Achievwin
★

US,
2024-05-03 15:43
(46 d 02:54 ago)

Posting: # 23977
Views: 1,470

## Probability of Success in BE studies [Design Issues]

Recently I was asked to give Probability of success for a proposed BE study, My thinking is Target study power (usually 80%) is POS with additional correction factor due to the variability during study conduct applied to this target power, is my understanding correct?

Challenge is that do you substract or a multiply the variability factor?

e.g. POS = Target Power (90) - 30 (CV)= 60 0r 90X(1-0.30)=63%

Achievwin
Helmut
★★★

Vienna, Austria,
2024-05-03 16:15
(46 d 02:22 ago)

@ Achievwin
Posting: # 23979
Views: 1,285

## Probability of Success in BE studies

Hi Achievwin,

❝ Recently I was asked to give Probability of success for a proposed BE study, My thinking is Target study power (usually 80%) is POS with additional correction factor due to the variability during study conduct applied to this target power, is my understanding correct?

Not sure whether I understand you correctly. POS is a Bayesian concept, where you need some prior information. Let’s start with a conventional sample size estimation based purely on assumptions.

library(PowerTOST) CV     <- 0.25 theta0 <- 0.95 target <- 0.80 sampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target, details = FALSE) +++++++++++ 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 True ratio = 0.95,  CV = 0.25 Sample size (total)  n     power 28   0.807439

Say, you obtained the CV and T/R-ratio in another study with 24 subjects. Based on that, you can take the uncertainty of the CV (#1), of the T/R-ratio (#2), or both (#3) into account.

m <- 24 # sample size of prior study

1. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "CV", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++        Sample size est. with uncertain CV ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 CV = 0.25 with 22 df Sample size (ntotal)  n   exp. power 32   0.822645
2. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "theta0", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++      Sample size est. with uncertain theta0 ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 CV = 0.25 Sample size (ntotal)  n   exp. power 44   0.810063
3. expsampleN.TOST(CV = CV, theta0 = theta0, design = "2x2", targetpower = target,                 prior.parm = list(m = m, design = "2x2"), prior.type = "both", details = FALSE) ++++++++++++ Equivalence test - TOST ++++++++++++   Sample size est. with uncertain CV and theta0 ------------------------------------------------- Study design:  2x2 crossover log-transformed data (multiplicative model) alpha = 0.05, target power = 0.8 BE margins = 0.8 ... 1.25 Ratio = 0.95 with 22 df CV = 0.25 with 22 df Sample size (ntotal)  n   exp. power 48   0.801190
As usual, the T/R-ratio is the killer.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Achievwin
★

US,
2024-05-06 16:49
(43 d 01:47 ago)

@ Helmut
Posting: # 23985
Views: 1,202

## Probability of Success in BE studies

❝ Not sure whether I understand you correctly. POS is a Bayesian concept, where you need some prior information.

I am sorry I am equally confused in this example where do we find POS? what all I see is Sample size and anticipated power with certain N.

How come we have three different N with same assumptions?

❝ As usual, the T/R-ratio is the killer.

----- Thanks for reiterating my thought all along many of my colleagues are having issue in understanding T/R is main culprit than ISCV in Sample size estimates.

Please edcuate me on how to connect Power with POS?

d_labes
★★★

Berlin, Germany,
2024-05-06 17:16
(43 d 01:20 ago)

@ Achievwin
Posting: # 23986
Views: 1,191

## Probability of Success in BE studies

Hi Achievwin,

❝ I am sorry I am equally confused in this example where do we find POS? what all I see is Sample size and anticipated power with certain N.

What you see is sample size and expected power!
Expected power is synonym with Probability of success. Sometimes also called assurance.

If you have need consult the file 'Expected_Power_for_TOST.pdf' in the docs folder
(c:\Program Files\R\library\PowerTOST\doc\ for my installation) of the package PowerTOST. Its a little bit theoretic and mainly mathematical but describes in a comprehensive manner what expected power is and how it will be calculated.

Regards,

Detlew
Achievwin
★

US,
2024-05-06 17:31
(43 d 01:05 ago)

@ d_labes
Posting: # 23988
Views: 1,177

## Probability of Success in BE studies

Thank you for the take home message

Expected power is synonym with Probability of success. Sometimes also called assurance.

Helmut
★★★

Vienna, Austria,
2024-05-06 17:31
(43 d 01:06 ago)

@ Achievwin
Posting: # 23987
Views: 1,178

## Assumptions (plural)

Hi Achievwin,

❝ How come we have three different N with same assumptions?

As outlined above, you can make three different assumptions.
1. Uncertain CV → n = 28
2. Uncertain T/R-ratio → n = 44
3. Uncertain CV and uncertain T/R-ratio → n = 48
As always with Bayesian methods, the Prior is important. Play with my example and change the size of the pilot study (i.e., the value m). The smaller, the larger the sample size of the next. There­fore, small pilot studies are not a good idea. It may sound stupid, but the best for sample size estimation is a failed pivotal study…

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes
Achievwin
★

US,
2024-05-06 17:51
(43 d 00:45 ago)

@ Helmut
Posting: # 23989
Views: 1,177

## Assumptions (plural)

❝ ❝ How come we have three different N with assumptions?

❝ … three assumptions,

❝   1. Uncertain CV → n = 28

❝   2. Uncertain T/R-ratio → n = 44

❝   3. Uncertain CV and uncertain T/R-ratio → n = 48

Thank you Helmut.... now even I can understand......