Page 126 - Contributed Paper Session (CPS) - Volume 7

CPS2044 Mohd Asrul Affendi A. et al.
−1
( ) ( ) , <
′
[ ] [ ]
′
ℎ(|, , ()) =
−1
( ) ( ) , ≥
{ [ + ()] [ + ()]
′
′
The cumulative hazard function H(t│a,x,z(t))associated with T can be obtained
as;
(|, , ())
−1
∫ ( )( ) , <
′
[ ] [ ]
′
= 0
−1
∫ ( ) ( ) , ≥
′
′
{ 0 [ + ()] [ + ()]
Thus;
(|, , ())

( ) , <
′
[ ]
=

( ) + ( ) − ( ) , ≥
′
′
′
{ [ ] [ + ] [ + ]
The survival function S(t│a,x,z(t)) follows as;
(|, , ()) = exp[ −(|, , ())]
(|, , ())

[− ( ) ] , <
′
[ ]
=

[− [( ′ ) + ( ′ ) − ( ′ ) ]] , ≥
{ [ ] [ + ] [ + ]

Parameter Estimation for Weibull Time-Varying Covariate Model:
Following Lessafre and Lawson (2013), Jamil et al. (2017), Olaniran and Yahya
(2017), Olaniran and Abdullah (2017), Olaniran and Abdullah (2018a), Olaniran
and Abdullah (2018b) among others the likelihood of a parametric survival
model with right censored times can be define as;
() = ∏ ( |) ∏ ( |) (7)

Where uce denote uncensored and ce denotes right censored. The likelihood
in (7) can be simplified if a censoring indicator si that takes 0 for censored and
1 for uncensored is assumed. Thus,
() = ∏ ℎ( |) ( |) (8)

=1
For the case of time‐dependent covariate, we define c_i to be the time
dependent indicator as a piece‐wise function;
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