Exposure–risk modeling for time-to-event data 125
5.5.2 Recurrent events in multistate models
A simple multistate model for recurrent events contains states of having had 1,
2, 3,... events. The gap time between events can be modeled as the transition
time between the states of having k events to having k + 1 events. Let T
ik
be
the time to the kth e vent after having the k −1th, one may assume the hazard
of the kth event as
h
k
(t) = h
0k
(t) exp(X
T
i
β
k
) (5.37)
where h
0k
(t) and β
k
are state specific, but some components may be shared.
When they are all shared, this mo de l describes a renewal process with com-
pletely the same risk of having next event. This assumption is valid only for
very special cases, such as the time to the next failure of a replaced