Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 18

of clustered interval-censored data, in addition to the basic issues discussed
before for univariate data, a new issue is to make inference about the associ-
ation between the related failure time variables. For this and in general, two
commonly approaches are the frailty model approach and copula model ap-
proach (Hougaard (2000)). The former uses some latent variables to represent
the association or correlation, while the latter provides a very flexible way
to model the joint survival function. Sun (2006) and Zhang and Sun (2010b)
provided more discussion on them and a relatively complete coverage of the
literature available for the analysis of clustered interval-censored data, espe-
cially multivariate interval-censored data.
As discussed in Sun (2006) and Zhang and Sun (2010b), many authors
have considered the inference about multivariate interval-censored data such
as nonparametric estimation of the joint survival function and regression anal-
ysis. Some recent references on this include Chen et al. (2009), Hens et al.
(2009), and Nielsena and Parner (2000). Specifically, Chen et al. (2009) and
Nielsena and Parner (2000) studied multivariate current status data and gen-
eral interval-censored data, respectively, while Hens et al. (2009) discussed
the analysis of bivariate current status data. With respect to future research
on multivariate interval-censored data, one direction is nonparametric estima-
tion. Although there exist some algorithms for nonparametric estimation of
a survival function based on bivariate interval-censored data, a great deal of
work is needed for problems such as the estimation for general multivariate
data and the variance estimation. The asymptotic properties of the existing
estimates are also still largely unknown. For regression analysis of multivari-
ate interval-censored data, most of the existing methods are either parametric
approaches or marginal approaches. It is obvious that the former may not
be preferred unless there exists strong evidence for the assumed parametric
model, while the latter may not be ecient.
Unlike for multivariate interval-censored data, there exists little literature
on general clustered interval-censored data except Kim (2010), Xiang et al.