A partly parametric additive risk model

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