title: Grid multi-category response logistic models.
abstract: BACKGROUND
  Multi-category response models are very important complements to binary logistic models in medical decision-making. Decomposing model construction by aggregating computation developed at different sites is necessary when data cannot be moved outside institutions due to privacy or other concerns. Such decomposition makes it possible to conduct grid computing to protect the privacy of individual observations.
  
  
  METHODS
  This paper proposes two grid multi-category response models for ordinal and multinomial logistic regressions. Grid computation to test model assumptions is also developed for these two types of models. In addition, we present grid methods for goodness-of-fit assessment and for classification performance evaluation.
  
  
  RESULTS
  Simulation results show that the grid models produce the same results as those obtained from corresponding centralized models, demonstrating that it is possible to build models using multi-center data without losing accuracy or transmitting observation-level data. Two real data sets are used to evaluate the performance of our proposed grid models.
  
  
  CONCLUSIONS
  The grid fitting method offers a practical solution for resolving privacy and other issues caused by pooling all data in a central site. The proposed method is applicable for various likelihood estimation problems, including other generalized linear models.
authors.affiliation: Department of Biostatistics & Bioinformatics, Duke University, Durham, NC, 27708, USA. yuan.wu@duke.edu.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Wu
authors.affiliation: Division of Biomedical Informatics, Department of Medicine, University of California, San Diego, La Jolla, CA, 92093, USA.
authors.forename: Xiaoqian
authors.initials: X
authors.lastname: Jiang
authors.affiliation: Division of Biomedical Informatics, Department of Medicine, University of California, San Diego, La Jolla, CA, 92093, USA.
authors.forename: Shuang
authors.initials: S
authors.lastname: Wang
authors.affiliation: Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai, 200240, China.
authors.forename: Wenchao
authors.initials: W
authors.lastname: Jiang
authors.affiliation: Department of Electronic Engineering, Shanghai Jiaotong University, Shanghai, 200240, China.
authors.forename: Pinghao
authors.initials: P
authors.lastname: Li
authors.affiliation: Division of Biomedical Informatics, Department of Medicine, University of California, San Diego, La Jolla, CA, 92093, USA.
authors.forename: Lucila
authors.initials: L
authors.lastname: Ohno-Machado
mesh_terms: D000066491:Clinical Decision-Making; D003219:Confidentiality; D006801:Humans; D033181:Information Dissemination; D016015:Logistic Models; D015233:Models, Statistical