for Cox's hazard regression model

ABSTRACT. This article is concerned with variable selection methods for the pro-portional hazards regression model. Including too many covariates causes extra variability and inflated confidence intervals for regression parameters, so regimes for discarding the less informative ones are needed. Our framework has p covari-ates designated as 'protected ' while variables from a further set of q covariates are examined for possible in- or exclusion. In addition to deriving results for the AIC method, defined via the partial likelihood, we develop a focussed information cri-terion that for given interest parameter finds the best subset of covariates. Thus the FIC might find that the best model for predicting median survival time might be different from the best model for estimating survival probabilities, and the best overall model for analysing survival for men might not be the same as the best overall model for analysing survival for women. We also develop methodology for model averaging, where the final estimate of a quantity is a weighted average of estimates computed for a range of submodels. Our methods are illustrated in simulations and for a survival study of Danish skin cancer patients. KEY WORDS: Akaike's information criterion, covariate selection, Cox regression, focussed information criteria, median survival time, model averagin