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5.1 Literature review

There are both parametric and nonparametric change-point hazard rate models in
literatures. In general, the parametric methods are likelihood based. Most existing
methods consider neither covariates nor dependent censoring. Some relatively new
methods, such as the one proposed by Wu (2003) and the one by Dupuy (2006), model
covariates in the change-point hazard rate model. However, to our best knowledge,
there is no published work that jointly considers independent and dependent censoring
together with covariates in change-point hazard rate models.

5.1.1 The likelihood based approaches

Matthews and Farewell (1982)^,s approach is popular in this field. The model they
considered is:

This model has three parameters, ʌɪ,p and θ. Here θ represents a change-point;

ρ represents the change in a hazard function before and after a change-point. Same
as other early work, covariate was not included in the model. It is clear that the
standard asymptotic likelihood inference on these parameters will not be applicable.
Assume the null hypothesis is no change-point, i.e. 0 = 0. Let the log-likelihood
statistic be denoted by L(λ₁,p, θ). Matthews and Farewell applied the likelihood ra-

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