Page 128 - Contributed Paper Session (CPS) - Volume 7

CPS2044 Mohd Asrul Affendi A. et al.
3. Result and Discussion
The estimates of the proposed method obtained were compared with
estimates using Cox proportional hazard implemented in SPLUS via coxph,
Weibull fixed covariate regression via survreg, and Weibull time-varying
covariate regression via flexsurvreg. The results based on performance metrics
are presented in the table 1 The proposed method is PWTVC (Proposed
Weibull time-varying covariate).

Table 1: Simulation results for average bias (bias(θ ̂)), average standard error (SE(θ ̂))
and average mean square error (MSE(θ ̂)) based on 1000 replications for sample size
n=100 and censoring rate 20%.
Fixed covariate model Time varying covariate model
Metrics Parameter Coxph FC Survreg FC Coxph TVC Flexsurvreg PWTVC

0.2634 0.2751 0.2634 0.2519 0.1878
̂
() 0.9863 0.1616 0.9863 0.2976 0.1160
, 0.7219 0.2256 0.7219 0.2757 0.1561
-0.8891 -0.9374 -0.8891 -0.9237 -1.3363
̂
() 2.0374 0.1657 2.0374 1.5003 0.0237
, 0.5741 -0.3858 0.5741 0.2883 -0.6563
0.8599 0.9544 0.8599 0.9166 1.8209
̂
() 5.1237 0.0536 5.1237 2.3395 0.0140
, 0.8507 0.1998 0.8507 0.1591 0.4551
Table 1 shows the results for moderate sample size 100 and low censoring
rate 20%. For all the performance metrics used, the results of the proposed
method are better than the competing methods except in the estimation of
the fixed covariate effect β. Specifically, the proposed method is more stable
in terms of low average standard error, consistent in terms of low average bias
as well as efficient in terms of low mean square error. However, the interesting
results are more attributable to the time varying effect parameter γ which is
our main focus.

4. Conclusion
In this paper, we have presented a simulation strategy for generating HIV-
TB survival time with time-varying covariate for Weibull distribution. We also
developed the corresponding likelihood-based estimator for estimating the
parameters of parametric Weibull time-varying covariate model. The results
from the simulation studies affirm the adequacy of the simulation strategy as
well as the estimation method regarding consistency and efficiency. We also
stressed the use of parametric distribution when the underlying distribution is
known in advance.

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