The shape of the hazard function in breast carcinoma: curability of the disease revisited

The question of curability of breast carcinoma remains controversial. Because the probability of cure essentially is an asymptotic notion, the corresponding estimation problems call for special statistical methods. Such methods should account for an intimate connection between the probability of cure and the shape of the hazard function.

The study was performed on survival data for 13,166 women with breast carcinoma identified through the Utah Cancer Registry and stratified by clinical stage and age at diagnosis. For these patients, the follow-up period was 30 years. Three estimation procedures were used for estimating the hazard function from the data: the life table estimator, a kernel counterpart of the Nelson-Aalen estimator, and a parametric estimator specifically designed for two-component hazards. The parametric estimate of the hazard function was used to provide estimates of cure rates for each category of patients.

For all categories of patients under study, the estimated hazard functions passed through a clear-cut maximum, showing a tendency to decrease as time approached the end of a follow-up period. The hazards appeared to be nonproportional across the strata. The estimated values of the cure rate and the corresponding confidence intervals were determined for each stratum of patients with breast carcinoma.

The results of the current study strongly suggest that cure is a possible outcome of breast carcinoma treatment. The condition of proportionality of risks is not met in breast carcinoma survival data.