Survival analysis as used in the medical context is focused on the
concepts of survival function and hazard rate, the latter of these being the
basis both for the Cox regression model and of the counting process approach.
In spite of apparent simplicity, hazard rate is really an elusive concept,
especially when one tries to interpret its shape considered as a function of
time. It is then helpful to consider the hazard rate from a different point of
view than what is common, and we will here consider survival times modeled as
first passage times in stochastic processes. The concept of quasistationary
distribution,which is a well-defined entity for various Markov processes, will
turn out to be useful.
¶ We study these matters for a number of Markov processes, including
the following: finite Markov chains; birth-death processes; Wiener processes
with and without randomization of parameters; and general diffusion processes.
An example of regression of survival data with a mixed inverse Gaussian
distribution is presented.
¶ The idea of viewing survival times as first passage times has been
much studied by Whitmore and others in the context of Wiener processes and
inverse Gaussian distributions. These ideas have been in the background
compared to more popular appoaches to survival data, at least within the field
of biostatistics,but deserve more attention.