A flexible parametric procedure is given to model the hazard function as a linear combination of cubic B-splines and to obtain maximum likelihood estimates from censored survival data. The approach yields smooth estimates of the hazard and survivorship functions that are intermediate in structure between strongly parametric and non-parametric models. A simple method is described for selecting the number and location of knots. Simulation results show favorable root mean square error compared to non-parametric estimates for both the hazard and survivorship functions. Three methods are given to calculate confidence intervals based on the delta method, profile likelihood, and bootstrap, respectively. The procedure is applied to estimate hazard rates for acquired immunodeficiency syndrome (AIDS) following infection with human immunodeficiency virus (HIV). Spline methods can accommodate complex censoring mechanisms such as those that arise in the AIDS setting. To illustrate, HIV infection incidence is estimated for a cohort of hemophiliacs in which the dates of HIV infection are interval-censored and some subjects were born after the onset of the HIV epidemic.