The name is absent

54

For time t, we have

S^,(i) = exp{-.5t²exp(∕¾B + ∕¾Age)},                (3.21)

R(t) = exp{-.5texp(∕¾_cB + ∕¾_cAge)},               (3.22)

where β₁ = .5, β₂ = .4, β_lc = .6 and ∕⅜_c = ∙3.

The joint distribution of T and C is specified by the Frank copula as below:

— l)(ɑɑ(ɑ) — 11

•Ж c; ɑ) = log_α{l ₊ -----ɪ-----¾           (3.23)

α-l

We tested Kendall’s τ — 0.8, corresponding to a = 0.00000001258 with different
percentages of events, dependent and independent censoring.

In order to generate the observations of event time and informative censoring time,
we used the results by Nelsen (1986):

• Step 1, generate two independent Uniform(0,l) random variables и and v .

. Step 2, let v = log_α{l ₊ ,⅛-,¹.> _tt}.

Then we get the cumulative distribution functions и and v for two variables, which
satisfy the relationship specified by the Frank copula. We get S(f) and R(t) through
и and v. Plug them into Equations 3.21 and 3.22, and then get ⅛ and tc as shown
below:

₌   /-21og(5(⅛))

^τ у exp(Z'_iβ')

₌ -21og(B(t))

^c exp(W-β_c)

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