A linear model is suggested for the influence of covariates on the intensity function. This approach is less vulnerable than the Cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed. A method of non-parametric estimation of regression functions is presented. This results in plots that may give information on the change over time in the influence of covariates. A test method and two goodness of fit plots are also given. The approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx.