The name is absent



41

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

Pr(√i >tli> xi, Ci = xi) = -pz-----—-

Jxi f(x,xi)dx

_ Pr(Ti >t,Ci = xi)

Pτ(Ti ≥ xi, C1 = xi)

= ɪ - Hv{Fi(tGβxi)-,a}

1 - Hv{Fi(xiβGi(xi)-,a}           '

where H1,(a,ba} =                  . 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

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

Di(xj) = Pi(xj-ι) - Pi(xj).                        (3.6)

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

As far as the dependent censoring is concerned, we also need estimates of βc since
βc 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 xi, we want to compute the probability



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