Geometric Method of Determining Hazard for the Continuous Survival Function

A basic assumption in proportional intensity models is the proportionality, that each covariate has a multiplicative effect on the intensity. The proportionality assumption is a strong assumption which is not always necessarily reasonable and thus needs to be checked. The survival analysis often employs graphic methods to study hazard proportionality. In this paper a geometrical method for determining the value of the hazard function on the basis of the continuous survival function was proposed. This method can be used to compare the intensity of the event for objects belonging to two subgroups of the analysed population. If we have graphs of survival function, then an analysis of the tangents at a specific time and their roots enables us to find the intensity and to study the relationship between them for different subgroups. This method can also be useful when studying the proportionality of hazard. It is a condition for the use of the Cox proportional hazards model. The above method was used to evaluate the effect of unemployment benefit and gender on unemployment and on the intensity of finding a job.