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Statistical Applications in Genetics and Molecular Biology

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Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments

Gordon K Smyth
  • Walter and Eliza Hall Institute
Published Online: 2004-02-12 | DOI: https://doi.org/10.2202/1544-6115.1027

The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.

Keywords: microarrays; empirical Bayes; linear models; hyperparameters; differential expression

Published Online: 2004-02-12

Citation Information: Statistical Applications in Genetics and Molecular Biology. Volume 3, Issue 1, Pages 1–25, ISSN (Online) 1544-6115, DOI: https://doi.org/10.2202/1544-6115.1027, February 2004

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Cardiovascular Research, 2013, Volume 99, Number 4, Page 769
J.-H. Lim, R. D. Iggo, and D. Barker
Nucleic Acids Research, 2013, Volume 41, Number 11, Page 5582
Paul Huber, Tanya Crum, Lynn M. Clary, Tom Ronan, Adelaide V. Packard, and Peter G. Okkema
Cellular and Molecular Life Sciences, 2013, Volume 70, Number 21, Page 4157
Lishan Wang, Weidong Zang, Dongli Xie, Weidong Ji, Yaosheng Pan, Zhiqiang Li, Jiawei Shen, and Yongyong Shi
Tumor Biology, 2013, Volume 34, Number 3, Page 1679
Wei Zhu, Chen Li, and Zhilong Ai
Pathology & Oncology Research, 2013, Volume 19, Number 3, Page 597
M. Radonjic, N. L. M. Cappaert, E. F. J. de Vries, C. E. F. de Esch, F. C. Kuper, A. van Waarde, R. A. J. O. Dierckx, W. J. Wadman, A. P. M. Wolterbeek, R. H. Stierum, and D. M. G. de Groot
Toxicological Sciences, 2013, Volume 133, Number 1, Page 112
R. W. Grant, B. M. Vester Boler, T. K. Ridge, T. K. Graves, and K. S. Swanson
Animal Genetics, 2013, Volume 44, Number 5, Page 560
Leo Lahti, Anne Salonen, Riina A. Kekkonen, Jarkko Salojärvi, Jonna Jalanka-Tuovinen, Airi Palva, Matej Orešič, and Willem M. de Vos
PeerJ, 2013, Volume 1, Page e32
S. Hambleton, S. Goodbourn, D. F. Young, P. Dickinson, S. M. B. Mohamad, M. Valappil, N. McGovern, A. J. Cant, S. J. Hackett, P. Ghazal, N. V. Morgan, and R. E. Randall
Proceedings of the National Academy of Sciences, 2013, Volume 110, Number 8, Page 3053
Mary Portillo, Javier Cabrera, Keith Lindsey, Jen Topping, Maria Fe Andrés, Mariana Emiliozzi, Juan C. Oliveros, Gloria García-Casado, Roberto Solano, Hinanit Koltai, Nathalie Resnick, Carmen Fenoll, and Carolina Escobar
New Phytologist, 2013, Volume 197, Number 4, Page 1276
Ahmed Hossain, Andrew R. Willan, and Joseph Beyene
Communications in Statistics - Simulation and Computation, 2013, Volume 42, Number 7, Page 1563
Xiao-Bing Huang, Jing Li, Lu Zheng, Guo-Hua Zuo, Ke-Qiang Han, Hong-Yan Li, and Ping Liang
Pathology & Oncology Research, 2013, Volume 19, Number 2, Page 251
Hisashi Noma and Shigeyuki Matsui
Statistics in Medicine, 2013, Volume 32, Number 11, Page 1904
C. Hutter, M. Kauer, I. Simonitsch-Klupp, G. Jug, R. Schwentner, J. Leitner, P. Bock, P. Steinberger, W. Bauer, N. Carlesso, M. Minkov, H. Gadner, G. Stingl, H. Kovar, and E. Kriehuber
Blood, 2012, Volume 120, Number 26, Page 5199
S. Corti, M. Nizzardo, C. Simone, M. Falcone, M. Nardini, D. Ronchi, C. Donadoni, S. Salani, G. Riboldi, F. Magri, G. Menozzi, C. Bonaglia, F. Rizzo, N. Bresolin, and G. P. Comi
Science Translational Medicine, 2012, Volume 4, Number 165, Page 165ra162
K. Xu, Z. J. Wu, A. C. Groner, H. H. He, C. Cai, R. T. Lis, X. Wu, E. C. Stack, M. Loda, T. Liu, H. Xu, L. Cato, J. E. Thornton, R. I. Gregory, C. Morrissey, R. L. Vessella, R. Montironi, C. Magi-Galluzzi, P. W. Kantoff, S. P. Balk, X. S. Liu, and M. Brown
Science, 2012, Volume 338, Number 6113, Page 1465
Haidong Zhu, Xiaoling Wang, Huidong Shi, Shaoyong Su, Gregory A. Harshfield, Bernard Gutin, Harold Snieder, and Yanbin Dong
The Journal of Pediatrics, 2013, Volume 162, Number 5, Page 1004
Erin J. Gardiner, Murray J. Cairns, Bing Liu, Natalie J. Beveridge, Vaughan Carr, Brian Kelly, Rodney J. Scott, and Paul A. Tooney
Journal of Psychiatric Research, 2013, Volume 47, Number 4, Page 425
Y. Rahmatallah, F. Emmert-Streib, and G. Glazko
Bioinformatics, 2012, Volume 28, Number 23, Page 3073
Su Fang Wu, Wen Yan Qian, Jia Wen Zhang, Yong Bin Yang, Yuan Liu, Yu Dong, Zhen Bo Zhang, Ya Ping Zhu, and You Ji Feng
Archives of Gynecology and Obstetrics, 2013, Volume 287, Number 4, Page 771
V. Robles-Reglero, I. Santamarta, R. Álvarez-Álvarez, J.F. Martín, and P. Liras
Journal of Biotechnology, 2013, Volume 163, Number 1, Page 69
Eric F. Schmidt, Jennifer L. Warner-Schmidt, Benjamin G. Otopalik, Sarah B. Pickett, Paul Greengard, and Nathaniel Heintz
Cell, 2012, Volume 149, Number 5, Page 1152
Ganna Shevchenko, Magnus Wetterhall, Jonas Bergquist, Kina Höglund, Lars I. Andersson, and Kim Kultima
Journal of Proteome Research, 2012, Page 121030111932006
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Journal of Proteome Research, 2012, Volume 11, Number 11, Page 5235
G. Sateesh Babu and S. Suresh
Expert Systems with Applications, 2013, Volume 40, Number 5, Page 1519
Ada Collura, Laetitia Marisa, Diletta Trojan, Olivier Buhard, Anaïs Lagrange, Arnaud Saget, Marianne Bombled, Patricia Méchighel, Mira Ayadi, Martine Muleris, Aurélien de Reynies, Magali Svrcek, Jean-François Fléjou, Jean-Claude Florent, Florence Mahuteau-Betzer, Anne-Marie Faussat, and Alex Duval
Cellular and Molecular Life Sciences, 2013, Volume 70, Number 4, Page 729
N. Burnichon, A. Buffet, B. Parfait, E. Letouze, I. Laurendeau, C. Loriot, E. Pasmant, N. Abermil, L. Valeyrie-Allanore, J. Bertherat, L. Amar, D. Vidaud, J. Favier, and A.-P. Gimenez-Roqueplo
Human Molecular Genetics, 2012, Volume 21, Number 26, Page 5397
Sharon L. Barrans, Simon Crouch, Matthew A. Care, Lisa Worrillow, Alex Smith, Russell Patmore, David R. Westhead, Reuben Tooze, Eve Roman, and Andrew S Jack
British Journal of Haematology, 2012, Volume 159, Number 4, Page 441
Matthew L. Settles, Tristan Coram, Terence Soule, and Barrie D. Robison
Molecular Ecology Resources, 2012, Volume 12, Number 6, Page 1079
I. Nookaew, M. Papini, N. Pornputtapong, G. Scalcinati, L. Fagerberg, M. Uhlen, and J. Nielsen
Nucleic Acids Research, 2012, Volume 40, Number 20, Page 10084
Tara Pouyani, Suzanne Papp, and Lana Schaffer
In Vitro Cellular & Developmental Biology - Animal, 2012, Volume 48, Number 8, Page 493
George C. Russell, Julio Benavides, Dawn M. Grant, Helen Todd, Jackie Thomson, Vipul Puri, Mintu Nath, and David M. Haig
Virus Research, 2012, Volume 169, Number 1, Page 246
Michael A. Campbell, Alyssa Gleichsner, Lindsay Hilldorfer, David Horvath, and Jeffrey Suttle
Functional & Integrative Genomics, 2012, Volume 12, Number 3, Page 533
Vicente Fresquet, Eloy F. Robles, Anton Parker, Javier Martinez-Useros, Maria Mena, Raquel Malumbres, Xabier Agirre, Susana Catarino, David Arteta, Lourdes Osaba, Manuela Mollejo, Jesus M. Hernandez-Rivas, Maria Jose Calasanz, Masanori Daibata, Martin J.S. Dyer, Felipe Prosper, Esperanza Vizcarra, Miguel-Ángel Piris, David Oscier, and Jose Angel Martinez-Climent
British Journal of Haematology, 2012, Volume 158, Number 6, Page 712
Girum Tadesse Tessema, Trond Møretrø, Lars Snipen, Even Heir, Askild Holck, Kristine Naterstad, and Lars Axelsson
Canadian Journal of Microbiology, 2012, Volume 58, Number 9, Page 1112
Triantafyllos Paparountas, Maria Nefeli Nikolaidou-Katsaridou, Gabriella Rustici, and Vasilis Aidinis
International Journal of Systems Biology and Biomedical Technologies, 2012, Volume 1, Number 3, Page 1
M. Pavon, M. Parreno, M. Tellez-Gabriel, F. Sancho, M. Lopez, M. Cespedes, I. Casanova, A. Lopez-Pousa, M. Mangues, M. Quer, A. Barnadas, X. Leon, and R. Mangues
Carcinogenesis, 2012, Volume 33, Number 9, Page 1707
C. Vitali, F. Mingozzi, A. Broggi, S. Barresi, F. Zolezzi, J. Bayry, G. Raimondi, I. Zanoni, and F. Granucci
Blood, 2012, Volume 120, Number 6, Page 1237
E. Asensio-Juan, C. Gallego, and M. A. Martinez-Balbas
Nucleic Acids Research, 2012, Volume 40, Number 19, Page 9429
Jana Asselman, Dieter I. M. De Coninck, Stephen Glaholt, John K. Colbourne, Colin R. Janssen, Joseph R. Shaw, and Karel A. C. De Schamphelaere
Environmental Science & Technology, 2012, Volume 46, Number 15, Page 8448
Peng Liu and Chong Wang
Journal of Probability and Statistics, 2012, Volume 2012, Page 1
Pim Dekker, David Gunn, Tony McBryan, Roeland W. Dirks, Diana van Heemst, Fei-Ling Lim, Aart G. Jochemsen, Matty Verlaan-de Vries, Julia Nagel, Peter D. Adams, Hans J. Tanke, Rudi G.J. Westendorp, and Andrea B. Maier
Mechanisms of Ageing and Development, 2012, Volume 133, Number 7, Page 498
Shannon L. Costigan, Julieta Werner, Jacob D. Ouellet, Lauren G. Hill, and R. David Law
Aquatic Toxicology, 2012, Volume 122-123, Page 44
C. W. Ribeiro, F. E. L. Carvalho, S. B. Rosa, M. Alves-Ferreira, C. M. B. Andrade, M. Ribeiro-Alves, J. A. G. Silveira, R. Margis, and M. Margis-Pinheiro
Plant Biology, 2012, Volume 14, Number 6, Page 944
Lieceng Zhu, Xuming Liu, Haiyan Wang, Chitvan Khajuria, John C. Reese, R. Jeff Whitworth, Ruth Welti, and Ming-Shun Chen
Molecular Plant-Microbe Interactions, 2012, Volume 25, Number 7, Page 920
Tine L.M. Hectors, Caroline Vanparys, Anna Pereira-Fernandes, Dries Knapen, and Ronny Blust
Toxicology Letters, 2012, Volume 212, Number 2, Page 180
Stefanie De Bodt, Jens Hollunder, Hilde Nelissen, Nick Meulemeester, and Dirk Inzé
New Phytologist, 2012, Volume 195, Number 3, Page 707
A. H. Achtman, S. Pilat, C. W. Law, D. J. Lynn, L. Janot, M. L. Mayer, S. Ma, J. Kindrachuk, B. B. Finlay, F. S. L. Brinkman, G. K. Smyth, R. E. W. Hancock, and L. Schofield
Science Translational Medicine, 2012, Volume 4, Number 135, Page 135ra64
Zhaoping Hong and Heng Lian
Computational Statistics & Data Analysis, 2012, Volume 56, Number 12, Page 4146
I. J. Donaldson, S. Amin, J. J. Hensman, E. Kutejova, M. Rattray, N. Lawrence, A. Hayes, C. M. Ward, and N. Bobola
Nucleic Acids Research, 2012, Volume 40, Number 9, Page 3990
Dong Xin Feng, Céline Tasset, Mathieu Hanemian, Xavier Barlet, Jian Hu, Dominique Trémousaygue, Laurent Deslandes, and Yves Marco
New Phytologist, 2012, Volume 194, Number 4, Page 1035
C. Majer, C. Xu, K. W. Berendzen, and F. Hochholdinger
Philosophical Transactions of the Royal Society B: Biological Sciences, 2012, Volume 367, Number 1595, Page 1542
Katherine Taylor, Olga Kolokoltsova, Michael Patterson, Allison Poussard, Jennifer Smith, D. Mark Estes, and Slobodan Paessler
Vaccine, 2012, Volume 30, Number 27, Page 4095
Babak Shahbaba, Catherine M. Shachaf, and Zhaoxia Yu
Statistics in Medicine, 2012, Volume 31, Number 10, Page 988
M. Wysocki, H. Chen, J. P. Steibel, D. Kuhar, D. Petry, J. Bates, R. Johnson, C. W. Ernst, and J. K. Lunney
Animal Genetics, 2012, Volume 43, Number 3, Page 328
H. Qin, K. Blaschke, G. Wei, Y. Ohi, L. Blouin, Z. Qi, J. Yu, R.-F. Yeh, M. Hebrok, and M. Ramalho-Santos
Human Molecular Genetics, 2012, Volume 21, Number 9, Page 2054
Molecular Ecology, 2013, Volume 22, Number 3, Page 602
Catherine Lachance, Marlène Fortier, Véronique Thimon, Robert Sullivan, Janice L. Bailey, and Pierre Leclerc
International Journal of Andrology, 2010, Volume 33, Number 1, Page 33
C. P. Cabrera, I. C. Dunn, M. Fell, P. W. Wilson, D. W. Burt, D. Waddington, R. Talbot, P. M. Hocking, A. Law, S. Knott, C. S. Haley, and D. J. de Koning
Animal Genetics, 2012, Volume 43, Number 2, Page 163
Minou Nowrousian
Fungal Biology Reviews, 2007, Volume 21, Number 4, Page 171
Tiejun Tong, Homin Jang, and Yuedong Wang
Journal of Multivariate Analysis, 2012, Volume 107, Page 232
Juan Jesús Marín-Méndez, Ana Patiño-García, Victor Segura, Felipe Ortuño, Mª. Dolores Gálvez, and César A. Soutullo
Journal of Affective Disorders, 2012, Volume 138, Number 3, Page 479
Harri Kiiveri and Frank de Hoog
Computational Statistics & Data Analysis, 2012, Volume 56, Number 9, Page 2626
N. Asomaning and K.J. Archer
Computational Statistics & Data Analysis, 2012, Volume 56, Number 6, Page 1748
Klaus Jung, Marian Grade, Jochen Gaedcke, Peter Jo, Lennart Opitz, Heinz Becker, B. Michael Ghadimi, and Tim Beißbarth
Computer Methods and Programs in Biomedicine, 2010, Volume 100, Number 2, Page 132
Guillemette Marot, Jean-Louis Foulley, and Florence Jaffrézic
Computational Statistics & Data Analysis, 2009, Volume 53, Number 5, Page 1630
Ping Xu, Guy N. Brock, and Rudolph S. Parrish
Computational Statistics & Data Analysis, 2009, Volume 53, Number 5, Page 1674
Mike Guether, Raffaella Balestrini, Matthew Hannah, Ji He, Michael K. Udvardi, and Paola Bonfante
New Phytologist, 2009, Volume 182, Number 1, Page 200
Ana M.C. Barradas, Hugo A.M. Fernandes, Nathalie Groen, Yoke Chin Chai, Jan Schrooten, Jeroen van de Peppel, Johannes P.T.M. van Leeuwen, Clemens A. van Blitterswijk, and Jan de Boer
Biomaterials, 2012, Volume 33, Number 11, Page 3205
Marco Muselli, Massimiliano Costacurta, and Francesca Ruffino
Artificial Intelligence in Medicine, 2009, Volume 45, Number 2-3, Page 163
D. J. O'Connell, J. W. K. Ho, T. Mammoto, A. Turbe-Doan, J. T. O'Connell, P. S. Haseley, S. Koo, N. Kamiya, D. E. Ingber, P. J. Park, and R. L. Maas
Science Signaling, 2012, Volume 5, Number 206, Page ra4
Luis E. Nieto-Barajas, Peter Müller, Yuan Ji, Yiling Lu, and Gordon B. Mills
Biometrics, 2012, Volume 68, Number 3, Page 859
Ming Yuan and Christina Kendziorski
Biometrics, 2006, Volume 62, Number 4, Page 1089
G. Yu, Y. Zhao, J. He, D. M. Lonard, C.-A. Mao, G. Wang, M. Li, and X. Li
Journal of Molecular Cell Biology, 2010, Volume 2, Number 4, Page 192
S. Heikkinen, S. Vaisanen, P. Pehkonen, S. Seuter, V. Benes, and C. Carlberg
Nucleic Acids Research, 2011, Volume 39, Number 21, Page 9181
D. K. Birks, A. M. Donson, P. R. Patel, C. Dunham, A. Muscat, E. M. Algar, D. M. Ashley, B. K. Kleinschmidt-DeMasters, R. Vibhakar, M. H. Handler, and N. K. Foreman
Neuro-Oncology, 2011, Volume 13, Number 12, Page 1296
H. E. Lockstone
Briefings in Bioinformatics, 2011, Volume 12, Number 6, Page 634
Samia Daldoul, Sabine Guillaumie, Götz M. Reustle, Gabi Krczal, Abdelwahed Ghorbel, Serge Delrot, Ahmed Mliki, and Michael U. Höfer
Plant Science, 2010, Volume 179, Number 5, Page 489
E. Schafer, R. Irizarry, S. Negi, E. McIntyre, D. Small, M. E. Figueroa, A. Melnick, and P. Brown
Blood, 2010, Volume 115, Number 23, Page 4798
Mark A. van de Wiel and Kyung In Kim
Biometrics, 2007, Volume 63, Number 3, Page 806
P. Chen, T. Lepikhova, Y. Hu, O. Monni, and S. Hautaniemi
Nucleic Acids Research, 2011, Volume 39, Number 18, Page e123
I. Salaverria, C. Philipp, I. Oschlies, C. W. Kohler, M. Kreuz, M. Szczepanowski, B. Burkhardt, H. Trautmann, S. Gesk, M. Andrusiewicz, H. Berger, M. Fey, L. Harder, D. Hasenclever, M. Hummel, M. Loeffler, F. Mahn, I. Martin-Guerrero, S. Pellissery, C. Pott, M. Pfreundschuh, A. Reiter, J. Richter, M. Rosolowski, C. Schwaenen, H. Stein, L. Trumper, S. Wessendorf, R. Spang, R. Kuppers, W. Klapper, and R. Siebert
Blood, 2011, Volume 118, Number 1, Page 139
Shamina M. Rangwala, Xiaoyan Li, Loren Lindsley, Xiaomei Wang, Stacey Shaughnessy, Thomas G. Daniels, Joseph Szustakowski, N.R. Nirmala, Zhidan Wu, and Susan C. Stevenson
Biochemical and Biophysical Research Communications, 2007, Volume 357, Number 1, Page 231
A. H. Goodall, P. Burns, I. Salles, I. C. Macaulay, C. I. Jones, D. Ardissino, B. de Bono, S. L. Bray, H. Deckmyn, F. Dudbridge, D. J. Fitzgerald, S. F. Garner, A. Gusnanto, K. Koch, C. Langford, M. N. O'Connor, C. M. Rice, D. Stemple, J. Stephens, M. D. Trip, J.-J. Zwaginga, N. J. Samani, N. A. Watkins, P. B. Maguire, and W. H. Ouwehand
Blood, 2010, Volume 116, Number 22, Page 4646
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Blood, 2011, Volume 117, Number 10, Page 2891
Plant, Cell & Environment, 2011, Volume 34, Number 9, Page 1488
M. Seizl, L. Lariviere, T. Pfaffeneder, L. Wenzeck, and P. Cramer
Nucleic Acids Research, 2011, Volume 39, Number 14, Page 6291
Laurel E. Ecke, Jessica N. Cleck, Peter White, Jonathan Schug, Lauren Mifflin, and Julie A. Blendy
The International Journal of Neuropsychopharmacology, 2011, Volume 14, Number 08, Page 1111
Michiel B. Vandegehuchte, Dieter De Coninck, Tine Vandenbrouck, Wim M. De Coen, and Colin R. Janssen
Environmental Pollution, 2010, Volume 158, Number 10, Page 3323
Anne-Laure Boulesteix, Vincent Guillemot, and Willi Sauerbrei
Biometrical Journal, 2011, Volume 53, Number 4, Page 673
Caiyan Li, Zhi Wei, and Hongzhe Li
Journal of Biopharmaceutical Statistics, 2010, Volume 20, Number 2, Page 209
Christina Scheel, Elinor Ng Eaton, Sophia Hsin-Jung Li, Christine L. Chaffer, Ferenc Reinhardt, Kong-Jie Kah, George Bell, Wenjun Guo, Jeffrey Rubin, Andrea L. Richardson, and Robert A. Weinberg
Cell, 2011, Volume 145, Number 6, Page 926
Kerstin Endlweber, Kristin Krome, Gerhard Welzl, Anton Rudolf Schäffner, and Stefan Scheu
Soil Biology and Biochemistry, 2011, Volume 43, Number 6, Page 1130
Emily K. Piper, Louise A. Jackson, Helle Bielefeldt-Ohmann, Cedric Gondro, Ala E. Lew-Tabor, and Nicholas N. Jonsson
International Journal for Parasitology, 2010, Volume 40, Number 4, Page 431
Molecular Ecology, 2011, Volume 20, Number 11, Page 2341
H. Liu, Y. Kim, S. Sharkis, L. Marchionni, and Y.-Y. Jang
Science Translational Medicine, 2011, Volume 3, Number 82, Page 82ra39
Akihiro Hirakawa, Chikuma Hamada, and Isao Yoshimura
Statistics & Probability Letters, 2011, Volume 81, Number 7, Page 870
In-Hee Lee, Gerald H Lushington, and Mahesh Visvanathan
Journal of Clinical Bioinformatics, 2011, Volume 1, Number 1, Page 11
Seung Cho Lee, Angelika Mustroph, Rashmi Sasidharan, Divya Vashisht, Ole Pedersen, Teruko Oosumi, Laurentius A.C.J. Voesenek, and Julia Bailey-Serres
New Phytologist, 2011, Volume 190, Number 2, Page 457
C. Kahramanoglou, A. S. N. Seshasayee, A. I. Prieto, D. Ibberson, S. Schmidt, J. Zimmermann, V. Benes, G. M. Fraser, and N. M. Luscombe
Nucleic Acids Research, 2011, Volume 39, Number 6, Page 2073
Molecular Ecology, 2011, Volume 20, Number 6, Page 1144
Jemila S. Hamid, Pingzhao Hu, Nicole M. Roslin, Vicki Ling, Celia M. T. Greenwood, and Joseph Beyene
Human Genomics and Proteomics, 2009, Volume 2009, Page 1
Bart Buitenhuis, Christine M Røntved, Stefan M Edwards, Klaus L Ingvartsen, and Peter Sørensen
BMC Genomics, 2011, Volume 12, Number 1, Page 130
Gilles Guillot, Maja Olsson, Mikael Benson, and Mats Rudemo
Mathematical Biosciences, 2007, Volume 205, Number 2, Page 195
Maria Sievertzon, Peter Nilsson, and Joakim Lundeberg
Expert Review of Molecular Diagnostics, 2006, Volume 6, Number 3, Page 481
Molecular Ecology, 2007, Volume 16, Number 8, Page 1749
K. R. B. Sporer, W. Chiang, R. J. Tempelman, C. W. Ernst, K. M. Reed, S. G. Velleman, and G. M. Strasburg
Animal Genetics, 2011, Volume 42, Number 1, Page 75
B V Balgobind, C M Zwaan, D Reinhardt, T J C M Arentsen-Peters, I H I M Hollink, V de Haas, G J L Kaspers, E S J M de Bont, A Baruchel, J Stary, C Meyer, R Marschalek, U Creutzig, M L den Boer, R Pieters, and M M van den Heuvel-Eibrink
Leukemia, 2010, Volume 24, Number 12, Page 2048
M. J. Tallis, Y. Lin, A. Rogers, J. Zhang, N. R. Street, F. Miglietta, D. F. Karnosky, P. De Angelis, C. Calfapietra, and G. Taylor
New Phytologist, 2010, Volume 186, Number 2, Page 415
Plant, Cell & Environment, 2010, Volume 33, Number 10, Page 1742
M. J. Nueda, J. Carbonell, I. Medina, J. Dopazo, and A. Conesa
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Molecular Ecology, 2006, Volume 15, Number 3, Page 575
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Hongying Dai and Richard Charnigo
Canadian Journal of Statistics, 2010, Volume 38, Number 3, Page 315
G. M. Doody, M. A. Care, N. J. Burgoyne, J. R. Bradford, M. Bota, C. Bonifer, D. R. Westhead, and R. M. Tooze
Nucleic Acids Research, 2010, Volume 38, Number 16, Page 5336
J. Bentham, A. C. Michell, H. Lockstone, D. Andrew, J. E. Schneider, N. A. Brown, and S. Bhattacharya
Human Molecular Genetics, 2010, Volume 19, Number 17, Page 3394
J. D. Dougherty, E. F. Schmidt, M. Nakajima, and N. Heintz
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K. D. Rasmussen, S. Simmini, C. Abreu-Goodger, N. Bartonicek, M. Di Giacomo, D. Bilbao-Cortes, R. Horos, M. Von Lindern, A. J. Enright, and D. O'Carroll
Journal of Experimental Medicine, 2010, Volume 207, Number 7, Page 1351
Y. Loe-Mie, A.-M. Lepagnol-Bestel, G. Maussion, A. Doron-Faigenboim, S. Imbeaud, H. Delacroix, L. Aggerbeck, T. Pupko, P. Gorwood, M. Simonneau, and J.-M. Moalic
Human Molecular Genetics, 2010, Volume 19, Number 14, Page 2841
M. Berta, A. Giovannelli, F. Sebastiani, A. Camussi, and M. L. Racchi
Plant Biology, 2010, Volume 12, Number 2, Page 341
A. M. Clark, L. D. Goldstein, M. Tevlin, S. Tavare, S. Shaham, and E. A. Miska
Nucleic Acids Research, 2010, Volume 38, Number 11, Page 3780
Kristine Krajnak, G. Roger Miller, Stacey Waugh, Claud Johnson, Shengqiao Li, and Michael L. Kashon
Journal of Occupational and Environmental Medicine, 2010, Volume 52, Number 6, Page 584
Plant, Cell & Environment, 2010, Page no
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B. Nota, N. M. Van Straalen, B. Ylstra, and D. Roelofs
Insect Molecular Biology, 2010, Volume 19, Number 3, Page 315
A. Willems, K. De Gendt, J. Allemeersch, L. B. Smith, M. Welsh, J. V. Swinnen, and G. Verhoeven
International Journal of Andrology, 2009, Volume 33, Number 3, Page 507
Molecular Ecology, 2010, Volume 19, Number 9, Page 1842
D. Hose, T. Reme, T. Meissner, J. Moreaux, A. Seckinger, J. Lewis, V. Benes, A. Benner, M. Hundemer, T. Hielscher, J. D. Shaughnessy, B. Barlogie, K. Neben, A. Kramer, J. Hillengass, U. Bertsch, A. Jauch, J. De Vos, J.-F. Rossi, T. Mohler, J. Blake, J. Zimmermann, B. Klein, and H. Goldschmidt
Blood, 2009, Volume 113, Number 18, Page 4331
Fraser J. Sim, Martha S. Windrem, and Steven A. Goldman
Neuron Glia Biology, 2009, Volume 5, Number 3-4, Page 45
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P. Staib, C. Zaugg, B. Mignon, J. Weber, M. Grumbt, S. Pradervand, K. Harshman, and M. Monod
Microbiology, 2010, Volume 156, Number 3, Page 884
Molecular Ecology, 2010, Volume 19, Number 6, Page 1200
V. Brault, S. Tanguy, C. Reinbold, G. Le Trionnaire, J. Arneodo, S. Jaubert-Possamai, G. Guernec, and D. Tagu
Journal of General Virology, 2010, Volume 91, Number 3, Page 802
A. J. Jasinska, S. Service, O.-w. Choi, J. DeYoung, O. Grujic, S.-y. Kong, M. J. Jorgensen, J. Bailey, S. Breidenthal, L. A. Fairbanks, R. P. Woods, J. D. Jentsch, and N. B. Freimer
Human Molecular Genetics, 2009, Volume 18, Number 22, Page 4415
Plant, Cell & Environment, 2009, Volume 32, Number 11, Page 1548
I. A. Parish, S. Rao, G. K. Smyth, T. Juelich, G. S. Denyer, G. M. Davey, A. Strasser, and W. R. Heath
Blood, 2009, Volume 113, Number 19, Page 4575
Holger Fröhlich, Achim Tresch, and Tim Beißbarth
Biometrical Journal, 2009, Volume 51, Number 2, Page 304
Plant, Cell & Environment, 2009, Volume 32, Number 9, Page 1211
Piya Rujkijyanont, Sally-Lin Adams, Joseph Beyene, and Yigal Dror
British Journal of Haematology, 2009, Volume 145, Number 6, Page 806
Lucia Gagliardi, Cheri Hotu, Graeme Casey, Wilton J. Braund, King-Hwa Ling, Thomas Dodd, James Manavis, Peter G. Devitt, Richard Cutfield, Zbigniew Rudzki, Hamish S. Scott, and David J. Torpy
Clinical Endocrinology, 2009, Volume 70, Number 6, Page 883
Nicole C. Hauser, Marija Dukalska, Kurt Fellenberg, and Steffen Rupp
Journal of Biophotonics, 2009, Volume 2, Number 4, Page 262
Claudio D' Onofrio, Agnieszka Cox, Christopher Davies, and Paul K. Boss
Functional Plant Biology, 2009, Volume 36, Number 4, Page 323
Sabine Stahl, Carina Ittrich, Philip Marx-Stoelting, Christoph Köhle, Özge Altug-Teber, Olaf Riess, Michael Bonin, Jürgen Jobst, Stephan Kaiser, Albrecht Buchmann, and Michael Schwarz
Hepatology, 2005, Volume 42, Number 2, Page 353
Barbara Sarholz and Hans-Peter Piepho
Biometrical Journal, 2008, Volume 50, Number 6, Page 927
C. T. Fulp, G. Cho, E. D. Marsh, I. M. Nasrallah, P. A. Labosky, and J. A. Golden
Human Molecular Genetics, 2008, Volume 17, Number 23, Page 3740
Molecular Ecology, 2008, Volume 17, Number 21, Page 4740
Genetics Research, 2008, Volume 90, Number 04, Page 347
Nicola J. Armstrong
Statistica Neerlandica, 2008, Volume 62, Number 3, Page 364
Plant, Cell & Environment, 2008, Volume 31, Number 8, Page 1097
Plant, Cell & Environment, 2008, Volume 31, Number 3, Page 301
Jacqueline Boultwood, Andrea Pellagatti, Helen Cattan, Charles H. Lawrie, Aristoteles Giagounidis, Luca Malcovati, Matteo G. Della Porta, Martin Jädersten, Sally Killick, Carrie Fidler, Mario Cazzola, Eva Hellström-Lindberg, and James S. Wainscoat
British Journal of Haematology, 2007, Volume 139, Number 4, Page 578
Charles Kooperberg, Aaron Aragaki, Andrew D. Strand, and James M. Olson
Statistics in Medicine, 2005, Volume 24, Number 15, Page 2281
Piya Rujkijyanont, Joseph Beyene, Kuiru Wei, Fahad Khan, and Yigal Dror
British Journal of Haematology, 2007, Volume 137, Number 6, Page 537
N. Bochkina and S. Richardson
Biometrics, 2007, Volume 63, Number 4, Page 1117
T Liu, C Laurell, G Selivanova, J Lundeberg, P Nilsson, and K G Wiman
Cell Death and Differentiation, 2007, Volume 14, Number 3, Page 411
Nam-Ky Nguyen and E. R. Williams
Applied Stochastic Models in Business and Industry, 2006, Volume 22, Number 5-6, Page 631
Plant, Cell and Environment, 2007, Volume 30, Number 1, Page 85
Celia G. Zhang, Arlene D. Gonzales, Megan W. Choi, Brett A. Chromy, J. Patrick Fitch, and Sandra L. McCutchen-Maloney
PROTEOMICS, 2005, Volume 5, Number 7, Page 1877
Nathalie Druart, Marisa Rodríguez-Buey, Greg Barron-Gafford, Andreas Sjödin, Rishikesh Bhalerao, and Vaughan Hurry
Functional Plant Biology, 2006, Volume 33, Number 2, Page 121

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