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Sengwee Toh,1 Robert Wellman,2 R Yates Coley,2 Casie Horgan,1 Jessica Sturtevant,1 Erick Moyneur,3 Cheri Janning,4 Roy Pardee,2 Karen J Coleman,5 David Arterburn,2 Kathleen McTigue,6 Jane Anau,2 Andrea J Cook2 On behalf of the PCORnet Bariatric Study Collaborative 1Department of Population Medicine, Harvard Medical School and Harvard Pilgrim Health Care Institute, Boston, MA, USA; 2Kaiser Permanente Washington Health Research Institute, Seattle, WA, USA; 3StatLog Econometrics, Inc., Montreal, QC, Canada; 4Duke Clinical and Translational Science Institute, Durham, NC, USA; 5Kaiser Permanente Southern California, Pasadena, CA, USA; 6Department of Medicine, University of Pittsburgh, Pittsburgh, PA, USA Purpose: Sharing of detailed individual-level data continues to pose challenges in multicenter studies. This issue can be addressed in part by using analytic methods that require only summary-level information to perform the desired multivariable-adjusted analysis. We examined the feasibility and empirical validity of 1) conducting multivariable-adjusted distributed linear regression and 2) combining distributed linear regression with propensity scores, in a large distributed data network.Patients and methods: We compared percent total weight loss 1-year postsurgery between Roux-en-Y gastric bypass and sleeve gastrectomy procedure among 43,110 patients from 36 health systems in the National Patient-Centered Clinical Research Network. We adjusted for baseline demographic and clinical variables as individual covariates, deciles of propensity scores, or both, in three separate outcome regression models. We used distributed linear regression, a method that requires only summary-level information (specifically, sums of squares and cross products matrix) from sites, to fit the three ordinary least squares linear regression models. A comparison set of analyses that used pooled deidentified individual-level data from sites served as the reference.Results: Distributed linear regression produced results identical to those from the corresponding pooled individual-level data analysis for all variables in all three models. The maximum numerical difference in the parameter estimate or standard error for all the variables was 3×10−11 across three models.Conclusion: Distributed linear regression analysis is a feasible and valid analytic method in multicenter studies for one-time continuous outcomes. Combining distributed regression with propensity scores via modeling offers more privacy protection and analytic flexibility. Keywords: distributed regression, propensity score, distributed data networks, privacy-protecting methods

The classic deformation known as simple shear has been investigated within the framework of nonlinear elasticity for isotropic incompressible hyperelastic materials in a large variety of contexts, most notably in the analysis of the mechanical behaviour of soft matter. One of the major difficulties in providing a realistic physical interpretation of this idealised homogeneous deformation is the fact that the conventional mathematical model of simple shear using a plane stress assumption to determine the hydrostatic pressure implies that a normal traction must be applied to the slanted faces of the deformed specimen. However, such a traction is not applied in practice. To resolve this dilemma, we retain the classic plane stress assumption to determine the hydrostatic pressure but modify the basic kinematics to consider a simple shear deformation superposed on a uniform lateral extension or compression of the specimen. The amount of lateral stretch is treated as a stabilising factor determined so that the predicted normal traction is minimised and thus the fidelity of the model with experimental protocols is enhanced. This new approach is illustrated for a variety of classical strain-energy densities for isotropic hyperelastic materials that have been used to model the mechanical behaviour of soft matter. [ABSTRACT FROM AUTHOR]