  We present a new backfitting algorithm estimating the complex structured
non-parametric survival model of Scheike (2001) without having to use
smoothing. The considered model is a non-parametric survival model with two
time-scales that are equivalent up to a constant that varies over the subjects.
Covariate effects are modelled linearly on each time scale by additive Aalen
models. Estimators of the cumulative intensities on the two time-scales are
suggested by solving local estimating equations jointly on the two time-scales.
We are able to estimate the cumulative intensities solving backfitting
estimating equations without using smoothing methods and we provide large
sample properties and simultaneous confidence bands. The model is applied to
data on myocardial infarction providing a separation of the two effects
stemming from time since diagnosis and age.
