Biomedical Engineering Reference
In-Depth Information
general approach adopted while avoiding the somewhat more cumbersome no-
tation required to account for loss to follow-up. In Section 8.4, we describe the
extension required in order to tackle the more general setting whereby loss to
follow-up indeed occurs during the study. We discuss estimation of alternative
target parameters of interest in Section 8.5. We provide concluding remarks
in Section 8.6, and close this chapter with some bibliographic references in
Section 8.7.
8.2
Formulation of Causal Framework
8.2.1
Definition of Parameter
Suppose that t
0
= 0 < t
1
< t
2
< ::: < t
m+1
form a suciently fine grid
including all possible times until a monitoring event or death observable within
the study time frame. In particular, t
m+1
is the time elapsed since baseline
until the last study monitoring time. Denote by T
0
the time until the event
of interest, by T
00
the time until death, and by T = min(T
0
;T
00
) the time
until either the event of interest or death. For simplicity of discussion, we
assume that a patient is assigned, at baseline, to either a treatment or control
group. This assumption is made for convenience and can readily be relaxed
to account for multiple treatment groups. The underlying unit data structure
for a typical study participant can be represented as a time-ordered vector
X = ( M
0
;A; Y
0
;
0
; M
1
; Y
1
;
1
;:::; M
m
; Y
m
;
m
; M
m+1
; Y
m+1
) ;
where M
k
is a vector of covariates at time t
k
, A is the binary baseline treatment
indicator, Y
k
= I
(0;t
k
]
(T) is the indicator of survival until time t
k
without
having experienced the event of interest, and
k
is the indicator of being
monitored at time t
k+1
. The observed unit data structure for a typical study
Search WWH ::
Custom Search