Weighted Least Squares Estimation for Aalen's Additive Risk Model

Abstract Cox's proportional hazards model has so far been the most popular model for the regression analysis of censored survival data. However, the additive risk model of Aalen can provide a useful and biologically more plausible alternative. Aalen's model stipulates that the conditional hazard function for a subject, whose covariates are Y = (Y 1, …, Yp )', has the form h(t | Y) = Y' α(t), where α = (α 1, …, αp )' is an unknown vector of hazard functions. This article discusses inference for α based on a weighted least squares (WLS) estimator of the vector of cumulative hazard functions. The asymptotic distribution of the WLS estimator is derived and used to obtain confidence intervals and bands for the cumulative hazard functions. Both a grouped data and a continuous data version of the estimator are examined. An extensive simulation study is carried out. The method is applied to grouped data on the incidence of cancer mortality among Japanese atomic bomb survivors.

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