Modelling Survival Data With Time-Dependent Covariates

Abstract

In the present article, we discuss a flexible method for modeling censored survival data using penalized smoothing splines when the covariates values 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 and the baseline cumulative hazard function remain unsolved. The basic concept in the present article is to use the logistic regression model and generalized additive models with B-splines to estimate the survival function. The valiant n-fold cross-validationmethod for generalized additive models(GAM) is proposed when selecting the optimum smoothing parameters. 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) for the purpose of facilitating the decision as to when to undertake liver transplantation.