Aalen's additive risk model allows the influence of each covariate to
vary separately over time. Although allowing greater flexibility of te
mporal structure than a Cox model, Aalen's model is more limited in th
e number of covariates it can handle. We introduce a partly parametric
version of Aalen's model in which the influence of only a few covaria
tes varies nonparametrically over time, and that of the remaining cova
riates is constant. Efficient procedures for fitting this new model ar
e developed and studied. The approach is applied to data from the Medi
cal Research Council's myelomatosis trials.