Kernel smoothing of Aalen's linear regression model

The linear regression model by Aalen for failure time analysis allows the inclusion of time-dependent covariates as well as the variation of covariate effects over time. For estimation Aalen considers cumulative hazard functions and derives estimates by applying counting process theory. Since often hazard functions themselves are of primary interest rather than cumulative hazard functions, in this paper we consider kernel estimation of the hazard functions, particularly in the presence of time-dependent covariates. Different kinds of bandwidths and kernel functions are discussed. A comparison of the considered methods is illustrated by data from the Stanford Heart Transplant Study