The name is absent

39

• Marginal cumulative distribution functions for T_i and C_i are:

F_i(t∖Z_i,W_i) = 1 - S_i(t∖Z_i,W_i)

= 1 - exp{-Λ_o(O exp(Z_iβ)},

G_i(t∖Z_i,W_i) = 1 - R_i(t∖Z_i, W_i)

= 1 - exp{-Φ_o(Oexp(W_i^,∕¾)}, (³∙³)

where S_i(t) and R_i(t) represent survival fonctions, and denote cumulative baseline
hazard fonctions by ʌo(i) and Φq(0> respectively.

We will use F_i(t) and G_i(t) to denote above marginal cumulative distribution
fonctions. For a given Copula H with parameter a, the joint cumulative distribution
function of T_i and C_i can be modeled as follows:

J_i(t,c) = Pr(T_i<t,C_i<c)

= H{F_i(t),G_i(c)∙,a}                      (3.4)

The identifiability of the parameters in the above model has been shown by Heck-
man and Honore (1989) and several corresponding estimation methods have been
proposed. However, those methods only work for some special cases. According to
Peng and Fine (2007), a general estimation method is not yet seen in the literature.

3.3.2 Conditional survival probability functions

To fit the joint model, we extended the idea of “redistribution of mass” by Efron
(1967) to deal with the dependent censoring problem. Before the occurrence of the

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