Additive Risk Model Using Piecewise Constant Hazard Function

We study a weighted least squares estimator for Aalen's additive risk model with right-censored survival data which allows for a very flexible handling of covariates. We divide the follow-up period into intervals and assume a constant hazard rate in each interval. The model is motivated as a piecewise approximation of a hazard function composed of three parts: arbitrary nonparametric functions for some covariate effects, smoothly varying functions for others, and known (or constant) functions for yet others. The proposed estimator is an extension of the grouped data version of the Huffer and McKeague (1991 Huffer , F. W. , McKeague , I. W. ( 1991 ). Weighted least squares estimation for Aalen's additive risk model . Journal of the American Statistical Association 86 : 114 – 129 .Taylor & Francis Online], Web of Science ®] , Google Scholar]) estimator. For our model, since the number of parameters is finite (although large), conventional approaches (such as maximum likelihood) are easy to formulate and implement. The approach is illustrated by simulations, and is compared to the previous studies. The method is also applied to the Framingham study data.