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

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).