Biomedical Engineering Reference
In-Depth Information
parison criteria. An open source, user-friendly implementation in the form of
an R package is briefly described in Section 7.5. The performances of a subset
of competing models are compared via a comprehensive simulation study in
Section 7.6. The methods are illustrated in detail with survival times from
a breast cancer data set in Section 7.7. We conclude with a discussion in
Section 7.8.
7.2
Bayesian Models
7.2.1
Notations
We rst introduce some notations. For subject i, i = 1;:::;n, let T
i
be the
unobserved event time, [Li,
i
;R
i
) the observed censoring interval containing Ti,
i
,
and x
i
a p-dimensional vector of covariates.
We specify a ne time grid, G = f0 = a
0
< a
1
< a
2
< ::: < a
K
<
a
K+1
= 1g, which covers all the endpoints of observed censoring intervals.
Let
k
= a
k
a
k1
denote the width of the k-th interval, k = 1;:::;K.
We write Li
i
= a
`
i
and R
i
= a
r
i
, i = 1;:::;n. We note that when r
i
=
K + 1 (or R
i
= 1), [L
i
;R
i
) reduces to right-censored data. Also, let h
0
(t)
be the baseline hazard function, H
0
(t) =
R
t
0
h
0
(u)du the cumulative baseline
hazard function, and (t) the p-dimensional vector function of time-varying
regression coecients. Finally, let D
obs
= f[L
i
;R
i
); x
i
; i = 1;:::;ng denote
the observed interval-censored data.
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