Page 58 - Contributed Paper Session (CPS) - Volume 2

CPS1419 Jinheum K. et al.
significant -value of <0.0001. The intensity of the educated group is
3.874 times higher than that of the non-educated group with a -value
of <0.0001. The estimate of the variance of the normal frailty is
2
1.1039, showing non-homogeneity between individuals with a -value
of <0.0001. Furthermore, Figure 1 displays the estimated transition
intensities between states such as 0 → 1, 0 → 2, and 1 → 2 under the
combinations of two risk factors, gender and education background.
Figure 2 shows the estimated individual frailty. As expected, for the 0 →
1 transition, the intensities of men (long-dashed and dotted-and-long-
dashed curves) are greater than those of women (solid and dotted
curves) irrespective of educational background; for the 0 → 2 transition,
the intensity of educated women is significantly greater than those of
the rest of combinations of gender and educational background.

5. Concluding remarks
In this article, we extend the approach of the methods proposed
under interval censoring only on a non-fatal event to analyzing semi-
competing risks data with interval censoring on both non-fatal and fatal
events. In our proposed model, we assume a Weibull distribution for
the baseline transition intensity and take into account frailty in order to
incorporate dependency between transitions. Regarding manipulation
of interval-censored event time, Barrett et al. (2011) assumed that the
exact event time can be observed uniformly over all time points in the
interval. Instead, we employed the method proposed by Collett (2015)
by partitioning the interval into several sub-intervals in which events can
occur. Subsequently, weight allocations on sub-intervals are imposed to
construct the modified likelihood functions. For parameter estimation,
numerical integration for the frailty distribution was executed by using
adaptive importance sampling, followed by quasi-Newton optimization
in the maximization step.
In simulation studies, we considered three types of regression
coefficients to compare the effects of the covariates on the hazard rate
of a fatal event before and after experiencing a non-fatal event. Both
SD and SEM are very close to each other and the CPs of the regression
parameters are close to a nominal level of 0.95 irrespective of types of
the regression coefficients considered. In addition, sensitivity analysis
was conducted to investigate how the parameter estimates behave to
the misspecificationof the frailty distribution. There were no differences

47 | I S I W S C 2 0 1 9