Variable selection strategies in survival models with multiple imputations

In this paper, the variable selection strategies (criteria) are thoroughly discussed and their use in various survival models is investigated. The asymptotic efficiency property, in the sense of Shibata Ann Stat 8: 147-164, 1980, of a class of variable selection strategies which includes the AIC and all criteria equivalent to it, is established for a general class of survival models, such as parametric frailty or transformation models and accelerated failure time models, under minimum conditions. Furthermore, a multiple imputations method is proposed which is found to successfully handle censored observations and constitutes a competitor to existing methods in the literature. A number of real and simulated data are used for illustrative purposes.