Biomedical Engineering Reference
In-Depth Information
from the \IntCox" approach in analyzing interval-censored data. We illustrate ap-
plications of the methods in Section 11.4 using data from an HIV application and
conclude with a discussion in Section 11.5.
11.2
Data and Models
11.2.1
Data Structure
The data structure for interval-censored time-to-event data is typically denoted by
(t
1
;t
2
], where t
1
and t
2
are the observed left/right-endpoints of the intervals. In fact,
this structure is very general and includes left-censored, right-censored, and observed
exact time as follows:
•Left-censored: If t
1
is a missing value or zero, then t
2
is considered left-
censored.
•Right-censored: If t
2
is a missing value, then t
1
is considered right-censored.
•Complete time: If t
1
= t
2
and t
1
is not missing, then t
1
is the complete time.
•Interval-censored: If neither t
1
nor t
2
is missing and t
1
< t
2
, then the time is
considered interval-censored in the interval (t
1
;t
2
].
Therefore, for n patients in a biomedical clinical trial or publication health appli-
cation, the observed time-to-event data structure is (ti1,
i1
;t
i2
] for i = 1; ;n along
with a covariate vector of Xi
i
from each patient, where Xi
i
= (x
i1
; ;x
ip
) and one
or more of the x can represent an indicator variable for assessing treatment effect.
11.2.2
Statistical Models
A well-known statistical model in analyzing right-censored time-to-event data is the
Cox (Cox, 1972) proportional hazards regression (in short, Cox regression) model,
which can account for covariate information on patients in addition to their observed
survival times. The Cox model is specified in terms of the hazard function instead
of the survival function, and assumes that additive changes in the concomitant vari-
ables correspond to multiplicative changes in the hazard function or, equivalently,
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