TIME-DEPENDENT EFFECTS OF FIXED COVARIATES IN COX REGRESSION

A nonparametric modification is proposed for Cox's proportional hazard s model (Cox, 1972, Journal of the Royal Statistical Society, Series B 34, 187-220), where the covariates are fixed, but their effects are a llowed to vary in time. Parameters are introduced for the covariate ef fects at the (uncensored) survival times. Estimates are obtained by ma ximizing the penalized partial log-likelihood that arises if a penalty function of first order differences of consecutive parameters is subt racted from the partial log-likelihood. The choice of the smoothing pa rameter, which determines the weight of the penalty, is based on Akaik e's Information Criterion. The methods are illustrated in a set of ova rian cancer data and in a set of kidney transplantation data.