The name is absent

45

Equation 3.11 is better written as Z∕^σ)(∕3, ∕3_c). In this dissertation, we will simply
denote L^l-^τ'> (β, β_c) and [β-^cr>(β, β_c) as LS^r> (/3) and lβ^c∖β_cβ

3.3.4 Iteration steps

Because the extended joint partial likelihood function involves unknown quantities
such as P_i(xj), Q_i(xj), Dβxβ, E_i(xβ) and etc., we use iterations to get final estimates
for βs and β_cs. 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,β_c) (see Equation 3.12) => Let m = 1; β(¹∖ β^

Step 2, =⅛> β^l>^m∖ βi^m'> → S⅛^m∖tβR⅛ⁿ∖t)

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

Step 3, => Again, maximize L(β,β_c) (Equation 3.12) => ∕3^^m+1∖ βi^m+1^

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