The name is absent



45

Equation 3.11 is better written as Z∕σ)(∕3, ∕3c). In this dissertation, we will simply
denote
Ll-τ'> (β, βc) and [β-cr>(β, βc) as LSr> (/3) and cβcβ

3.3.4 Iteration steps

Because the extended joint partial likelihood function involves unknown quantities
such as
Pi(xj), Qi(xj), Dβxβ, Ei(xβ) and etc., we use iterations to get final estimates
for
βs and βcs. Note that we model events and dependent censoring as competing
risks as explained in Section 3.3.1. Thus, we need to solve two sets of functions. We
treat failures as the event of interest in one case and treat dependent censoring as
the event of interest in the other case. The iteration flow is listed first, and then each
step is explained in detail.

The iteration flow,

Step 1. Initialize β^,βc°^ => <Sθ0∖t), .Rθ0∖t)

=> e∕0Y),gΓ(∙) => Д0)ОШ(0)(-) =≠ Д(0)(-)Л0)(-)

=> Maximize L(β,βc) (see Equation 3.12) => Let m = 1; β(1 β^

Step 2, =⅛> βl>m βim'> → S⅛mtβR⅛nt)

* ⅛mj(∙).⅛rol(∙) * ⅛"'(∙),<⅛"l(∙) => D,w(∙),⅛<m>(∙)

Step 3, => Again, maximize L(β,βc) (Equation 3.12) => ∕3^m+1βim+1^



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