Page 123 - Contributed Paper Session (CPS) - Volume 7

CPS2044 Mohd Asrul Affendi A. et al.

Parametric Weibull Time-Varying Covariate
Model for HIV-TB Mortality
1
Mohd Asrul Affendi Abdullah , Oyebayo Ridwan Olaniran , Siti Afiqah
2
Muhammad Jamil
1
1 Department of Mathematics and Statistics, Faculty of Applied Science and Technology,
Universiti Tun Hussein Onn Malaysia
2 Department of Statistics, Faculty of Physical Sciences, University of Ilorin

Abstract
Parametric Weibull survival model has been applied to several failure time
distribution of many diseases including the co-infection of Human
Immunodeficiency Virus HIV and Tuberculosis (TB). However, covariate(s) in
the Weibull survival regression may depend on time. A typical example in HIV-
TB co-infection is the occurrence of TB infection at varying time in HIV patients.
This modelling situation violates the standard assumption of proportional
hazard models like Cox or ordinary Weibull regression that do not incorporate
the time-varying effect. Simulating time-varying covariate model poses a
serious problem in survival analysis because the covariate that needs to be
generated to obtain the hazard or survival function depends on time. In this
paper, we present a simulation strategy for generating a parametric Weibull
time-varying covariate model. We also present an estimation technique for the
model using the maximum likelihood method. The validity of the simulation
scheme as well as the estimation method was observed using bias and mean
square error criterion. Comparison between the estimation method with
standard Cox regression and Weibull regression model under fixed and time-
varying covariate assumption was also achieved. Appreciable supremacy was
observed for the proposed method over the competing methods.

Keywords
Simulation; Weibull distribution; Time-varying covariate; HIV-TB co-infection

1. Introduction
The occurrence of a particular event such as the time of death, time of
relapse, time of recovery, is commonly associated with survival analysis
(Collett, 2015). The usual trend in survival analysis is to observe the distribution
so that an appropriate method could be perfectly applied to the event of
study. Generally, when the event distributions are known in advance, the
parametric method can be applied. Otherwise, non-parametric or semi-
parametric methods are often suitable for the analysis. Besides, in modelling
the lifetime data, sometimes, the semi-parametric method could be more
accurate depending on the situation of the data (Leffondré et al., 2013).

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