Abstract
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).
Highlights
Several prognostic models for primary biliary cirrhosis (PBC) data have been developed using the Cox proportional hazards model, and the values of all covariates were determined at the time when the patient entered the study [1]
We introduced the probabilistic interpretation of generalized additive models (GAMs) and constructed the maximum likelihood principle of GAM for the analysis of survival data having time-dependent covariates
We proposed the information criterion based on the variant v-fold CV when choosing the optimal smoothing parameters in application of GAM
Summary
Several prognostic models for PBC data have been developed using the Cox proportional hazards model, and the values of all covariates were determined at the time when the patient entered the study [1]. We propose the variant multifold CV method for GAM when choosing the optimum smoothing parameters in order to estimate the survival function and predict the shortterm survival (say, for the following six months) at any time during the course of the disease. Another useful idea in our analysis is the concept of competing risk. By adding the liver transplantation as one of timedependent covariate, one can test the significance of liver transplantation
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