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∩(0mm) /r oʌ
Ao ^^ ----дТГд------- tɔ-ə)
" "min
 ʌθ(^mɑæ) — ʌθ(^) fc- .ʌ
ʌɪ - ---д---ʒ--- (b∙4)
"max "
where θ is the change-point; and θmm and θmax 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:
λ0cexp{W-βc) , 0 ≤ t < θ,
λc(t) = <
λlcexp(W-βc) , t>θ.
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