The name is absent

42

that this subject i is dependently censored through time c. For c > x_i, we have

₌ ffaffa,x_t)dx
⅛i∖^c)        r∞ f.₍     ∖ j

J_xi ffa,zfadx

= Pr(C^,_i ≥ c∖C_i > x_i,T_i = x_i)

_ PfaC_i ≥ c,T_i = x_i)
Pr(C^,_i ≥ x_i,T_i = x_i)

₌ ɪ - H_u{F_ifa_i),G_i(c)-a}

1 - H_u{F_ifa_i),G_ifa_i)-a}'                     '

where H_u(a,b∙,a) = ^дн^’В?).1        .

^u ∖  ’   ’    /             OU        / ʌ ,  ,4

I (u,υ)=(α,o)

Let E_i fa fa represent the piece of mass that a failed subject i losses at dependent

censoring time Xj. Again, for Xj > x_i, we define that

Note that there are a few restrictions of above notations listed in Section 3.3.3.

3.3.3 Partial likelihood functions

In order to consider the event and dependent censoring simultaneously, we introduce
copula-based indicator functions D_i fa fa and E_i fa fa, which can take any value be-
tween 0 and 1; while traditional indicators can only take two values, either 0 or 1.
For a subject with dependent censoring, we assume that its contribution to the likeli-
hood function is decreasing gradually at each observed event time point, represented
by P_i (i) and D_i fa fa. Intuitively, this subject is going to fail gradually rather than
immediately, as the traditional survival analysis assumes.

We define an extended Cox partial likelihood function for an event as follows:

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