cakhatri Regular India, 20171130 09:44 Posting: # 18024 Views: 1,789 

Dear All, I would like to know 1.What BE limits should be taken into consideration while estimating sample size for replicate design studies for USFDA & EMA. Should it be 80125% ? We normally use FARTSSIE Why the Question 1. For a product with 51% ISCV (from a completed partial replicate study UKMHRA) by using FARTSSIE we arrived at different sample size for EMA  Sample size estimated =27 (80% Power, 95105% T/R, Method C1, BE Limits 69.84 to 143.19%)  Sample size estimated = 76 (80% Power,95105% T/R, No reference Scaled BE Limits80125%) Which sample size should we consider for pivotal study Regards Chirag 
Helmut Hero Vienna, Austria, 20171130 10:58 @ cakhatri Posting: # 18025 Views: 1,641 

Hi Chirag, » What BE limits should be taken into consideration while estimating sample size for replicate design studies for USFDA & EMA. If you want to go with referencescaling, none! They depend on the CV_{wR} and are obtained in the actual study. Hence, you need simulations, where your assumed CV_{wR} is the mean. Either use the tables provided by the two Lászlós* or package PowerTOST for R. The software is open source and comes free of costs. » Should it be 80125% ? No (see above). Only if you don’t want referencescaling (i.e., conventional ABE). Actually referencescaling was introduced to avoid the extreme sample sizes required for ABE. » We normally use FARTSSIE FARTSSIE cannot perform the necessary simulations and therefore, is not suitable for any of the referencescaling methods. » For a product with 51% ISCV (from a completed partial replicate study UKMHRA) by using FARTSSIE we arrived at different sample size for EMA » »  Sample size estimated =27 (80% Power, 95105% T/R, Method C1, BE Limits 69.84 to 143.19%) »  Sample size estimated = 76 (80% Power,95105% T/R, No reference Scaled BE Limits80125%)
PowerTOST , start the Rconsole, and type library(PowerTOST) . If you want to make yourself familiar with PowerTOST , type help(package=PowerTOST) .Try these examples, where "2x2x4" denotes the 4perod full replicate, "2x2x3" the 3period full replicate, and "2x3x3" the 3sequence 3period (partial) replicate.
theta0=0.95 to the function calls but don’t blame me if the study fails. If you want 90% power instead of the default 80%, add the argument targetpower=0.90 .I suggest to perform a power analysis (recommended by ICH E9) assessing the influence of deviations from assumptions (lower/higher CV_{wR}, T/R deviating more than expected from 100%, less eligible subjects due to dropouts). Try (with the default partial replicate):
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Astea Regular Russia, 20171130 22:50 (edited by Astea on 20171201 14:18) @ Helmut Posting: # 18028 Views: 1,567 

» FARTSSIE cannot perform the necessary simulations and therefore, is not suitable for any of the referencescaling methods. Just few words in defence of FARTSSIE. May be the approximations are rude, far from exact PowerTOST (see #), but the results overally seems to be correlated for CV>30%:
design 2x2x4 2x2x3 (2x3x3 from Table) here F  FARTSSIE22 (note: sample size should be additionally rounded) R  PowerTOST v.1.4.6, sampleN.scABEL T Table from Endrényi L, Tóthfalusi L. Sample Sizes for Designing Bioequivalence Studies for Highly Variable Drugs. J Pharm Pharmaceut Sci. 2011;15(1):73–84. (*edit: the last columns refers to 2x3x3 design) 
Helmut Hero Vienna, Austria, 20171201 11:42 @ Astea Posting: # 18029 Views: 1,522 

Hi Astea, » Just few words in defence of FARTSSIE. May be the approximations are rude, far from exact PowerTOST (see #), but the results overally seems to be correlated for CV>30%: Nope. The EMA’s ABEL not only means extending the limits (based on the observed – not the assumed CV_{wR}) but also assessing the GMRrestriction. It’s a complex framework and therefore, no simple formula exists to calculate power. Try this one:
For all CVs FARTSSIE’s sample sizes will give the desired power for ABE (column pwr.ABE ) but not for ABEL (column pwr.FARTSSIE ). For CV 30% it will be too high (since only 34 subjects are required) but for CV >30% too low (more subjects are required). Only sampleN.scABEL() will give sample sizes (n.ABEL ) with at least the desired power (pwr.ABEL ).As expected, FARTSSIE screws completely up if one wants to assess the Type I Error. Set “Method C1” and the 4period replicate. Try Calculate Power with CV 30%, T/R 125%, sample size 34. I got
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Astea Regular Russia, 20171201 14:16 @ Helmut Posting: # 18031 Views: 1,479 

Dear Helmut! Thank you for enlightening this question! The advadvantage of R is doubtless. I just wanted to show FARTSSIE not worser than other rude methods of sample size estimation (remember nomogram and so on). (Sorry, I've made a mistake in the previous post, the data from the paper refers to partial replicate design 2x3x3.) By the way, for extreme numbers from the paper by Endrényi L, Tóthfalusi L. we also get slightly underpowered study:
> power.scABEL(CV=0.8,n=54,theta0=0.95,design="2x3x3") 
cakhatri Regular India, 20171204 06:00 @ Astea Posting: # 18032 Views: 1,389 

Dear Helmut & Astea, Thankyou for the response. Honestly this is too much of statistics for me to understand. We are discussing with our statisticians & medical writing team to fully understand the response and implement accordingly. I shall revert in case of any queries Thankyou once again Regards Chirag 
Helmut Hero Vienna, Austria, 20171204 15:07 @ cakhatri Posting: # 18034 Views: 1,359 

Hi Chirag, your statisticians should read the relevant papers and register here / ask questions directly. Better than Chinese Whispers. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
cakhatri Regular India, 20171205 05:33 @ Helmut Posting: # 18035 Views: 1,322 

Dear Helmut, Very True. The statistician was advised to do so and has already created a login yesterday or day before. Regards Chirag 
d_labes Hero Berlin, Germany, 20171206 09:52 @ Astea Posting: # 18037 Views: 1,236 

Dear Astea! » ... » By the way, for extreme numbers from the paper by Endrényi L, Tóthfalusi L. we also get slightly underpowered study: » > power.scABEL(CV=0.8,n=54,theta0=0.95,design="2x3x3") » [1] 0.79917 » > power.scABEL(CV=0.8,n=72,theta0=0.9,design="2x3x3") » [1] 0.79782 » ... The sample sizes in the paper of the two Laszlos are based on 10 000 simulations (only). Additionally the seed of the pseudorandom number generator for the sims was presumably different. Try this: > power.scABEL(CV=0.8, n=54, theta0=0.95, design="2x3x3", nsims=10000) With nsims=1E6 and setseed=F on the other hand I don't succeed to obtain power>0.8 (20 tries).One more reason to use PowerTOST's power.scABEL() / sampleN.scABEL() functions . Also w.r.t the tables in the paper of the two Laszlos.— Regards, Detlew 
mittyri Senior Russia, 20171207 16:03 @ d_labes Posting: # 18043 Views: 1,134 

Dear Detlew, here comes a magik (citing the paper): The precision of the estimation was evaluated by running the simulations twenty times at twentytwo different conditions (different CV’s, different GMR’s and different designs). Seed was sampled 'unfortunately' about 20 times? — Kind regards, Mittyri 
d_labes Hero Berlin, Germany, 20171207 18:21 (edited by d_labes on 20171208 14:38) @ mittyri Posting: # 18044 Views: 1,124 

Dear mittyri, » here comes a magik (citing the paper): » The precision of the estimation was evaluated by running the simulations twenty times at twentytwo different conditions (different CV’s, different GMR’s and different designs). » » » Seed was sampled 'unfortunately' about 20 times? What do you mean by 'unfortunately'? This sentence describes an investigation of how precise the simulated power values are. Read the paragraph forward: "The standard deviation of the simulated powers (20 values under each combination of CV, GMR and design, each with 10 000 sims; my insertion) was calculated under each condition; the mean of these standard deviations was 0.460. Thus, the precision of the power estimation is about ±0.5%." They must have of course always choosen a different seed for the 20 repetitions under each combination of CV, GMR and design. Else you would get always the same result under each combination. Of course they had also the opportunity to obtain a precision estimate via binomial distribution, without the burden of all that calculations. But then the random number generator had to be ideal. BTW: Both Laszlos recommend to use PowerTOST if they were asked . — Regards, Detlew 
mittyri Senior Russia, 20171208 22:56 @ d_labes Posting: # 18048 Views: 1,047 

Dear Detlew, thank you for clarification I tried to figure out the precision of PowerTOST estimations with the following code:
library("ggplot2") please correct if it is wrong. The resulted plot: BAsed on the mean and se calculated from sd and n=20 I would say that sample mean 80% in PowerTOST is a real unfortune » BTW: Both Laszlos recommend to use PowerTOST if they were asked . Fully agree and thanks again for this wonderful package. — Kind regards, Mittyri 
Helmut Hero Vienna, Austria, 20171209 17:00 @ mittyri Posting: # 18049 Views: 1,010 

Hi mittyri, » I tried to figure out the precision of PowerTOST estimations with the following code: » scABELdata$power[j] < power.scABEL(CV=0.8, n=54, theta0=0.95, » design="2x3x3", nsims=10000, » setseed=F) » please correct if it is wrong. I think so. You got the right answer to a wrong question. For theta0=0.95 and targetpower=0.8 sample sizes are 57 for design="2x3x3" and 56 for design="2x2x3" . Therefore, with 54 power will be <0.8 for both designs:
» […] I would say that sample mean 80% in PowerTOST is a real unfortune On the contrary; fortunately works as designed with the right sample sizes. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
mittyri Senior Russia, 20171209 21:05 @ Helmut Posting: # 18050 Views: 996 

Hi Helmut, sorry if my thoughts were unclear in previous post. As Astea has noted, 2 Laszlos in their paper estimated the required minimum sample size as 54 subjects for "2x3x3" design (CV=0.8, theta0=0.95). They claimed that "The precision of the estimation was evaluated by running the simulations twenty times". My question was: is it possible for PowerTOST? Is it possible to get the mean power of 80% using the mean of 20 runs?
library("ggplot2") So the answer is: yes, that's possible, but you need to be unlucky (the probability is about 7%) — Kind regards, Mittyri 
Astea Regular Russia, 20171210 00:10 @ mittyri Posting: # 18051 Views: 978 

Dear All! Thank you for clarifying this question! Interesting consequences! How much time did you spend on plotting with 1E6 reps? My comp hanged over when I tried to get more than 1E4... » So the answer is: yes, that's possible, but you need to be unlucky (the probability is about 7%) For 72 subjects and theta0=0.9 we get even worser: 98.21 are less than 0.8 (checked with 10^{4} reps). 
Helmut Hero Vienna, Austria, 20171210 20:27 @ Astea Posting: # 18052 Views: 933 

Hi Astea, » How much time did you spend on plotting with 1E6 reps? My comp hanged over when I tried to get more than 1E4... 2:15 hours on my 2½ years old CPU for 1e5 rep’s × nsims=1e5 – since this is the default in power.scABEL() .— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
Astea Regular Russia, 20171210 21:13 @ Helmut Posting: # 18053 Views: 925 

Dear Helmut! » 2:15 hours on my 2½ years old CPU for 1e5 rep’s × nsims=1e5 – since this is the default in power.scABEL() .Citius, Altius, Fortius! 