
231Sample Size and Value of Information for Cost-Effectiveness Trials
Cov x
E2
− x
E1
, x
C 2
− x
C1
( )
= ρσ
E
σ
C
1
+
1
⎛
⎝
⎜
⎞
⎠
⎟
=
2ρσ
E
σ
C
=
2ρσ
E
σ
C
(8C.4)
and hence the two sample size formulae become identical in this special
caseas
n
CE
= n
BT
= 2 z
α
+ z
β
( )
2
k
2
σ
E
2
+ σ
C
2
− 2kρσ
E
σ
C
⎡
⎣
⎤
⎦
2
(8C.5)
Therefore, when the standard deviations of the cost and efcacy are equal,
Briggs & Tambour’s (2001) sample size formula is a special case of this when
the correlation coefcient of the two treatment arms is equal.