The name is absent

41

assumption specified by the copula H, for t > ,τ₁. we have

Pr(√_i >t∖l_i> x_i, C_i = x_i) = -pz-----—-

J_xi f(x,x_i)dx

_ Pr(T_i >t,C_i = x_i)

Pτ(T_i ≥ x_i, C₁ = x_i)

₌ ɪ - H_v{F_i(t∖Gβx_i)-,a}

1 - H_v{F_i(x_iβG_i(x_i)-,a}           '

where H₁,(a,b∖a} =                  . Denote the above conditional survival

I {u,υ)=(a,b)

probability by F⅛(t).

Then the piece of mass that the censored subject i loses at time Xj is denoted as

D_i(xβ), where Xj is the event time of subject j and Xj > x_i. Assuming that x_i,
i = 1, ...,n are sorted in ascending order without ties, we define D_i(xβ as follows:

D_i(x_j) = P_i(xj-ι) - P_i(xj).                        (3.6)

Similarly, all other subjects dependently censored before time Xj lose some mass at
the event time point Xj, denoted as D_i(xβ as well.

As far as the dependent censoring is concerned, we also need estimates of β_c since
β_c is included in the Pβt). As mentioned, we put events and dependent censoring in
the competing-risks settings. That is to say, by treating dependent censoring as the
event of interest, we can get the counterpart functions. At last, we get parameter es-
timates by maximizing likelihood functions for both events and dependent censoring,
respectively.

Specifically, for a subject i fails at time x_i, we want to compute the probability

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