Longevity and concentration in survival times: the log-scale-location family of failure time models

Evidence suggests that the increasing life expectancy levels at birth wit- nessed over the past centuries are associated with a decreasing concentration of the survival times. The purpose of this work is to study the relationships that exist be- tween longevity and concentration measures for some regression models for the evo- lution of survival. In particular, we study a family of survival models that can be used to capture the observed trends in longevity and concentration over time. The para- metric family of log-scale-location models is shown to allow for modeling different trends of expected value and concentration of survival times. An extension towards mixture models is also described in order to take into account scenarios where a fraction of the population experiences short term survival. Some results are also pre- sented for such framework. The use of both the log-scale-location family and the mixture model is illustrated through an application to period life tables from the Hu- man Mortality Database.