Page 124 - Contributed Paper Session (CPS) - Volume 7

CPS2044 Mohd Asrul Affendi A. et al.
Many authors had applied parametric survival procedure in AIDS studies,
among others are Elfaki et al. (2012) and Singh & Totawattage (2013), used
Weibull distribution to model time to event in HIV/AID studies, Kiani et al.
(2012) used Gompertz distribution. On the other hand, Lopez-Gatell et al.
(2007) studied the effect of tuberculosis on the progression of the HIV-1
disease. The study focused on the effects of time-varying incident TB on time
to AIDS-related, and all-cause mortality with the changes in CD4 cell count
among HIV-1 infected women exposed to highly active antiretroviral therapy
(HAART), non-exposed and combined. The marginal structural model is used
with considering time-varying confounding. It was further observed that the
confounding effect of TB onset for exposed HAART is on the high side. Some
semi-parametric models including the Cox proportional hazard model have
been developed to capture time-varying covariate effect(s). Tseng et al. (2014)
considered a Cox-like model called extended hazard to model fixed and time-
varying covariate model. Therneau and Lumley (2016) used the counting
process strategy to build a Cox model for the fixed and time-varying covariate.
Within the parametric context, Sparling et al. (2006) developed parametric
time-varying covariate models for interval-censored data. However, it has
been observed that parametric methods are more accurate for modelling of
complex data structures (Aalen et al., 2008, Jackson, 2016). An example of the
complex data structure is time-varying covariate which may be model as a
parameter of the assumed distribution. In this paper, we modelled the fixed
and time-varying covariate effect of Weibull distribution using its scale
parameter.

2. Materials and Methods
Weibull Time-Varying Covariate Model for HIV-TB Mortality: Rodrıguez
(2010) described four modelling approaches for parametric survival models
namely; parametric families, proportional hazard, accelerated failure time and
proportional odds. However, we decided to use the parametric families
approach because of its simplicity and flexibility. Now, suppose T is an event
time that follows a Weibull distribution with shape and scale parameters define
as(a,b), its density function, hazard function and survival function are (Alharpy
and Ibrahim (2013));

(|, ) = ( ) ( ) −1 [− ( ) ], > 0, , > 0 (1)

ℎ(|, ) = ( ) ( ) −1 , > 0, , > 0 (2)

(|, ) = [− ( ) ], > 0, , > 0. (3)

If we consider the parametric family approach, the covariate associated with

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