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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 lβc∖βcβ
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'> → S⅛m∖tβR⅛n∖t)
* ⅛mj(∙).⅛rol(∙) * ⅛"'(∙),<⅛"l(∙) => D,w(∙),⅛<m>(∙)
Step 3, => Again, maximize L(β,βc) (Equation 3.12) => ∕3^m+1∖ βim+1^