Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 719389, 13 pages
http://dx.doi.org/10.1155/2013/719389
Research Article
Gray’s Time-Varying Coefficients Model for Posttransplant Survival of Pediatric Liver Transplant Recipients with a Diagnosis of Cancer
Yi Ren,
1 Chung-Chou H. Chang,
1,2,3 Gabriel L. Zenarosa,
4 Heather E. Tomko,
5 Drew Michael S. Donnell,
1 Hyung-joo Kang,
1,6 Mark S. Roberts,
2,3,4,5 and
Cindy L. Bryce2,3,5
1Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15261, USA
2Department of Medicine, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15261, USA
3Department of Clinical and Translational Science, School of Medicine, University of Pittsburgh, Pittsburgh, PA 15261, USA
4Department of Industrial Engineering, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA
5Department of Health Policy and Management, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15261, USA
6Health Geography Lab/Biostatistics Research Group, Division of Preventive and Behavioral Medicine, University of Massachusetts Medical School, Worcester, MA 01605, USA
Received 30 November 2012; Revised 2 March 2013; Accepted 10 April 2013
Academic Editor: Shu-hui Chang
Copyright © 2013 Yi Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Transplantation is often the only viable treatment for pediatric patients with end-stage liver disease. Making well-informed decisions on when to proceed with transplantation requires accurate predictors of transplant survival. The standard Cox proportional hazards (PH) model assumes that covariate effects are time-invariant on right-censored failure time; however, this assumption may not always hold. Gray’s piecewise constant time-varying coefficients (PC-TVC) model offers greater flexibility to capture the temporal changes of covariate effects without losing the mathematical simplicity of Cox PH model. In the present work, we examined the Cox PH and Gray PC-TVC models on the posttransplant survival analysis of 288 pediatric liver transplant patients diagnosed with cancer. We obtained potential predictors through univariable and multivariable models with forward selection for the Cox PH and Gray PC-TVC models, which coincide. While the Cox PH model provided reasonable average results in estimating covariate effects on posttransplant survival, the Gray model using piecewise constant penalized splines showed more details of how those effects change over time.