EXPLORING THE NATURE OF COVARIATE EFFECTS IN THE PROPORTIONAL HAZARDS MODEL

We discuss an exploratory technique for investigating the nature of covariate effects in Cox's proportional hazards model. This technique features an additive term-SIGMA-1p f(j)(X(ij)), in place of the usual linear term-SIGMA-1p X(ij)beta-j, where X(i1), X(i2), ..., X(ip) are covariate values for the ith individual. The f(j)(.) are unspecified smooth functions that are estimated using scatterplot smoothers. These functions can be used for descriptive purposes or to suggest transformations of the covariates. The estimation technique is a variation of the local scoring algorithm for generalized additive models (Hastie and Tibshirani, 1986, Statistical Science 1, 297-318).