Proportional excess hazards

Assume that the excess risk of an individual over a known background rate can be well approximated by the proportional hazards model. Such might be the case for a cohort at risk of dying from causes that are independent of those that affect the general population. We propose estimators for both the regression parameters and the nonparametric baseline hazard function. The estimators are shown to be consistent, asymptotically normal and efficient. Analogues of the Wald, score and likelihood ratio test are provided,The relevance of the asymptotic results to samples of sizes 500 and 100 is illustrated by simulation. The model is used to estimate the prognostic significance of stage and histology in adults with non-Hodgkin's lymphoma.