Bioequivalence and Bioavailability Forum • calculation of power with power.TOST

Ken Peh
★

Malaysia,
2013-07-29 21:03
(4290 d 08:55 ago)

Posting: # 11117
Views: 6,185

calculation of power with power.TOST [🇷 for BE/BA]

Dear All,

We would like to estimate the power of a BE study that has been completed. The no of subjects enrolled was 28 but 3 dropped out. Hence, left only 25 subjects.

In R-Software, we key the data using two different approaches :-
No 1

power.TOST(CV=0.29, n=25, theta0=0.95)

[1] 0.618512

No 2

power.TOST(CV=0.29, n=25, theta0=0.95, theta1=0.83, theta2=1.09)

[1] 0.07853425

Which is the right way to key in data ? The first one or the second one ? :confused:

Do we have to key in the value of lower and upper BE limit obtained from the study ? Why after putting in the lower and upper BE limit, the power is only about 8% versus 62%.

Your input is highly appreciated.

Thank you.

Regards,
Ken

Edit: Category changed. [Helmut]

Helmut
★★★

Vienna, Austria,
2013-07-29 23:30
(4290 d 06:28 ago)

@ Ken Peh
Posting: # 11118
Views: 5,758

power.TOST (CV & n; everything else optional—with defaults)

Post reply

Hi Ken!

❝ We would like to estimate the power of a BE study that has been completed.

Oh, is your authority still requiring this? :no:

❝ Which is the right way to key in data ? The first one or the second one ?

No. 1

Since you didn’t type in the lower (theta1) and upper (theta2) acceptance limits for bioequivalence, the defaults of 0.80 and 1/0.80=1.25 are used. But if you want you can state them. Try:

power.TOST(CV=0.29, n=25, theta0=0.95, theta1=0.80, theta2=1.25)

[1] 0.618512

You can play the game the other way ’round: How many subjects would we need for 61.85% power if CV is 29%?

sampleN.TOST(CV=0.29, targetpower=0.6185)



+++++++++++ Equivalence test - TOST +++++++++++

            Sample size estimation

-----------------------------------------------

Study design:  2x2 crossover 

log-transformed data (multiplicative model)



alpha = 0.05, target power = 0.6185

BE margins        = 0.8 ... 1.25 

Null (true) ratio = 0.95,  CV = 0.29



Sample size (total)

 n     power

26   0.640848

26 – not 25 – because in study planning you get always even numbers in a 2×2 design. Note that I did not use theta0, theta1, and theta2 because 0.95, 0.80, and 1.25 are the defaults.

❝ Do we have to key in the value of lower and upper BE limit obtained from the study ? Why after putting in the lower and upper BE limit, the power is only about 8% versus 62%.

No. That would mean asking for the chance to be bioequivalent (with CV 29%, ratio 95%) within limits of 83–109%. This range is much narrower than 80–125% – therefore, you get a much lower power. I guess your values are the confidence limits obtained in the study, right?

BTW, BE-limits are based on the maximum acceptable difference, say 20%. In log-scale they are symmetrical around zero [ln(1–0.20), ln(1/(1+0.20)] = [-0.2231, +0.2231]. After back-transformation they are asymetrical around 100% [ℯ^-0.2231, ℯ^+0.2231] = 80–125%. Hey, that’s upper = 1/lower. ;-)

Therefore, in Power.TOST you could only give theta1 or theta2; the reciprocal would be calculated automatically. Try:

power.TOST(CV=0.29, n=25, theta0=0.95, theta1=0.80)

power.TOST(CV=0.29, n=25, theta0=0.95, theta2=1.25)

For details:

require(PowerTOST)

help(power.TOST)

@Detlew: Maybe PowerTOST should throw a warning if the input’s theta2 ≠ 1/theta1 (to the precision of the input)? Or is this over the top?

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ElMaestro ★★★ Denmark, 2013-07-29 23:54 (4290 d 06:04 ago) @ Helmut Posting: # 11119 Views: 5,218	power.TOST (CV & n; everything else optional—with defaults) Post reply
	Hi Helmut, ❝ @Detlew: Maybe PowerTOST should throw a warning if the input’s `theta2` ≠ `1/theta1` (to the precision of the input)? Or is this over the top? Nice idea, actually. I am anticipating a borderline grumpy reply like "Take my code and do it better." from him — Pass or fail! ElMaestro

d_labes
★★★

Berlin, Germany,
2013-07-30 13:57
(4289 d 16:01 ago)

@ ElMaestro
Posting: # 11123
Views: 5,265

power.TOST acceptance range unbalanced

Post reply

Hi Old sailor, hi Helmut,

❝ ❝ @Detlew: Maybe PowerTOST should throw a warning if the input’s theta2 ≠ 1/theta1 (to the precision of the input)? Or is this over the top?

I'm not quite sure if this is worth a warning.
It is quite unusual to use other BE acceptance limits than theta2=1/theta1 or vice versa. But ... maybe some guy wishes to do so, for instance if a regulator deemed him to do so, see Canada "Critical dose drugs": The 90% confidence interval of the relative mean AUC* of the test to reference formulation should be within 90.0% to 112.0% inclusive.

The implemented algorithm is valid also if theta2 ≠ 1/theta1, I think.

❝ Nice idea, actually. I am anticipating a borderline grumpy reply like "Take my code and do it better." from him :-D :-D

Only for those who criticise peanuts while on the other hand stating "not often using PowerTOST". Thank you for not using PowerTOST. Me too since I got stuck with SAS :cool:

.

@Ken: Since you have dropouts I'm sure that your data are unbalanced. Therefore I recommend you the function power2.TOST().

Key in the number of subjects in the sequence groups, the GMR (0.95?) from your study and the CV:

power2.TOST(CV=0.29, n=c(14,11), theta0=0.95)

[1] 0.6106208

I have assumed worse case that all dropouts are from the same sequence group. Note the drop of power compared to your calculation via power.TOST() which assumes balanced studies.

—
Regards,

Detlew

Ken Peh ★ Malaysia, 2013-07-30 20:53 (4289 d 09:05 ago) @ d_labes Posting: # 11132 Views: 5,108	power.TOST acceptance range unbalanced Post reply
	Dear Detlew, Thank you very much for your guidance. Will use power2.TOST to recalculate. Regards, Ken

Ken Peh ★ Malaysia, 2013-07-30 21:03 (4289 d 08:55 ago) @ Helmut Posting: # 11133 Views: 5,112	power.TOST (CV & n; everything else optional—with defaults) Post reply
	Dear Helmut, Thank you very much for your prompt reply. ❝ Oh, is your authority still requiring this? Yes, it is still in the guideline. I have brought this up to the authority but it has not been discussed yet. The generic is BE to comparator but the power is less than 80%. Will leave it out and answer when asked by the authority. Regards, Ken