Smooth hazard functions for survival time data

In medical prognosis based on survival analysis, there is an interest in visualizing the shape of the hazard function. In fully parametric models, the shape of the hazard function is constrained by the properties of the chosen distribution (Weibull, log-logistic, lognormal, Gompertz, gamma). The semi-parametric Cox model only assumes proportional hazards and has no specification of the baseline hazard. In Stata 8 a method of illustrating hazard functions using a kernel smooth of the hazard contributions is implemented for the Cox model which will allow more flexibile shapes. However, if the proportional hazards assumption is violated, then a method based on smoothing the Nelson-Aalen cumulative hazard function followed by numerical differentiation to give the hazard function and then further kernel density smoothing of the resulting function may be useful. This method will be illustrated using data from ART-CC, an international collaboration of 12 cohorts with data on over 19,000 HIV positive patients. The hazard of AIDS or death by risk factor groups defined by initial CD4 count (a measure of immune system functioning) or injection drug use (IDU) is modelled from the time of starting antiretroviral therapy for up to 5 years.