Vital variables and survival processes

Abstract: The focus of a survival study is partly on the distribution of survival times, and partly on the health or quality of life of patients while they live. Health varies over time, and survival is the most basic aspect of health, so the two aspects are closely intertwined. Depending on the nature of the study, a range of variables may be measured; some constant in time, others not; some regarded as responses, others as explanatory risk factors; some directly and personally health-related, others less directly so. This paper begins by classifying variables that may arise in such a setting, emphasizing in particular, the mathematical distinction between vital and non-vital variables. We examine also various types of probabilistic relationships that may exist among variables. Independent evolution is an asymmetric relation, which is intended to encapsulate the notion of one process driving the other; $X$~is a driver of~$Y$ if $X$ evolves independently of the history of~$Y$. This concept arises in several places in the study of survival processes.