Page 28 - Contributed Paper Session (CPS) - Volume 5

CPS657 Folorunso Serifat A. et al.
De Angelis et.al. (1999) and Lambert et.al. (2007) reported that Cure fraction
models can also be extended for analyses of relative survival.
The main aim of this research is to apply a new mixture cure model that is
capable of handling and accommodating non-normality in survival data and
which will give a better information of the proportion of Ovarian cancer
patients that have benefitted from medical intervention.

2. Methodology
2.1 The Model (Mixture Cure Model)
This model which was first developed by (Boag, 1949) and was modified by
(Berkson \& Gage, 1952) can be defined as:

() = + (1 − ) () (1)

Where:
() = The survival functions of the entire population
() = The survival functions of the uncured patients

= The proportion of cure patients that is the cure fraction rate.
2.2 Estimations of Cure Fraction Model (Mixture Cure Model)
The estimation employed shall be parametric in nature. Given the cure model
in equation (1), the estimate of parameter is given as:

() − ()
= (2)
1 − ()

The likelihood estimation of cure fraction model is:
= [( )] [( )] 1 −

2.3 Distributions of Cure Models
Some existing univariate distributions were examined for the mixture cure
model to estimate the corresponding c (proportion of cure patients), their
median time to cure and variances. The following are some of the reviewed
parametric cure fraction models.
2.3.1 Generalised Gamma
−1
> 0, > 0, , > 0, > 0
() = ( ) − ( )
Γ()

Where > 0 is a scale parameter, > 0 and > 0 are shape
parameters and () is the gamma function of x.
2.3.2 Log-normal
1 1 − 2
(; , ) = 2 ( ) , , > 0
√2

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