaard} and Clarke, {Toni Kim} and Coleman, {Jonathan R.I.} and Luc{\'i}a Colodro-Conde and Baptiste Couvy-Duchesne and Nick Craddock and Crawford, {Gregory E.} and Gail Davies and Franziska Degenhardt and Derks, {Eske M.} and Nese Direk and Dolan, {Conor V.} and Dunn, {Erin C.} and Eley, {Thalia C.} and Valentina Escott-Price and Kiadeh, {Farnush Farhadi Hassan} and Finucane, {Hilary K.} and Foo, {Jerome C.} and Forstner, {Andreas J.} and Josef Frank and Gaspar, {H{\'e}l{\'e}na A.} and Michael Gill and Goes, {Fernando S.} and Gordon, {Scott D.} and Jakob Grove and Hall, {Lynsey S.} and {S{\o}holm Hansen}, Christine and Hansen, {Thomas F.} and Stefan Herms and Hickie, {Ian B.} and Per Hoffmann and Georg Homuth and Carsten Horn and Hottenga, {Jouke Jan} and Hougaard, {David M.} and Howard, {David M.} and Marcus Ising and Rick Jansen and Ian Jones and Jones, {Lisa A.} and Eric Jorgenson and Knowles, {James A.} and Kohane, {Isaac S.} and Julia Kraft and Kretzschmar, {Warren W.} and Zolt{\'a}n Kutalik and Yihan Li and Lind, {Penelope A.} and MacIntyre, {Donald J.} and MacKinnon, {Dean F.} and Maier, {Robert M.} and Wolfgang Maier and Jonathan Marchini and Hamdi Mbarek and Patrick McGrath and Peter McGuffin and Medland, {Sarah E.} and Divya Mehta and Middeldorp, {Christel M.} and Evelin Mihailov and Yuri Milaneschi and Lili Milani and Mondimore, {Francis M.} and Montgomery, {Grant W.} and Sara Mostafavi and Niamh Mullins and Matthias Nauck and Bernard Ng and Nivard, {Michel G.} and Nyholt, {Dale R.} and O'Reilly, {Paul F.} and Hogni Oskarsson and Owen, {Michael J.} and Painter, {Jodie N.} and {B{\o}cker Pedersen}, Carsten and {Gi{\o}rtz Pedersen}, Marianne and Peterson, {Roseann E.} and Peyrot, {Wouter J.} and Giorgio Pistis and Danielle Posthuma and Quiroz, {Jorge A.} and Per Qvist and Rice, {John P.} and Riley, {Brien P.} and Margarita Rivera and {Saeed Mirza}, Saira and Robert Schoevers and Schulte, {Eva C.} and Ling Shen and Jianxin Shi and Shyn, {Stanley I.} and Engilbert Sigurdsson and Sinnamon, {Grant C.B.} and Smit, {Johannes H.} and Smith, {Daniel J.} and Hreinn Stefansson and Stacy Steinberg and Fabian Streit and Jana Strohmaier and Tansey, {Katherine E.} and Henning Teismann and Alexander Teumer and Wesley Thompson and Thomson, {Pippa A.} and Thorgeirsson, {Thorgeir E.} and Matthew Traylor and Jens Treutlein and Vassily Trubetskoy and Uitterlinden, {Andr{\'e} G.} and Daniel Umbricht and {Van der Auwera}, Sandra and {van Hemert}, {Albert M.} and Alexander Viktorin and Visscher, {Peter M.} and Yunpeng Wang and Webb, {Bradley T.} and Weinsheimer, {Shantel Marie} and J{\"u}rgen Wellmann and Gonneke Willemsen and Witt, {Stephanie H.} and Yang Wu and Xi, {Hualin S.} and Jian Yang and Futao Zhang and Volker Arolt and Baune, {Bernhard T.} and Klaus Berger and Boomsma, {Dorret I.} and Sven Cichon and Udo Dannlowski and {de Geus}, {E. J.C.} and DePaulo, {J. Raymond} and Enrico Domenici and Katharina Domschke and T{\~o}nu Esko and Grabe, {Hans J.} and Hamilton, {Steven P.} and Caroline Hayward and Heath, {Andrew C.} and Kendler, {Kenneth S.} and Stefan Kloiber and Glyn Lewis and Li, {Qingqin S.} and Susanne Lucae and Madden, {Pamela A.F.} and Magnusson, {Patrik K.} and Martin, {Nicholas G.} and Andres Metspalu and Ole Mors and {Bo Mortensen}, Preben and Bertram M{\"u}ller-Myhsok and Merete Nordentoft and N{\"o}then, {Markus M.} and O'Donovan, {Michael C.} and Paciga, {Sara A.} and Pedersen, {Nancy L.} and Penninx, {Brenda W.J.H.} and Perlis, {Roy H.} and Porteous, {David J.} and Potash, {James B.} and Martin Preisig and Marcella Rietschel and Catherine Schaefer and Schulze, {Thomas G.} and Smoller, {Jordan W.} and Kari Stefansson and Henning Tiemeier and Rudolf Uher and Henry V{\"o}lzke and Weissman, {Myrna M.} and Thomas Werge and Lewis, {Cathryn M.} and Levinson, {Douglas F.} and Gerome Breen and B{\o}rglum, {Anders D.} and Sullivan, {Patrick F.} and {Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium}",

note = "Funding Information: We acknowledge funding from the Australian National Health & Medical Research Council ( 1173790 , 1113400 ), Australian Research Council ( FL180100072 ), and the National Institute of Mental Health ( R01MH124871 , R01MH121545 ). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938 . For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse ( U01 MH109528 and U01 MH1095320 ). Some statistical analyses were carried out on the NL Genetic Cluster Computer ( http://www.geneticcluster.org/ ) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com . Funding Information: We acknowledge funding from the Australian National Health & Medical Research Council (1173790, 1113400), Australian Research Council (FL180100072), and the National Institute of Mental Health (R01MH124871, R01MH121545). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938. For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse (U01 MH109528 and U01 MH1095320). Some statistical analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org/) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com. Study motivation, N.R.W. A.M.McI.; theory, X.W. P.M.V. N.R.W.; simulations & analyses, X.W.; data preparation, A.W. J.A.R. G.N. M.J.A.; first draft, X.W. N.R.W. P.M.V.; final draft, all authors read and approved the manuscript. The authors declare no competing interests. Publisher Copyright: {\textcopyright} 2023 American Society of Human Genetics",

year = "2023",

month = jul,

day = "6",

doi = "10.1016/j.ajhg.2023.06.006",

language = "English",

volume = "110",

pages = "1207--1215",

journal = "American Journal of Human Genetics",

issn = "0002-9297",

publisher = "Cell Press",

number = "7",

}

Wang, X, Walker, A, Revez, JA, Wray, NR, Abdellaoui, A, Dolan, CV , Hottenga, JJ, Mbarek, H, Middeldorp, CM, Milaneschi, Y, Nivard, MG, Peyrot, WJ, Posthuma, D, Visscher, PM, Willemsen, G , Boomsma, DI , de Geus, EJC, Breen, G, Børglum, AD, Sullivan, PF & Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium 2023, 'Polygenic risk prediction: why and when out-of-sample prediction R² can exceed SNP-based heritability', American Journal of Human Genetics, vol. 110, no. 7, pp. 1207-1215. https://doi.org/10.1016/j.ajhg.2023.06.006

TY - JOUR

T1 - Polygenic risk prediction

T2 - why and when out-of-sample prediction R2 can exceed SNP-based heritability

AU - Wang, Xiaotong

AU - Walker, Alicia

AU - Revez, Joana A.

AU - Ni, Guiyan

AU - Adams, Mark J.

AU - McIntosh, Andrew M.

AU - Wray, Naomi R.

AU - Ripke, Stephan

AU - Mattheisen, Manuel

AU - Trzaskowski, Maciej

AU - Byrne, Enda M.

AU - Abdellaoui, Abdel

AU - Agerbo, Esben

AU - Air, Tracy M.

AU - Andlauer, Till F.M.

AU - Bacanu, Silviu Alin

AU - Bækvad-Hansen, Marie

AU - Beekman, Aartjan T.F.

AU - Bigdeli, Tim B.

AU - Binder, Elisabeth B.

AU - Bryois, Julien

AU - Buttenschøn, Henriette N.

AU - Bybjerg-Grauholm, Jonas

AU - Cai, Na

AU - Castelao, Enrique

AU - Christensen, Jane Hvarregaard

AU - Clarke, Toni Kim

AU - Coleman, Jonathan R.I.

AU - Colodro-Conde, Lucía

AU - Couvy-Duchesne, Baptiste

AU - Craddock, Nick

AU - Crawford, Gregory E.

AU - Davies, Gail

AU - Degenhardt, Franziska

AU - Derks, Eske M.

AU - Direk, Nese

AU - Dolan, Conor V.

AU - Dunn, Erin C.

AU - Eley, Thalia C.

AU - Escott-Price, Valentina

AU - Kiadeh, Farnush Farhadi Hassan

AU - Finucane, Hilary K.

AU - Foo, Jerome C.

AU - Forstner, Andreas J.

AU - Frank, Josef

AU - Gaspar, Héléna A.

AU - Gill, Michael

AU - Goes, Fernando S.

AU - Gordon, Scott D.

AU - Grove, Jakob

AU - Hall, Lynsey S.

AU - Søholm Hansen, Christine

AU - Hansen, Thomas F.

AU - Herms, Stefan

AU - Hickie, Ian B.

AU - Hoffmann, Per

AU - Homuth, Georg

AU - Horn, Carsten

AU - Hottenga, Jouke Jan

AU - Hougaard, David M.

AU - Howard, David M.

AU - Ising, Marcus

AU - Jansen, Rick

AU - Jones, Ian

AU - Jones, Lisa A.

AU - Jorgenson, Eric

AU - Knowles, James A.

AU - Kohane, Isaac S.

AU - Kraft, Julia

AU - Kretzschmar, Warren W.

AU - Kutalik, Zoltán

AU - Li, Yihan

AU - Lind, Penelope A.

AU - MacIntyre, Donald J.

AU - MacKinnon, Dean F.

AU - Maier, Robert M.

AU - Maier, Wolfgang

AU - Marchini, Jonathan

AU - Mbarek, Hamdi

AU - McGrath, Patrick

AU - McGuffin, Peter

AU - Medland, Sarah E.

AU - Mehta, Divya

AU - Middeldorp, Christel M.

AU - Mihailov, Evelin

AU - Milaneschi, Yuri

AU - Milani, Lili

AU - Mondimore, Francis M.

AU - Montgomery, Grant W.

AU - Mostafavi, Sara

AU - Mullins, Niamh

AU - Nauck, Matthias

AU - Ng, Bernard

AU - Nivard, Michel G.

AU - Nyholt, Dale R.

AU - O'Reilly, Paul F.

AU - Oskarsson, Hogni

AU - Owen, Michael J.

AU - Painter, Jodie N.

AU - Bøcker Pedersen, Carsten

AU - Giørtz Pedersen, Marianne

AU - Peterson, Roseann E.

AU - Peyrot, Wouter J.

AU - Pistis, Giorgio

AU - Posthuma, Danielle

AU - Quiroz, Jorge A.

AU - Qvist, Per

AU - Rice, John P.

AU - Riley, Brien P.

AU - Rivera, Margarita

AU - Saeed Mirza, Saira

AU - Schoevers, Robert

AU - Schulte, Eva C.

AU - Shen, Ling

AU - Shi, Jianxin

AU - Shyn, Stanley I.

AU - Sigurdsson, Engilbert

AU - Sinnamon, Grant C.B.

AU - Smit, Johannes H.

AU - Smith, Daniel J.

AU - Stefansson, Hreinn

AU - Steinberg, Stacy

AU - Streit, Fabian

AU - Strohmaier, Jana

AU - Tansey, Katherine E.

AU - Teismann, Henning

AU - Teumer, Alexander

AU - Thompson, Wesley

AU - Thomson, Pippa A.

AU - Thorgeirsson, Thorgeir E.

AU - Traylor, Matthew

AU - Treutlein, Jens

AU - Trubetskoy, Vassily

AU - Uitterlinden, André G.

AU - Umbricht, Daniel

AU - Van der Auwera, Sandra

AU - van Hemert, Albert M.

AU - Viktorin, Alexander

AU - Visscher, Peter M.

AU - Wang, Yunpeng

AU - Webb, Bradley T.

AU - Weinsheimer, Shantel Marie

AU - Wellmann, Jürgen

AU - Willemsen, Gonneke

AU - Witt, Stephanie H.

AU - Wu, Yang

AU - Xi, Hualin S.

AU - Yang, Jian

AU - Zhang, Futao

AU - Arolt, Volker

AU - Baune, Bernhard T.

AU - Berger, Klaus

AU - Boomsma, Dorret I.

AU - Cichon, Sven

AU - Dannlowski, Udo

AU - de Geus, E. J.C.

AU - DePaulo, J. Raymond

AU - Domenici, Enrico

AU - Domschke, Katharina

AU - Esko, Tõnu

AU - Grabe, Hans J.

AU - Hamilton, Steven P.

AU - Hayward, Caroline

AU - Heath, Andrew C.

AU - Kendler, Kenneth S.

AU - Kloiber, Stefan

AU - Lewis, Glyn

AU - Li, Qingqin S.

AU - Lucae, Susanne

AU - Madden, Pamela A.F.

AU - Magnusson, Patrik K.

AU - Martin, Nicholas G.

AU - Metspalu, Andres

AU - Mors, Ole

AU - Bo Mortensen, Preben

AU - Müller-Myhsok, Bertram

AU - Nordentoft, Merete

AU - Nöthen, Markus M.

AU - O'Donovan, Michael C.

AU - Paciga, Sara A.

AU - Pedersen, Nancy L.

AU - Penninx, Brenda W.J.H.

AU - Perlis, Roy H.

AU - Porteous, David J.

AU - Potash, James B.

AU - Preisig, Martin

AU - Rietschel, Marcella

AU - Schaefer, Catherine

AU - Schulze, Thomas G.

AU - Smoller, Jordan W.

AU - Stefansson, Kari

AU - Tiemeier, Henning

AU - Uher, Rudolf

AU - Völzke, Henry

AU - Weissman, Myrna M.

AU - Werge, Thomas

AU - Lewis, Cathryn M.

AU - Levinson, Douglas F.

AU - Breen, Gerome

AU - Børglum, Anders D.

AU - Sullivan, Patrick F.

AU - Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium

N1 - Funding Information: We acknowledge funding from the Australian National Health & Medical Research Council ( 1173790 , 1113400 ), Australian Research Council ( FL180100072 ), and the National Institute of Mental Health ( R01MH124871 , R01MH121545 ). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938 . For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse ( U01 MH109528 and U01 MH1095320 ). Some statistical analyses were carried out on the NL Genetic Cluster Computer ( http://www.geneticcluster.org/ ) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com . Funding Information: We acknowledge funding from the Australian National Health & Medical Research Council (1173790, 1113400), Australian Research Council (FL180100072), and the National Institute of Mental Health (R01MH124871, R01MH121545). This work would not have been possible without the contributions of the investigators who comprise the PGC-MDD working group. The procedures followed in the PGC-MDD working group were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and that proper informed consent was obtained. Data analysis was conducted under the University of Queensland Human Research Ethics Committee approval HE002938. For a full list of acknowledgments and ethical statements of all individual cohorts, please see the original publications. The PGC has received major funding from the US National Institute of Mental Health and the US National Institute on Drug Abuse (U01 MH109528 and U01 MH1095320). Some statistical analyses were carried out on the NL Genetic Cluster Computer (http://www.geneticcluster.org/) hosted by SURFsara who support the PGC through grants to Danielle Posthuma. GWAS summary statistics from 23andMe were included in the meta-analyzed GWAS summary statistics. We thank the customers, research participants, and employees of 23andMe for making this work possible. The study protocol used by 23andMe was approved by an external AAHRPP-accredited institutional review board. The graphical abstract was created with BioRender.com. Study motivation, N.R.W. A.M.McI.; theory, X.W. P.M.V. N.R.W.; simulations & analyses, X.W.; data preparation, A.W. J.A.R. G.N. M.J.A.; first draft, X.W. N.R.W. P.M.V.; final draft, all authors read and approved the manuscript. The authors declare no competing interests. Publisher Copyright: © 2023 American Society of Human Genetics

PY - 2023/7/6

Y1 - 2023/7/6

N2 - In polygenic score (PGS) analysis, the coefficient of determination (R2) is a key statistic to evaluate efficacy. R2 is the proportion of phenotypic variance explained by the PGS, calculated in a cohort that is independent of the genome-wide association study (GWAS) that provided estimates of allelic effect sizes. The SNP-based heritability (hSNP2, the proportion of total phenotypic variances attributable to all common SNPs) is the theoretical upper limit of the out-of-sample prediction R2. However, in real data analyses R2 has been reported to exceed hSNP2, which occurs in parallel with the observation that hSNP2 estimates tend to decline as the number of cohorts being meta-analyzed increases. Here, we quantify why and when these observations are expected. Using theory and simulation, we show that if heterogeneities in cohort-specific hSNP2 exist, or if genetic correlations between cohorts are less than one, hSNP2 estimates can decrease as the number of cohorts being meta-analyzed increases. We derive conditions when the out-of-sample prediction R2 will be greater than hSNP2 and show the validity of our derivations with real data from a binary trait (major depression) and a continuous trait (educational attainment). Our research calls for a better approach to integrating information from multiple cohorts to address issues of between-cohort heterogeneity.

AB - In polygenic score (PGS) analysis, the coefficient of determination (R2) is a key statistic to evaluate efficacy. R2 is the proportion of phenotypic variance explained by the PGS, calculated in a cohort that is independent of the genome-wide association study (GWAS) that provided estimates of allelic effect sizes. The SNP-based heritability (hSNP2, the proportion of total phenotypic variances attributable to all common SNPs) is the theoretical upper limit of the out-of-sample prediction R2. However, in real data analyses R2 has been reported to exceed hSNP2, which occurs in parallel with the observation that hSNP2 estimates tend to decline as the number of cohorts being meta-analyzed increases. Here, we quantify why and when these observations are expected. Using theory and simulation, we show that if heterogeneities in cohort-specific hSNP2 exist, or if genetic correlations between cohorts are less than one, hSNP2 estimates can decrease as the number of cohorts being meta-analyzed increases. We derive conditions when the out-of-sample prediction R2 will be greater than hSNP2 and show the validity of our derivations with real data from a binary trait (major depression) and a continuous trait (educational attainment). Our research calls for a better approach to integrating information from multiple cohorts to address issues of between-cohort heterogeneity.

KW - meta-analysis

KW - out-of-sample prediction R

KW - polygenic risk prediction

KW - SNP-based heritability

UR - http://www.scopus.com/inward/record.url?scp=85164270154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85164270154&partnerID=8YFLogxK

U2 - 10.1016/j.ajhg.2023.06.006

DO - 10.1016/j.ajhg.2023.06.006

M3 - Article

C2 - 37379836

AN - SCOPUS:85164270154

SN - 0002-9297

VL - 110

SP - 1207

EP - 1215

JO - American Journal of Human Genetics

JF - American Journal of Human Genetics

IS - 7

ER -