[The hazard function]

Abstract

In cohort studies the event occurrence is usually described by the incidence rate and the survivor function. In comparison with these estimators the plot of the hazard function has the advantage to show the variations of the occurrence of the event along the period of observation, which often are important to be highlighted. Furthermore, when comparing individuals with different characteristics, the hazard function is a valuable support to check the assumption and to interpret the results of a Cox regression model. This paper illustrates the method for estimating the hazard function and an example is given from a real case by using the survival data of the breast cancers collected in the IMPACT study, aimed to detect the efficacy of the mammographic screening program. The relationship between the usual estimators and the hazard function is shown and its role in the survival regression modelling is emphasized. In the example the estimate of the hazard function allows to point out that the mortality rate of breast cancer in the first year after the diagnosis is lower than later and that the difference between the hazards of the invited cases and those of the not invited cases is approximately constant along the whole l0 years follow up, two important remarks both demonstrating the usefulness of the application of this function in the analysis of cohort studies.