Page 150 - Special Topic Session (STS) - Volume 3
P. 150
STS535 Edsel A. P. et al.
The class of joint stochastic models could now be described as follows. For
brevity, we use the alternate notation ≡ () for any process .
1. The health status process satisfies the condition: For all , ′ ∈ with
≠ ′,
and
We recall here that (, ) = − ∑ ′∈ (, ′).
2. The longitudinal marker process satisfies the condition: For all , ′ ∈
with ≠ ′,
and
We recall here that (, ) = − ∑ ′∈ (, ′).
3. The multivariate counting process describing the recurrent events
occurrences satisfies: For infinitesimal positive h, with
∈ {(0,0, . . . ,0), (1,0, . . . ,0), (0,1, . . . ,0), . . . , (0,0, . . . ,1)},
we have
{(( + ℎ)−) − (−) = | ; = ; = ; − = } =
−
−
−
() ∏ [{ [ℰ ()] [; ]{ + () + () }ℎ} ×
3
3
3
0
=1
{1 − [ℰ ()] [; ]exp { + () + () }ℎ} 1− ].
3
3
0
3
The simplest effective age process could either be of form
ℰ () = or ℰ () = − (−) ,
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