Survival Analysis Using Additive Risk Models.

In this paper we study Aalens additive risk model for the regression analysis of censored survival data. The additive risk model provides a useful alternative to Coxs 1972 proportional hazards model when large sample size makes its application feasible. It is capable of providing detailed information concerning the temporal influence of each covariate. The temporal influences of the covariates are not assumed to be proportional as they are in Coxs model. Buckley has pointed out that additive risk models are biologically more plausible than proportional hazard models. Also, the use of the proportional hazards model when the true model is additive risk has been found by ONeil to result in serious asymptiotic bias. The first purpose of the present paper is to apply the additive risk model to the analysis of grouped data in which only the person-years at risk and number of uncensored deaths over successive time intervals, tabulated for various levels of the covariates, are available. This kind of data typically arises in epidemiological cohort studies involving the follow-up of large population groups over many years, see Breslow. Our approach is to use an estimator, constructed using the method of sieves, for which an asymptotic distribution theory was developed by McKeague. This estimator, called the integrated histogram sieve estimator, requires only grouped data. The second purpose of this paper is to derive the asymptotic distribution of Aalens least squares estimator.