Page 54 - Contributed Paper Session (CPS) - Volume 2

CPS1419 Jinheum K. et al.
data for which interval censoring is assumed only on intermediate events
(Barret et al., 2011). Thus, our proposed model can provide a little more
flexibility in dealing with data in a semi-competing framework. In this article,
we utilize the Cox PH model with the incorporation of a frailty effect.
Moreover, our proposed method enables us to grasp the dependency of
related events using frailty and yields estimates of meaningful transition
intensities. The results will be illustrated from simulation studies and real data
analysis as well.
The rest of the paper is organized as follows. Section 2 explains the
structure of the proposed model, along with notations, and computation
procedures for parameter estimation. In particular, the quasi-Newton
optimization is used to estimate the parameters in the model. In Section 3, we
conduct extensive simulation studies to demonstrate the performance of the
proposed model. We calculate commonly used measures such as the relative
bias and coverage probability of the parameter estimates. Section 4 presents
real data analysis as an illustration. Finally, Section 5 provides a summary with
concluding remarks, including some drawbacks of the proposed models and
directions for future research.

2. Method
We consider an illness-death model (Anderson et al., 1993) that is one of
the most commonly used semi-competing risks models. As mentioned in the
previous section, the proposed model assumes that both non-fatal and fatal
events may be interval-censored, i.e., DIC. The model in our study has three
states: healthy (H), non-fatal (NF), and fatal (F), which denote by the numbers
0, 1, and 2, respectively. Under the illness-death model, there exist three
possible transitions between states: 0 → 1, 0 → 2, and 1 → 2. Thus, we have
four possible routes that a subject can experience from the beginning to the
end of study, i.e., route 1: 0 → 0, route 2: 0 → 2, route 3: 0 → 1, and route
4: 0 → 1 → 2.
Let be the time from study entry and define as the state of each

subject at time ≥ 0 . So, ∈ {0,1,2} in our model setup. Now let =

{(, ): (, ) = (0,1), (0,2), (1,2)} represent the possible transitions from state
to state . Given covariates = ( , , … , ) and frailty , define (|, )
′
2
1

as the transition intensity from state to state at time . That is,

( + = | = , , )

(|, ) = lim , (, ) ∈ ,

→0

and (|, ) = 0 for (, ) ∉ . Furthermore, through the Cox (Cox, 1975)

regression model, the transition intensity (|, ) can be expressed as

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