A Review of Various Models for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 34

8
<

P(U = 2) if I 6= (1;1)

conditions (2.3) and (2.4) hold. Typically, if the

:

P(U = 0) if I = (1;1);

censoring vector C ? T, then conditions (2.3) and (2.4) hold, such as the

models to be discussed in Section 2.2.2 and Section 2.2.3.

2.2.2 Various Models for C1 or C2 Data

1. The Current Status Model (Ayer et al., 1995) or Case 1 Interval Cen-

sorship (IC) Model (Groeneboom and Wellner, 1992). Assume

8
<

(1;C] if T C

(1) I =

:

(C;1) if T > C;

(2) T ? C;

(3) F C is non-informative.

Note: G() = f C (). Case 1 IC Model is quite intuitive and realistic. Ayer
et al. (1995), Groeneboom and Wellner (1992), Yu and Wong (1998),

and Schick and Yu (2000) establish various asymptotic properties of the

NPMLE of F. Huang (1996) claims a uniform strong consistency result

on the NPMLE under the continuity assumptions. But the claim is false
(see Schick and Yu (2000)).

2. Case 2 IC Model (Groeneboom and Wellner, 1992). Assume

8
<

(1;Y 1 ] if T Y 1

(1) I =

(Y 1 ;Y 2 ] if Y 1 < T Y 2

:

(Y 2 ;1) if T > Y 2 ;

(2) T ? C, where C = (Y 1 ;Y 2 ) and Y 1 < Y 2 ;

(3) F Y 1 ;Y 2 is noninformative.