Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 15

and Lachin (1997)) that specifies the relationship between the failure time T

and the covariate Z as

h(T) = 0 Z + " :

Here h : R + !R (R denotes the real line and R +

the positive half real line)

is an unknown strictly increasing function, a vector of regression parame-

ters as before, and the distribution of " is assumed to be known. The model

above gives different models depending on the specification of the distribution

of " and, in particular, it includes the proportional hazards model and the

proportional odds model as special cases.

Many inference procedures have been developed for regression analysis of

interval-censored data under the models mentioned above and other models.

For a relatively complete review of these procedures, the readers are again

referred to Sun (2006) and Zhang and Sun (2010b). One thing that is worth

pointing out is that for right-censored data, most of available inference proce-

dures involve regression parameters only. That is, one only deals with the finite

or parametric part of the underling semiparametric model. One well-known
such example is of course the partial likelihood approach for the proportional

hazards model. Unlike these methods developed for right-censored data, es-

timating regression parameters under interval-censoring usually involves esti-

mation of both parametric and nonparametric parts of the underlying models.

In other words, for interval-censored data, one has to deal with estimation of

some unknown baseline functions in order to estimate regression parameters

due to the complex structure of the data. To deal with this, one approach is

to apply some approximations to the unknown baseline hazard or cumulative

hazard function such as sieve approximation and spline functions (Lin and

Wang (2010); Yavuza and Lambert (2010); Zhang et al. (2010)).

Many problems still exist on regression analysis of interval-censored data.

For example, model checking is a common topic for any regression analysis

and, unlike the case for right-censored data, only some ad-hoc procedures

are available for interval-censored data (Sun (2006)). The situation is similar