The name is absent

44

where we treat the previous dependent censoring as the event of interest:

ь^(с)Ш = ∏⅛⅜)

J=I

₌ ΛΛ[ Q_i⅛)exp(I⅞)

HHl∑tιQ√¾)expWc)J          ^}

Similarly, we set Q∣β%j) = 1 for ¾ ≤ к. For a dependently censored subject i, set
Qi{xj) = 0, E_i{xβ = 1, and E_i(xβ = 0 for j > i.

We also need some additional setups for the independent censoring. For an in-
dependently censored subject i, due to the similar reasons mentioned above, we set
P_i(xβ) = Qi{xj) = 1 for j ≤ i, Pβxβ = Qi(xj) = 0 for j > i- For all j, we let
Di(xj) = Ei(xj) = 0. That is, for independent censoring, the subject i does not lose
mass at the time point Xj.

In summary, the way we treat events and independent censoring by the proposed
method is the same as the one by the traditional Cox method. Only dependent
censoring is treated differently.

Next, the parameters β and β_c can be estimated by maximizing the following
extended joint partial likelihood function,

Please note that the likelihood function lβ^τ'ββ') in Equation 3.10 depends not only
on parameter β, but also implicitly on parameter β_c through the functions Pβxβ and
Di(xj). So it is better written as Lβ¹"ⁱ(β, β_c). Similarly, the likelihood lβ^σββ_c) in

<<   54   55   56   57   58   59   60   >>

More intriguing information