The name is absent

86

It is a natural extension of Matthews and Farewell’s (1982) model by including
covariates. Instead of using one parameter ρ to represent the difference of hazard
functions before and after the change-point, we use Aq and ʌɪ, which can be estimated
in a relatively straightforward way.

To estimate the baseline hazard function, we propose:

^       A₀ (0) A∩(0_mm)                          /r oʌ

^Ao ^^ ----дТГд-------                         tɔ-ə)

" "min

       ʌθ(^mɑæ) — ʌθ(^)                           f_c- .ʌ

ʌɪ - ---д---ʒ---                     (b∙4)

"max "

where θ is the change-point; and θ_mm and θ_max are the starting and end time
point of the study period.

ʌo and A₁ are used to represent the slope of the cumulative hazard curve. Because
the hazard functions in the change-point model are special cases of the format of
Equations 3.1 and 3.2, the estimates of cumulative hazard functions in Equations
3.19 and 3.20 from the regression survival analysis are used to estimate As as a
reasonable approximation. Therefore, both independent and dependent censoring
can be included.

Similar to Chapter 4, when treating the dependent censoring as the event of
interest, the counterparts of above equations are as below:

λ_0cexp{W-β_c) , 0 ≤ t < θ,
λ_c(t) = <

λ_lcexp(W-β_c) , t>θ.

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