The name is absent

37

censoring) under the circumstances of dependent censoring will lead to more bias
than applying a different choice of copula does. Grethen’s Ph.D. dissertation (2004)
further concludes that, when evaluating the impact on the parameter estimation bias,
the choices on the value of τ dominate the choices on copula functions. In other words,
identifying the correct value of т will essentially minimize the parameter estimation
bias irrespective of the copula function used.

Based on such findings, we conveniently selected the Frank copula to model the
data of events and dependent censoring. The main advantage of using Frank copula
is that it enables Kendall’s τ to take any value between -1 and 1 that covers the whole
range of all possible associations.

3.3 Methodology - extended Cox proportional haz-
ards models

3.3.1 Event time and dependent censoring time models

We denote the event time as T, the informative censoring time as C, and the non-
informative censoring time as S. The observed survival time is denoted as X =
min{T,C,S). That is to say, only what happens first will be observed. We also
define two indicator functions ∂₁ — I(X = T) and J₂ = ʃ(ʌ' = C^,)∙ ɪɪɪθ ŋɑvariates Z
and W are associated with events and informative censoring, with dimensions p × n
and q × n respectively. They may be identical, overlapped, or completely distinct.

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