Selection between proportional and stratified hazards models based on expected log-likelihood

The problem of selecting between semi-parametric and proportional hazards models is considered. We propose to make this choice based on the expectation of the log-likelihood (ELL) which can be estimated by the likelihood cross-validation (LCV) criterion. The criterion is used to choose an estimator in families of semi-parametric estimators defined by the penalized likelihood. A simulation study shows that the ELL criterion performs nearly as well in this problem as the optimal Kullback-Leibler criterion in term of Kullback-Leibler distance and that LCV performs reasonably well. The approach is applied to a model of age-specific risk of dementia as a function of sex and educational level from the data of a large cohort study.