Summary It is shown how one can construct a model for a jump process depending on an arbitrary intensity measure with the property that if the measure is absolutely continuous it reduces to Cox's regression model for survival data. The model has the property that the maximum likelihood estimator of the parameters are Cox's estimate for the regression parameter and the Nelson-Aalen estimate for the measure. Cox's partial likelihood for the regression parameter becomes a partially maximized likelihood and the model has a property corresponding to S-ancillarity which explains the partial likelihood.