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84

al. (1985). He also extends the likelihood ratio method to find confidence regions for
the change-point θ and joint confidence regions for (θ, <f). He applies the results to
Stanford heart transplant data.

Dupuy (2006)

Dupuy (2006) extends the hazard function in Wu et al. (2003) by including the
effect of covariates. He also allows for the time-dependent covariates. Thus, the
hazard function he studies is:

λ(f ∣Z) = (α + ei{t>T}exp ∣ (β + 7⅛>τ∕z(f)j.           (5.1)

This paper deduces the format of the log-likelihood function for the above model.
Furthermore, Newton-Raphson method can be used to get the parameter estimator for
the change-point. Dupuy proved that the convergence of the estimators is warranted.
And the estimators are shown to be consistent.

However, dependent censoring is not taken into consideration. Thus, Dupuy’s
method is not directly applicable to the question in this research.

5.1.2 Non-parametric approaches

Wu et al. (2003)

The change-point model considered in Wu et al. (2003) is:

ʌ(t) = (α + 0⅞>τ})λo(t; 7),

(5.2)




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