Relationship between coefficients in parametric survival models for exponentially distributed survival time : registered unemployment in Poland

Survival analysis is a popular research tool in medicine and demography. It has been used for many years to study the duration of socio-economic phenomena. The aim of this article is to evaluate the relationship between the coefficients of the proportional hazards model (PH) and the accelerated failure time model (AFT), assuming an exponential distribution of survival time. The coefficients of the PH and AFT exponential models have the same magnitude but have opposite signs. It follows that there is a symmetric relation between the coefficients. In the case of exponential PH and AFT models, there is a relation of equality between the parameters describing the quality and fit of the model, as well as between the standard errors of the parameters of both models. In this case also, we can talk about a symmetric relation. The exponential PH model is valid if the exponential AFT model is valid. The study showed that the intensity of starting work was higher in the case of men, people with work experience, people with higher education and young people. The job search time was longer for women, people with no work experience, and people aged 60+, but shorter for people with higher education.