Linear splines and their tensor products are used to estimate the conditional log-hazard function based on possibly censored, positive response data and one or more covariates. An automatic procedure involving the maximum likelihood method, stepwise addition, stepwise deletion, and the Bayes Information Criterion is used to select the final model. The possible models contain proportional hazards models as a subclass, which makes it possible to diagnose departures from proportionality. Cubic splines and two additional log terms are incorporated into a similar model for the unconditional log-hazard function to allow for greater flexibility in the extreme tails. A user interface based on S is described.