Statistical tests and identifiability conditions for pooling and analyzing multisite datasets
Authors: Zhou Hao Henry , Singh Vikas , Johnson Sterling C. , Wahba Grace ,   the Alzheimer’s Disease Neuroimaging Initiative, Fleisher Adam , Preda Adrian , Pierce Aimee , Mintz Akiva , Lerner Alan , Norbash Alexander , Levey Allan I. , Rosen Allyson , Smith Amanda , Ulysse Anaztasia , Budson Andrew E. , Saykin Andrew J. , Kertesz Andrew , Oliver Angela , Hake Ann Marie , Burke Anna , Furst Ansgar J. , Sarrael Antero , Porsteinsson Anton P. , Toga Arthur W. , Lamb Ashley , Lee Athena , Raj Balebail Ashok , Lane Barton , Yanez Beatriz , Ances Beau , Mudge Benita ,   Berkeley, Lind Betty , Stefanovic Bojana , Goldstein Bonnie , Goldstein Bonnie S. , Bonakdarpour Borna , Matthews Brandy R. , Borowski Bret , Ott Brian R. , Reynolds Brigid , Miller Bruce L. , Spann Bryan M. , Sadowsky Carl , Ward Chad , Bernick Charles , Smith Charles D. ,   Charles DeCArli, Mathis Chet , Onyike Chiadi , Heyn Chris (Chinthaka) , Hosein Chris , Leach Christi , Belden Christine M. , van Dyck Christopher H. , Clark Christopher M. , Wu Chuang-Kuo , Jack Clifford R. , Albers Colleen S. , Brand Connie , Bodge Courtney , Nelson Craig , Tatsuoka Curtis , Carlsson Cynthia M. , Mathews Dana , Nguyen Dana , Catalinotto Daniel , D’Agostino Daniel , Silverman Daniel H.S. , Marson Daniel , Varon Daniel , Harvey Danielle , Fernandez Dariella , Wolk David A. , Bachman David , Bickford David , Clark David , Geldmacher David , Hart David , Holtzman David , Jones David , Knopman David , Perry David , Winkfield David , Fleischman Debra , Miller Delwyn D. , Reyes Denise , Gessert Devon , Gessert Devon , Kerwin Diana , Drost Dick , Massoglia Dino , Simpson Donna M. , Munic Donna , Scharre Douglas W. , Celmins Dzintra , Zimmerman Earl A. , Teng Edmond , Coleman Edward , Zamrini Edward , Mitsis Effie , Peskind Elaine R. , Lilly Eli , Ong Elise , Finger Elizabeth , Oates Elizabeth , Shaffer Elizabeth , Sosa Elizabeth , Woo Ellen , Rogalski Emily , Petrie Eric C. , Reiman Eric M. , Drake Erin , Franklin Erin , Householder Erin , Fletcher Evan , Parfitt Francine , Hefti Franz , Thai Gaby , Marshall Gad A. , Marshall Gad , Li Gail , Conrad Gary , Tremont Geoffrey , Bartzokis George , Hsiung Ging-Yuek Robin , Chiang Gloria , Pearlson Godfrey D. , Jicha Greg , Sorensen Greg , Jimenez Gustavo , Vanderswag Helen , Grossman Hillel , Capote Horacio , Bergman Howard , Chertkow Howard , Feldman Howard , Fillit Howard , Rosen Howard J. , Rosen Howard , Koleva Hristina , Shim Hyungsub , Rachinsky Irina , Fruehling J. Jay , Mintzer Jacobo , Hayes Jacqueline , Ziolkowski Jaimie , Brewer James , Lah James J. , Singleton-Garvin Jamika , Cellar Janet S. , Brosch Jared R. , Tinklenberg Jared , Karlawish Jason H. , Villanueva-Meyer Javier , Gunter Jeff , Kaye Jeffrey A. , Burns Jeffrey M. , Petrella Jeffrey R. , Salazar Jennifer , Yesavage Jerome A. , Yesavage Jerome , Allard Joanne , Lord Joanne L. , Hetelle Joel , Brockington John , Morris John C. , Hsiao John , Morris John , Olichney John , Trojanowki John Q. , Rogers John , Grafman Jordan , Quinn Joseph , Kass Joseph S. , Taylor Joy L. , Heidebrink Judith L. , Anderson Karen , Blank Karen , Crawford Karen , Smith Karen Ekstam , Bell Karen L. , Friedl Karl , Johnson Kathleen , Tingus Kathleen , DeMarco Kathryn , Sink Kaycee M. , Johnson Keith A. , Kantarci Kejal , Faber Kelley , Faber Kelley M. , Behan Kelly , Harless Kelly , Makino Kelly M. , Nudelman Kelly N. , Scherer Kelly , Spicer Kenneth , Chen Kewei , Nam Ki Won , Martin Kim , Poki-Walker Kim , Martin Kimberly S. , Arfanakis Konstantinos , Johnson Kris , Fargher Kristin , Lipowski Kristine , Nho Kwangsik , Womack Kyle , Flashman Laura A. , Beckett Laurel , Honig Lawrence S. , Thal Lean , Thal Leon , Shaw Leslie M. , Kuller Lew , Shen Li , Apostolova Liana , Teodoro Liberty , Hergesheimen Lindsey , Hergesheimer Lindsey , Silbert Lisa C. , Ravdin Lisa , Taylor-Reinwald Lisa , Schneider Lon S. , Daiello Lori A. , Mesulam M. Marcel , Ismail M. Saleem , Korecka Magdalena , Raichle Marc , Seltzer Marc , Mesulam Marek-Marsel , Carrillo Maria , Carroll Maria , Kataki Maria , Greig Maria T , Greig-Custo Maria T. , Albert Marilyn , Love Marissa Natelson , Mintun Mark A. , Farlow Martin R. , Sadowski Martin , Sabbagh Marwan N. , Creech Mary L. , Hynes Mary L. , Quiceno Mary , Oakley MaryAnn , Senjem Matt , Bernstein Matthew , Becerra Mauricio , Witbracht Megan , Keltz Melanie , Lamar Melissa , Butters Meryl , Yang Mia , Borrie Michael , Donohue Michael , Lin Michael , Weiner Michael W. , Weiner Michael , Figurski Michal , Assaly Michele , Rainka Michelle , Zmuda Michelle , Donohue Mike , Dang Mimi , Sheikh Mohammed O. , Gaikwad Mrunalini , Chowdhury Munir , Trncic Nadira , Johnson Nancy , Kowalksi Nancy , Pacini Nathaniel , Buckholtz Neil , Kowall Neil , Graff-Radford Neill R , Fox Nick , Cairns Nigel J. , Schuff Norbert , Foster Norm , Relkin Norman , Oyonumo Ntekim E. , Pomara Nunzio , Brawman-Mintzer Olga , James Olga , Ogunlana Olu , Lopez Oscar L. , Carmichael Owen , Doraiswamy P. Murali , Fatica Parianne , Johnson Patricia Lynn , Samuels Patricia , Aisen Paul , Malloy Paul , Thompson Paul , Ogrocki Paula , Maillard Pauline , Davies Peter , Hardy Peter , Snyder Peter J. , Snyder Peter , Tariot Pierre , Lu Po H. , Varma Pradeep , Vemuri Prashanthi , Doody Rachelle S. , Carter Raina , Shah Raj C. , Griffith Randall , Yeh Randy , Duara Ranjan , Tarawneh Rawan , Turner Raymond Scott , Hernando Raymundo , Sperling Reisa A. , Raman Rema , Carson Richard E. , Frank Richard , El Khouli Riham , Bartha Rob , Koeppe Robert A. , Santulli Robert B. , Green Robert C. , Killiany Ronald , Petersen Ronald , Rodriguez Rosemarie , Swerdlow Russell H. , Wolday Saba , Borges-Neto Salvador , Stark Samuel , Jacobson Sandra A. , Black Sandra , Harding Sandra , Weintraub Sandra , Asthana Sanjay , Vaishnavi Sanjeev , Dolen Sara , Mason Sara S. , Kremen Sarah , Walter Sarah , Herring Scott , Mackin Scott , Neu Scott , Finley Shannon , Sirrel Sherye A. , Kittur Smita , Pawluczyk Sonia , Schneider Stacy , Kielb Stephanie , Reeder Stephanie , Correia Stephen , Pasternack Stephen , Pasternak Stephen , Salloway Stephen , Johnson Sterling C. , Johnson Sterling , Chao Steven , Arnold Steven E. , Potkin Steven G. , Paul Steven , Potkin Steven , Kim Sungeun , Schultz Susan K. , Landau Susan , Rountree Susan , Foroud Tatiana M. , Wong Terence Z. , Villena Teresa , Neylan Thomas , Obisesan Thomas O. , Montine Tom , Lee T-Y , Pavlik Valory , Bates Vernice , Logovinsky Veronika , Sossi Vesna , Shibley Victoria , Lee Virginia , Martinez Walter , Jagust William , Brooks William M. , Pavlosky William , Potter William , Stern Yaakov , Au Yiu Ho , Cabrera Yuliana , Khachaturian Zaven 
Published: January 2018

When sample sizes are small, the ability to identify weak (but scientifically interesting) associations between a set of predictors and a response may be enhanced by pooling existing datasets. However, variations in acquisition methods and the distribution of participants or observations between datasets, especially due to the distributional shifts in some predictors, may obfuscate real effects when datasets are combined. We present a rigorous statistical treatment of this problem and identify conditions where we can correct the distributional shift. We also provide an algorithm for the situation where the correction is identifiable. We analyze various properties of the framework for testing model fit, constructing confidence intervals, and evaluating consistency characteristics. Our technical development is motivated by Alzheimer’s disease (AD) studies, and we present empirical results showing that our framework enables harmonizing of protein biomarkers, even when the assays across sites differ. Our contribution may, in part, mitigate a bottleneck that researchers face in clinical research when pooling smaller sized datasets and may offer benefits when the subjects of interest are difficult to recruit or when resources prohibit large single-site studies.