
174 Sample Size Calculations for Clustered and Longitudinal Outcomes
Time from baseline T
k
0 1 2 T
end
=(N
1
–1)
δ
XZT
T
end
X=0, Z=0
X=0, Z=1
X=1, Z=0
X=1, Z=1
η
00
η
01
η
10
η
11
= S
11
+
δ
XZT
S
11
FIGURE 5.2
Geometrical representations of fixed parameters in model (5.31) for a 2-by-2
factorial longitudinal cluster randomized trial.
Note: η
00
= δ
T
; η
01
= η
00
+δ
ZT
= δ
T
+δ
ZT
η
10
= η
00
+δ
XT
= δ
T
+δ
XT
; S
11
=
η
00
+ δ
XT
+ δ
ZT
= δ
T
+ δ
XT
+ δ
ZT
represents a hypothetical slope for the
(X = 1, Z = 1) arm under the null hypothesis H
0
: δ
XZT
= 0 in model (5.31);
and η
11
= η
00
+ δ
XT
+ δ
ZT
+ δ
XZT
= S
11
+ δ
XZT
.
2 units. In a balanced design, the sample sizes of the other cells are identical
to N
(1,1)
2
, i.e., ...