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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 986176, 9 pages
Research Article

Survival Data Analysis with Time-Dependent Covariates Using Generalized Additive Models

1Department of Engineering Informatics, Osaka Electro-Communication University, Osaka 572-8530, Japan
2Clinical Information Division, Data Science Center, EPS Corporation, Osaka 532-0003, Japan
3Nishinomiya Municipal Central Hospital, Hyogo 663-8014, Japan

Received 16 July 2011; Accepted 11 January 2012

Academic Editor: Hugo Palmans

Copyright © 2012 Masaaki Tsujitani 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.


We discuss a flexible method for modeling survival data using penalized smoothing splines when the values of covariates change for the duration of the study. The Cox proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. However, a number of theoretical problems with respect to the baseline survival function remain unsolved. We use the generalized additive models (GAMs) with B splines to estimate the survival function and select the optimum smoothing parameters based on a variant multifold cross-validation (CV) method. The methods are compared with the generalized cross-validation (GCV) method using data from a long-term study of patients with primary biliary cirrhosis (PBC).