A Review of Various Models for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 40

8
<

P(K = 0;Y 00 x) if I = fxg for some x

f Y K;1 (k;u) if I = (1;u]

Note: G(I) = Asymp-

P j=1 f Y K;j1 ;Y K;j (u;v)

:

if I = (u;v]

f Y K;K (v) if I = (v;1):

totic properties of the NPMLE of F under the MIC models have been

established in Huang (1999) and Yu et al. (2001). In particular, under
the MIC Model I,

j F(t) F(t)j a:s

sup
t

! 0:

Moreover,

p

n( F(t) F(t)) D ! N(0; t ):

2.3 About Multivariate IC Models

If T is a d-dimensional survival vector and each of its coordinates is subject to

censoring, then we have multivariate censored data. The National Longitudinal

Survey of Youth 1979-98 (NLSY) is actually bivariate IC data, as each unit
is potentially a married couple. In such a case, I is a random subset of R d ,

which is a product of d intervals and T 2I. Our observations are I 1 , ..., I n ,
which are i.i.d. copies of I again. The multivariate IC model is specified by

specifying the IC model for each each Ii. i . Wong and Yu (1999), Van der Vaart
and Wellner (2000), and Yu et al. (2005) establish some consistency results

for the GMLE with the bivariate interval-censored data.