Abstract
Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose ℓ 1 -norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the ℓ1 -norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.
| Original language | English (US) |
|---|---|
| Article number | 14052 |
| Journal | Scientific reports |
| Volume | 7 |
| Issue number | 1 |
| DOIs | |
| State | Published - Dec 1 2017 |
ASJC Scopus subject areas
- General
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Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty. / Du, Lei; Liu, Kefei; Yao, Xiaohui; Yan, Jingwen; Risacher, Shannon L.; Han, Junwei; Guo, Lei; Saykin, Andrew J.; Shen, Li; Weiner, Michael W.; Aisen, Paul; Petersen, Ronald; Jack, Clifford R.; Jagust, William; Trojanowki, John Q.; Toga, Arthur W.; Beckett, Laurel; Green, Robert C.; Morris, John; Shaw, Leslie M.; Khachaturian, Zaven; Sorensen, Greg; Carrillo, Maria; Kuller, Lew; Raichle, Marc; Paul, Steven; Davies, Peter; Fillit, Howard; Hefti, Franz; Holtzman, David; Mesulam, M. Marcel; Potter, William; Snyder, Peter; Schwartz, Adam; Montine, Tom; Thomas, Ronald G.; Donohue, Michael; Walter, Sarah; Gessert, Devon; Sather, Tamie; Jiminez, Gus; Balasubramanian, Archana B.; Mason, Jennifer; Sim, Iris; Harvey, Danielle; Bernstein, Matthew; Fox, Nick; Thompson, Paul; Schuff, Norbert; Decarli, Charles; Borowski, Bret; Gunter, Jeff; Senjem, Matt; Vemuri, Prashanthi; Jones, David; Kantarci, Kejal; Ward, Chad; Koeppe, Robert A.; Foster, Norm; Reiman, Eric M.; Chen, Kewei; Mathis, Chet; Landau, Susan; Cairns, Nigel J.; Franklin, Erin; Taylor-Reinwald, Lisa; Lee, Virginia; Korecka, Magdalena; Figurski, Michal; Crawford, Karen; Neu, Scott; Foroud, Tatiana M.; Potkin, Steven; Faber, Kelley; Kim, Sungeun; Nho, Kwangsik; Thal, Leon; Buckholtz, Neil; Albert, Marilyn; Frank, Richard; Hsiao, John; Kaye, Jeffrey; Quinn, Joseph; Silbert, Lisa; Lind, Betty; Carter, Raina; Dolen, Sara; Schneider, Lon S.; Pawluczyk, Sonia; Beccera, Mauricio; Teodoro, Liberty; Spann, Bryan M.; Brewer, James; Vanderswag, Helen; Fleisher, Adam; Heidebrink, Judith L.; Lord, Joanne L.; Mason, Sara S.; Albers, Colleen S.; Knopman, David; Johnson, Kris; Doody, Rachelle S.; Villanueva-Meyer, Javier; Pavlik, Valory; Shibley, Victoria; Chowdhury, Munir; Rountree, Susan; Dang, Mimi; Stern, Yaakov; Honig, Lawrence S.; Bell, Karen L.; Ances, Beau; Carroll, Maria; Creech, Mary L.; Franklin, Erin; Mintun, Mark A.; Schneider, Stacy; Oliver, Angela; Marson, Daniel; Geldmacher, David; Love, Marissa Natelson; Griffith, Randall; Clark, David; Brockington, John; Roberson, Erik; Grossman, Hillel; Mitsis, Effie; Shah, Raj C.; Detoledo-Morrell, Leyla; Duara, Ranjan; Greig-Custo, Maria T.; Barker, Warren; Onyike, Chiadi; D'Agostino, Daniel; Kielb, Stephanie; Sadowski, Martin; Sheikh, Mohammed O.; Ulysse, Anaztasia; Gaikwad, Mrunalini; Murali Doraiswamy, P.; Petrella, Jeffrey R.; Borges-Neto, Salvador; Wong, Terence Z.; Coleman, Edward; Arnold, Steven E.; Karlawish, Jason H.; Wolk, David A.; Clark, Christopher M.; Smith, Charles D.; Jicha, Greg; Hardy, Peter; Sinha, Partha; Oates, Elizabeth; Conrad, Gary; Lopez, Oscar L.; Oakley, Mary Ann; Simpson, Donna M.; Porsteinsson, Anton P.; Goldstein, Bonnie S.; Martin, Kim; Makino, Kelly M.; Ismail, M. Saleem; Brand, Connie; Preda, Adrian; Nguyen, Dana; Womack, Kyle; Mathews, Dana; Quiceno, Mary; Levey, Allan I.; Lah, James J.; Cellar, Janet S.; Burns, Jeffrey M.; Swerdlow, Russell H.; Brooks, William M.; Apostolova, Liana; Tingus, Kathleen; Woo, Ellen; Silverman, Daniel H.S.; Lu, Po H.; Bartzokis, George; Graff-Radford, Neill R.; Parfitt, Francine; Poki-Walker, Kim; Farlow, Martin R.; Marie Hake, Ann; Matthews, Brandy R.; Brosch, Jared R.; Herring, Scott; Van Dyck, Christopher H.; Carson, Richard E.; MacAvoy, Martha G.; Varma, Pradeep; Chertkow, Howard; Bergman, Howard; Hosein, Chris; Black, Sandra; Stefanovic, Bojana; Caldwell, Curtis; Robin Hsiung, Ging Yuek; Mudge, Benita; Sossi, Vesna; Feldman, Howard; Assaly, Michele; Finger, Elizabeth; Pasternack, Stephen; Rachisky, Irina; Rogers, John; Trost, Dick; Kertesz, Andrew; Bernick, Charles; Munic, Donna; Rogalski, Emily; Lipowski, Kristine; Weintraub, Sandra; Bonakdarpour, Borna; Kerwin, Diana; Wu, Chuang Kuo; Johnson, Nancy; Sadowsky, Carl; Villena, Teresa; Scott Turner, Raymond; Johnson, Kathleen; Reynolds, Brigid; Sperling, Reisa A.; Johnson, Keith A.; Marshall, Gad; Yesavage, Jerome; Taylor, Joy L.; Lane, Barton; Rosen, Allyson; Tinklenberg, Jared; Sabbagh, Marwan N.; Belden, Christine M.; Jacobson, Sandra A.; Sirrel, Sherye A.; Kowall, Neil; Killiany, Ronald; Budson, Andrew E.; Norbash, Alexander; Lynn Johnson, Patricia; Obisesan, Thomas O.; Wolday, Saba; Allard, Joanne; Lerner, Alan; Ogrocki, Paula; Tatsuoka, Curtis; Fatica, Parianne; Fletcher, Evan; Maillard, Pauline; Olichney, John; Decarli, Charles; Carmichael, Owen; Kittur, Smita; Borrie, Michael; Lee, T. Y.; Bartha, Rob; Johnson, Sterling; Asthana, Sanjay; Carlsson, Cynthia M.; Tariot, Pierre; Burke, Anna; Milliken, Ann Marie; Trncic, Nadira; Fleisher, Adam; Reeder, Stephanie; Bates, Vernice; Capote, Horacio; Rainka, Michelle; Scharre, Douglas W.; Kataki, Maria; Kelly, Brendan; Zimmerman, Earl A.; Celmins, Dzintra; Brown, Alice D.; Pearlson, Godfrey D.; Blank, Karen; Anderson, Karen; Flashman, Laura A.; Seltzer, Marc; Hynes, Mary L.; Santulli, Robert B.; Sink, Kaycee M.; Gordineer, Leslie; Williamson, Jeff D.; Garg, Pradeep; Watkins, Franklin; Ott, Brian R.; Tremont, Geoffrey; Daiello, Lori A.; Salloway, Stephen; Malloy, Paul; Correia, Stephen; Rosen, Howard J.; Miller, Bruce L.; Perry, David; Mintzer, Jacobo; Spicer, Kenneth; Bachman, David; Pomara, Nunzio; Hernando, Raymundo; Sarrael, Antero; Schultz, Susan K.; Ekstam Smith, Karen; Koleva, Hristina; Nam, Ki Won; Shim, Hyungsub; Relkin, Norman; Chaing, Gloria; Lin, Michael; Ravdin, Lisa; Smith, Amanda; Ashok Raj, Balebail; Fargher, Kristin.
In: Scientific reports, Vol. 7, No. 1, 14052, 01.12.2017.Research output: Contribution to journal › Article › peer-review
TY - JOUR
T1 - Pattern Discovery in Brain Imaging Genetics via SCCA Modeling with a Generic Non-convex Penalty
AU - Du, Lei
AU - Liu, Kefei
AU - Yao, Xiaohui
AU - Yan, Jingwen
AU - Risacher, Shannon L.
AU - Han, Junwei
AU - Guo, Lei
AU - Saykin, Andrew J.
AU - Shen, Li
AU - Weiner, Michael W.
AU - Aisen, Paul
AU - Petersen, Ronald
AU - Jack, Clifford R.
AU - Jagust, William
AU - Trojanowki, John Q.
AU - Toga, Arthur W.
AU - Beckett, Laurel
AU - Green, Robert C.
AU - Morris, John
AU - Shaw, Leslie M.
AU - Khachaturian, Zaven
AU - Sorensen, Greg
AU - Carrillo, Maria
AU - Kuller, Lew
AU - Raichle, Marc
AU - Paul, Steven
AU - Davies, Peter
AU - Fillit, Howard
AU - Hefti, Franz
AU - Holtzman, David
AU - Mesulam, M. Marcel
AU - Potter, William
AU - Snyder, Peter
AU - Schwartz, Adam
AU - Montine, Tom
AU - Thomas, Ronald G.
AU - Donohue, Michael
AU - Walter, Sarah
AU - Gessert, Devon
AU - Sather, Tamie
AU - Jiminez, Gus
AU - Balasubramanian, Archana B.
AU - Mason, Jennifer
AU - Sim, Iris
AU - Harvey, Danielle
AU - Bernstein, Matthew
AU - Fox, Nick
AU - Thompson, Paul
AU - Schuff, Norbert
AU - Decarli, Charles
AU - Borowski, Bret
AU - Gunter, Jeff
AU - Senjem, Matt
AU - Vemuri, Prashanthi
AU - Jones, David
AU - Kantarci, Kejal
AU - Ward, Chad
AU - Koeppe, Robert A.
AU - Foster, Norm
AU - Reiman, Eric M.
AU - Chen, Kewei
AU - Mathis, Chet
AU - Landau, Susan
AU - Cairns, Nigel J.
AU - Franklin, Erin
AU - Taylor-Reinwald, Lisa
AU - Lee, Virginia
AU - Korecka, Magdalena
AU - Figurski, Michal
AU - Crawford, Karen
AU - Neu, Scott
AU - Foroud, Tatiana M.
AU - Potkin, Steven
AU - Faber, Kelley
AU - Kim, Sungeun
AU - Nho, Kwangsik
AU - Thal, Leon
AU - Buckholtz, Neil
AU - Albert, Marilyn
AU - Frank, Richard
AU - Hsiao, John
AU - Kaye, Jeffrey
AU - Quinn, Joseph
AU - Silbert, Lisa
AU - Lind, Betty
AU - Carter, Raina
AU - Dolen, Sara
AU - Schneider, Lon S.
AU - Pawluczyk, Sonia
AU - Beccera, Mauricio
AU - Teodoro, Liberty
AU - Spann, Bryan M.
AU - Brewer, James
AU - Vanderswag, Helen
AU - Fleisher, Adam
AU - Heidebrink, Judith L.
AU - Lord, Joanne L.
AU - Mason, Sara S.
AU - Albers, Colleen S.
AU - Knopman, David
AU - Johnson, Kris
AU - Doody, Rachelle S.
AU - Villanueva-Meyer, Javier
AU - Pavlik, Valory
AU - Shibley, Victoria
AU - Chowdhury, Munir
AU - Rountree, Susan
AU - Dang, Mimi
AU - Stern, Yaakov
AU - Honig, Lawrence S.
AU - Bell, Karen L.
AU - Ances, Beau
AU - Carroll, Maria
AU - Creech, Mary L.
AU - Franklin, Erin
AU - Mintun, Mark A.
AU - Schneider, Stacy
AU - Oliver, Angela
AU - Marson, Daniel
AU - Geldmacher, David
AU - Love, Marissa Natelson
AU - Griffith, Randall
AU - Clark, David
AU - Brockington, John
AU - Roberson, Erik
AU - Grossman, Hillel
AU - Mitsis, Effie
AU - Shah, Raj C.
AU - Detoledo-Morrell, Leyla
AU - Duara, Ranjan
AU - Greig-Custo, Maria T.
AU - Barker, Warren
AU - Onyike, Chiadi
AU - D'Agostino, Daniel
AU - Kielb, Stephanie
AU - Sadowski, Martin
AU - Sheikh, Mohammed O.
AU - Ulysse, Anaztasia
AU - Gaikwad, Mrunalini
AU - Murali Doraiswamy, P.
AU - Petrella, Jeffrey R.
AU - Borges-Neto, Salvador
AU - Wong, Terence Z.
AU - Coleman, Edward
AU - Arnold, Steven E.
AU - Karlawish, Jason H.
AU - Wolk, David A.
AU - Clark, Christopher M.
AU - Smith, Charles D.
AU - Jicha, Greg
AU - Hardy, Peter
AU - Sinha, Partha
AU - Oates, Elizabeth
AU - Conrad, Gary
AU - Lopez, Oscar L.
AU - Oakley, Mary Ann
AU - Simpson, Donna M.
AU - Porsteinsson, Anton P.
AU - Goldstein, Bonnie S.
AU - Martin, Kim
AU - Makino, Kelly M.
AU - Ismail, M. Saleem
AU - Brand, Connie
AU - Preda, Adrian
AU - Nguyen, Dana
AU - Womack, Kyle
AU - Mathews, Dana
AU - Quiceno, Mary
AU - Levey, Allan I.
AU - Lah, James J.
AU - Cellar, Janet S.
AU - Burns, Jeffrey M.
AU - Swerdlow, Russell H.
AU - Brooks, William M.
AU - Apostolova, Liana
AU - Tingus, Kathleen
AU - Woo, Ellen
AU - Silverman, Daniel H.S.
AU - Lu, Po H.
AU - Bartzokis, George
AU - Graff-Radford, Neill R.
AU - Parfitt, Francine
AU - Poki-Walker, Kim
AU - Farlow, Martin R.
AU - Marie Hake, Ann
AU - Matthews, Brandy R.
AU - Brosch, Jared R.
AU - Herring, Scott
AU - Van Dyck, Christopher H.
AU - Carson, Richard E.
AU - MacAvoy, Martha G.
AU - Varma, Pradeep
AU - Chertkow, Howard
AU - Bergman, Howard
AU - Hosein, Chris
AU - Black, Sandra
AU - Stefanovic, Bojana
AU - Caldwell, Curtis
AU - Robin Hsiung, Ging Yuek
AU - Mudge, Benita
AU - Sossi, Vesna
AU - Feldman, Howard
AU - Assaly, Michele
AU - Finger, Elizabeth
AU - Pasternack, Stephen
AU - Rachisky, Irina
AU - Rogers, John
AU - Trost, Dick
AU - Kertesz, Andrew
AU - Bernick, Charles
AU - Munic, Donna
AU - Rogalski, Emily
AU - Lipowski, Kristine
AU - Weintraub, Sandra
AU - Bonakdarpour, Borna
AU - Kerwin, Diana
AU - Wu, Chuang Kuo
AU - Johnson, Nancy
AU - Sadowsky, Carl
AU - Villena, Teresa
AU - Scott Turner, Raymond
AU - Johnson, Kathleen
AU - Reynolds, Brigid
AU - Sperling, Reisa A.
AU - Johnson, Keith A.
AU - Marshall, Gad
AU - Yesavage, Jerome
AU - Taylor, Joy L.
AU - Lane, Barton
AU - Rosen, Allyson
AU - Tinklenberg, Jared
AU - Sabbagh, Marwan N.
AU - Belden, Christine M.
AU - Jacobson, Sandra A.
AU - Sirrel, Sherye A.
AU - Kowall, Neil
AU - Killiany, Ronald
AU - Budson, Andrew E.
AU - Norbash, Alexander
AU - Lynn Johnson, Patricia
AU - Obisesan, Thomas O.
AU - Wolday, Saba
AU - Allard, Joanne
AU - Lerner, Alan
AU - Ogrocki, Paula
AU - Tatsuoka, Curtis
AU - Fatica, Parianne
AU - Fletcher, Evan
AU - Maillard, Pauline
AU - Olichney, John
AU - Decarli, Charles
AU - Carmichael, Owen
AU - Kittur, Smita
AU - Borrie, Michael
AU - Lee, T. Y.
AU - Bartha, Rob
AU - Johnson, Sterling
AU - Asthana, Sanjay
AU - Carlsson, Cynthia M.
AU - Tariot, Pierre
AU - Burke, Anna
AU - Milliken, Ann Marie
AU - Trncic, Nadira
AU - Fleisher, Adam
AU - Reeder, Stephanie
AU - Bates, Vernice
AU - Capote, Horacio
AU - Rainka, Michelle
AU - Scharre, Douglas W.
AU - Kataki, Maria
AU - Kelly, Brendan
AU - Zimmerman, Earl A.
AU - Celmins, Dzintra
AU - Brown, Alice D.
AU - Pearlson, Godfrey D.
AU - Blank, Karen
AU - Anderson, Karen
AU - Flashman, Laura A.
AU - Seltzer, Marc
AU - Hynes, Mary L.
AU - Santulli, Robert B.
AU - Sink, Kaycee M.
AU - Gordineer, Leslie
AU - Williamson, Jeff D.
AU - Garg, Pradeep
AU - Watkins, Franklin
AU - Ott, Brian R.
AU - Tremont, Geoffrey
AU - Daiello, Lori A.
AU - Salloway, Stephen
AU - Malloy, Paul
AU - Correia, Stephen
AU - Rosen, Howard J.
AU - Miller, Bruce L.
AU - Perry, David
AU - Mintzer, Jacobo
AU - Spicer, Kenneth
AU - Bachman, David
AU - Pomara, Nunzio
AU - Hernando, Raymundo
AU - Sarrael, Antero
AU - Schultz, Susan K.
AU - Ekstam Smith, Karen
AU - Koleva, Hristina
AU - Nam, Ki Won
AU - Shim, Hyungsub
AU - Relkin, Norman
AU - Chaing, Gloria
AU - Lin, Michael
AU - Ravdin, Lisa
AU - Smith, Amanda
AU - Ashok Raj, Balebail
AU - Fargher, Kristin
N1 - Funding Information: Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California. L. Du was supported by the National Natural Science Foundation of China (61602384); the Natural Science Basic Research Plan in Shaanxi Province of China (2017JQ6001); the China Postdoctoral Science Foundation (2017M613202); and the Fundamental Research Funds for the Central Universities (3102016OQD0065) at Northwestern Polytechnical University. This work was also supported by the National Institutes of Health R01 EB022574, R01 LM011360, U01 AG024904, P30 AG10133, R01 AG19771, UL1 TR001108, R01 AG 042437, R01 AG046171, R01 AG040770; the Department of Defense W81XWH-14-2-0151, W81XWH-13-1-0259, W81XWH-12-2-0012; the National Collegiate Athletic Association 14132004 at Indiana University.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose ℓ 1 -norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the ℓ1 -norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.
AB - Brain imaging genetics intends to uncover associations between genetic markers and neuroimaging quantitative traits. Sparse canonical correlation analysis (SCCA) can discover bi-multivariate associations and select relevant features, and is becoming popular in imaging genetic studies. The L1-norm function is not only convex, but also singular at the origin, which is a necessary condition for sparsity. Thus most SCCA methods impose ℓ 1 -norm onto the individual feature or the structure level of features to pursuit corresponding sparsity. However, the ℓ1 -norm penalty over-penalizes large coefficients and may incurs estimation bias. A number of non-convex penalties are proposed to reduce the estimation bias in regression tasks. But using them in SCCA remains largely unexplored. In this paper, we design a unified non-convex SCCA model, based on seven non-convex functions, for unbiased estimation and stable feature selection simultaneously. We also propose an efficient optimization algorithm. The proposed method obtains both higher correlation coefficients and better canonical loading patterns. Specifically, these SCCA methods with non-convex penalties discover a strong association between the APOE e4 rs429358 SNP and the hippocampus region of the brain. They both are Alzheimer's disease related biomarkers, indicating the potential and power of the non-convex methods in brain imaging genetics.
UR - http://www.scopus.com/inward/record.url?scp=85032193550&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85032193550&partnerID=8YFLogxK
U2 - 10.1038/s41598-017-13930-y
DO - 10.1038/s41598-017-13930-y
M3 - Article
C2 - 29070790
AN - SCOPUS:85032193550
VL - 7
JO - Scientific Reports
JF - Scientific Reports
SN - 2045-2322
IS - 1
M1 - 14052
ER -