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RegisterMarzo / Balant formula [Power / Sample Size]
Dear kumarnaidu,
the Marzo/Balant1) formula is one of the numerous approximate quick calculation formulas for estimating the sample size which arose in the good old ages
where computers were rare and software for exact sample size estimation seldom available.
The formula is very simple:
It was derived under the following prerequisites from a large sample approximation of the number of subjects (see 2)):
log-normal data, 2x2 crossover design, power = 0.8, 'true' ratio T/R=1, intra-subject variance ~ CV^2.
Especially the restriction to T/R = 1 makes the formula nowadays obsolete. These days sample size estimations usually uses a 'true' T/R of 0.95 or something similar.
A slightly better approximation for higher CV's is obtained by using
Here a comparison of the exact results (PowerTOST) and the Marzo/Balant formula(s):
uneven numbers in marzo, marzo2 rounded to next even
↓ too low, ↑ too high
In the current modern times there is no need for such formulas and they shouldn't be used any longer. Just fire up R-project and use the PowerTOST-package for your sample size estimation
.
1)Marzo, A.; Balant, L. P.
"Bioequivalence: an updated reappraisal addressed to applications o interchangeable multi-sorce pharmaceutical products"
Arzneim. – Forsch./Drug Res., Aulendorf, v. 45, n.2, p. 109-115, 1995
2)
Steven A. Julious
"Sample Sizes for Clinical Trials"
Chapman & Hall/CRC, Boca Raton, 2010
Chapter 7.2.1.2
the Marzo/Balant1) formula is one of the numerous approximate quick calculation formulas for estimating the sample size which arose in the good old ages
where computers were rare and software for exact sample size estimation seldom available.The formula is very simple:
n = 392 * CV^2It was derived under the following prerequisites from a large sample approximation of the number of subjects (see 2)):
log-normal data, 2x2 crossover design, power = 0.8, 'true' ratio T/R=1, intra-subject variance ~ CV^2.
Especially the restriction to T/R = 1 makes the formula nowadays obsolete. These days sample size estimations usually uses a 'true' T/R of 0.95 or something similar.
A slightly better approximation for higher CV's is obtained by using
n = 392 * se^2 with se^2 = log(CV^2 + 1) (marzo2).Here a comparison of the exact results (PowerTOST) and the Marzo/Balant formula(s):
CV exact marzo marzo2
0.100 6 4↓ 4↓
0.125 8 6↓ 6↓
0.150 10 10 10
0.175 14 12↓ 12↓
0.200 16 16 16
0.225 20 20 20
0.250 24 24 24
0.275 28 30↑ 30↑
0.300 32 36↑ 34↑
0.325 36 42↑ 40↑
0.350 42 48↑ 46↑
0.375 48 56↑ 52↑
0.400 54 64↑ 58↑uneven numbers in marzo, marzo2 rounded to next even
↓ too low, ↑ too high
In the current modern times there is no need for such formulas and they shouldn't be used any longer. Just fire up R-project and use the PowerTOST-package for your sample size estimation
.1)Marzo, A.; Balant, L. P.
"Bioequivalence: an updated reappraisal addressed to applications o interchangeable multi-sorce pharmaceutical products"
Arzneim. – Forsch./Drug Res., Aulendorf, v. 45, n.2, p. 109-115, 1995
2)
Steven A. Julious
"Sample Sizes for Clinical Trials"
Chapman & Hall/CRC, Boca Raton, 2010
Chapter 7.2.1.2
—
Regards,
Detlew
Regards,
Detlew
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