Bioequivalence and Bioavailability Forum

Hi Compliance,

❝ can any one tell us how to calculate sample size by using power-tost software.

Sure.

❝ we had tried a lot but unable to understand how to use this software.

That’s not what I call an exhaustive description of the problem. What did you try? What did not work?

Start the R-console and attach the library by typing library(PowerTOST). Type help(package=PowerTOST). The help-index opens in your preferred browser and shows a list of available functions.
Try sampleN.TOST. If you are just interested in sample size estimation, type simply ?sampleN.TOST).
On top below “Usage” you see all “arguments“ you may specify. Some are defaults; you can leave them out if your study is within the variables’ range.
Most simple case: You want to estimate* the sample size for a 2×2×2 cross-over, CV 20%, assumed T/R-ratio 95%, 80% power. Just type
sampleN.TOST(CV=0.2)
and you will get
+++++++++++ Equivalence test - TOST +++++++++++
            Sample size estimation
-----------------------------------------------
Study design:  2x2 crossover
log-transformed data (multiplicative model)

alpha = 0.05, target power = 0.8
BE margins        = 0.8 ... 1.25
Null (true) ratio = 0.95,  CV = 0.2

Sample size (total)
 n     power
20   0.834680
Note that everything in PowerTOST is given in fractions – not percentages.

If the output is too verbose for your taste, switch it off to get a data.frame:
sampleN.TOST(CV=0.2, print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1    2x2  0.05 0.2   0.95    0.8   1.25          20      0.8346802          0.8

Power 90% instead of 80%:
sampleN.TOST(CV=0.2, targetpower=0.9, print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1    2x2  0.05 0.2   0.95    0.8   1.25          26      0.9176333          0.9

Worse ratio:
sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1    2x2  0.05 0.2    0.9    0.8   1.25          50      0.9008663          0.9

Long half-life drug and/or study in patients? Note that the CV is CV_total and not CV_intra. Likely to be higher. 80% power is all we can afford:
sampleN.TOST(CV=0.5, targetpower=0.8, theta0=0.9, design="parallel", print=F, details=F)
    Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1 parallel  0.05 0.5    0.9    0.8   1.25         400      0.8007482          0.8

Sample size in the 2×2×2 above (50) larger than the clinical capacity? Try a 4-period full replicate design (TRTR|RTRT):
sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x2x4", print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1  2x2x4  0.05 0.2    0.9    0.8   1.25          26      0.9130555          0.9

Four periods lead to unacceptable high sampling volumes or you are concerned about dropouts? Try a 3-period full replicate (TRT|RTR):
sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x2x3", print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1  2x2x3  0.05 0.2    0.9    0.8   1.25          38      0.9066936          0.9

… or a partial replicate (TRR|RTR|RRT):
sampleN.TOST(CV=0.2, targetpower=0.9, theta0=0.9, design="2x3x3", print=F, details=F)
  Design alpha  CV theta0 theta1 theta2 Sample size Achieved power Target power
1  2x3x3  0.05 0.2    0.9    0.8   1.25          39      0.9131147          0.9

OK, the study is for EMA and we are allowed to widen the acceptance range for C_max only. CV with 50% is higher than the one of AUC. If we run the study in 26 subjects, how much power can we expect?
power.scABEL(CV=0.5, theta0=0.9, design="2x2x4", n=26)
[1] 0.78733

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• Avoid the word ‘calculate’. The input are either estimates themselves (CVs, ratios of previous studies) or assumptions (the expected ratio of the next study). You can only estimate something from un­cer­tain input. It’s not like 2 × 2 = 4.