Nav Coelho ● 20070720 18:14 (6322 d 09:59 ago) Posting: # 916 Views: 27,802 

Dear all, I have data from a parallel pilot study and am using that to estimate the sample size for a pivotal study. The formula that I am using requires an estimate of the inter subject variability which I don't have. I have the total variability (sqrt(MSE)). Is there a way to estimate intersubject variability from a parallel design or would it be correct to use the total variability instead? Would it be correct to estimate intersubject var as sd/mean for test and reference separately and then take the average? And one last question, how correct is it to take 60% of inter subject (calculated as sd/mean) to be the intrasubject variability? Thanks in Advance! Nav Coelho 
Helmut ★★★ Vienna, Austria, 20070720 18:29 (6322 d 09:44 ago) @ Nav Coelho Posting: # 917 Views: 24,714 

Dear Nav! ❝ I have data from a parallel pilot study and am using that to estimate the sample size for a pivotal study. The formula that I am using requires an estimate of the inter subject variability which I don't have. I have the total variability (sqrt(MSE)). Is there a way to estimate intersubject variability from a parallel design or would it be correct to use the total variability instead? Hhm, yes you have the total variability (inter + intrasubjects); the same will be true for your pivotal study. I don’t get your point of trying to estimate intersubject variability from total. Which formula are you referring to? ❝ Would it be correct to estimate intersubject var as sd/mean for test and reference separately and then take the average? ❝ ❝ And one last question, how correct is it to take 60% of inter subject (calculated as sd/mean) to be the intrasubject variability? I don’t think so (both questions). For an example please have a look at Chow SC, Wang H. On Sample Size Calculation in Bioequivalence Trials. J Pharmacokin Pharmacodyn. 2001;28(2):15569. and Errata given at J Pharmacokin Pharmacodyn. 2002;29(1):1012. You will also need two letters to the editor: Hauschke D. A Note on Sample Size Calculation in Bioequivalence Trials. J Pharmacokin Pharmacodyn. 2002;29(1):8994. Blood P. Sample Size Calculation in Bioeqivalence Trials. J Pharmacokin Pharmacodyn. 2002;29(1):957. H Wang H, SC Chow SC. Authors’ Response. J Pharmacokin Pharmacodyn. 2002;29(1):99. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Nav Coelho ● 20070720 20:38 (6322 d 07:35 ago) (edited on 20070720 22:51) @ Helmut Posting: # 918 Views: 24,663 

Thanks for your response Helmut. Well, I am not sure how to estimate the sample size for a parallel design? The formula that I am using uses intersubject variability and the reference is attached (Tutorial in Biostatisitcs: Sample sizes for clinical trials with Normal data by Steven A. Julious). Formula is on page 1970 #69. But how would you get the intersubject variability from the ANOVA for parallel design in order to calculate the sample size. Thanks for the reference, I'll take a look. Re: 60% of inter to estimate the intra: I am a statistician and I routinely see the PK individuals taking 60% of inter to be the intra for estimating sample size for a crossover design and always wondered about the validity of the approach. Appreciate your feedback! Nav  Edit: Full quote removed. Please see this post! [Jaime] 
Helmut ★★★ Vienna, Austria, 20070722 03:17 (6321 d 00:56 ago) @ Nav Coelho Posting: # 921 Views: 25,072 

Dear Nav, I’m not in my office, so be a little patient to get a thorough response – first I have to read your 66 pages of statistics. Just for completeness (because you sent me the paper by private mail): Julious SA. TUTORIAL IN BIOSTATISTICS. Sample sizes for clinical trials with Normal data. ❝ Well, I am not sure how to estimate the sample size for a parallel design? We’ll handle that… ❝ Re: 60% of inter to estimate the intra: I am a statistician and I routinely see the PK individuals taking 60% of inter to be the intra for estimating sample size for a crossover design and always wondered about the validity of the approach. Hey, that’s black magick! Examples
❝ 60% of inter to estimate the intra again as black magick. — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Helmut ★★★ Vienna, Austria, 20070723 19:44 (6319 d 08:29 ago) @ Nav Coelho Posting: # 925 Views: 28,144 

Dear Nav! ❝ […] But how would you get the intersubject variability from the ANOVA for parallel design in order to calculate the sample size. Some more references and explanations. In a parallel design we have no direct access to intersubject variability, what we see is the total (sometimes called pooled) variability. From a 2×2×2 crossover design we may estimate
❝ Re: 60% of inter to estimate the intra: I am a statistician and I routinely see the PK individuals taking 60% of inter to be the intra for estimating sample size for a crossover design and always wondered about the validity of the approach. I give you two examples from my 2×2 crossover studies (for low/medium/high intrasubject CV) to get an impression about the lacking relationship of CVintra/inter/total:^{2} Methyphenidate 20 mg MR single dose sprinkled, AUC_{t}, n=12 CVintra 7.00% [=36% of inter, 34% of total] CVinter 19.1%CVtotal 20.4%Paroxetine 30 mg IR steady state, AUC_{tau}, n=32 CVintra 25.2% [=46% of inter, 41% of total] ≈CVinter 55.1%CVtotal 62.1%Lansoprazole 30 mg single dose fasting, C_{max}, n=47 CVintra 47.0% [=187% (!) of inter, 86% of total] CVinter 25.1%CVtotal 54.6%I can’t see this rule of thumb of ‘CVintra = 60% CVinter’ to be applicable …
— Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
Nav Coelho ● 20070723 21:58 (6319 d 06:15 ago) @ Helmut Posting: # 927 Views: 24,516 

Dear Helmut, I really appreciate you taking the time to answer my questions in such detail. In regards to the sample size calculation for a parallel design, I agree that the worst case scenario for taking total CV as the estimate for inter CV would only result in slight overestimation in power. Thanks for the confirmation!! As for the 60% rule, you are absolutely right. It's not a one size fits all. Nav Edit: Full quote removed. Please see this post! [Helmut] 
BEQool ★ 20230418 11:59 (571 d 16:14 ago) @ Helmut Posting: # 23525 Views: 3,965 

Hello! It has been a long time since this was posted but I have been looking for ways to calculate intersubject CV and I saw these following equations: ❝ […] ❝ From a 2×2×2 crossover design we may estimate
And since it was mentioned that we may estimate CVs with these equations from a 2x2x2 crossover study I am curious if this equations for CVs also apply for other higher order designs? Best regards BEQool 
Helmut ★★★ Vienna, Austria, 20230420 12:19 (569 d 15:54 ago) @ BEQool Posting: # 23530 Views: 3,877 

Hi BEQool, ❝ ❝ ❝ From a 2×2×2 crossover design we may estimate ❝ And since it was mentioned that we may estimate CVs with these equations from a 2x2x2 crossover study I am curious if this equations for CVs also apply for other higher order designs? Yes. I strongly suggest to follow the ‘Two at a Time’approach instead of an ANOVA of pooled data (see there). — Diftor heh smusma 🖖🏼 Довге життя Україна! _{} Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
BEQool ★ 20230421 09:53 (568 d 18:20 ago) @ Helmut Posting: # 23532 Views: 3,851 

Great, thank you! 
zizou ★ Plzeň, Czech Republic, 20230421 23:23 (568 d 04:50 ago) (edited on 20230422 00:24) @ BEQool Posting: # 23536 Views: 3,776 

Dear BEQool, yes for intrasubject CV and no for inter/totalsubject CVs in general. The equations stated above are valid for 2treatment crossover designs. However e.g. for a 3×6×3 crossover design, i.e. with 3 treatments (R1R2T or pilot T1T2R), we may estimate
zizou 
BEQool ★ 20230422 20:20 (567 d 07:53 ago) @ zizou Posting: # 23537 Views: 3,754 

Thank you zizou for the explanation. So if we have e.g. 3x6x3 Williams crossover design (with 3 treatments), the number in the denominator depends on the approach we use? If we use "Two at a Time" approach with incomplete block designs, we are only evaluating 2 treatments and therefore we should use number 2 in the denominator; but if we use "All at Once" approach, we are evaluating all 3 treatments and we have to use number 3 in the denominator? Additional question (just to be sure): we also use number 2 in the denominator (to get intersubject variance) when we have replicate designs with 2 treatments (regradless of the partial or fullreplicate design)? 
zizou ★ Plzeň, Czech Republic, 20230422 23:06 (567 d 05:07 ago) (edited on 20230422 23:40) @ BEQool Posting: # 23538 Views: 3,729 

Dear BEQool. ❝ So if we have e.g. 3x6x3 Williams crossover design (with 3 treatments), the number in the denominator depends on the approach we use? Nevertheless someone else could check it. I read about it many years ago (mentioned here and statistical background somewhere else, I don't remember where). And "a long time ago in a galaxy far, far away" I also recalculated the estimate (obtained from ANOVA  GLM and equation with 3 as denominator) using the mixed model where the intersubject variability is obtained more directly. ❝ If we use "Two at a Time" approach with incomplete block designs, we are only evaluating 2 treatments and therefore we should use number 2 in the denominator; but if we use "All at Once" approach, we are evaluating all 3 treatments and we have to use number 3 in the denominator? So: "..., the analysis for each comparison should be conducted excluding the data from the treatments that are not relevant for the comparison in question." (EMA Guideline 1401) ❝ Additional question (just to be sure): we also use number 2 in the denominator (to get intersubject variance) when we have replicate designs with 2 treatments (regradless of the partial or fullreplicate design)? 
BEQool ★ 20230425 12:57 (564 d 15:16 ago) @ zizou Posting: # 23539 Views: 3,627 

Dear zizou, thanks for the answers. ❝ No, for both approaches the denominator is 3. It's not affected by whether the model is complete or incomplete. Nevertheless someone else could check it. I read about it many years ago (mentioned here and statistical background somewhere else, I don't remember where). And "a long time ago in a galaxy far, far away" I also recalculated the estimate (obtained from ANOVA  GLM and equation with 3 as denominator) using the mixed model where the intersubject variability is obtained more directly. I have checked it now I made up (Cmax) concentrations for 3x6x3 Williams design (with treatments A,B,C) with 18 subjects (complete dataset, all subjects completed all periods) and run it with Phoenix WNL. Here are the results: a) All at once approach Intersubject CV given directly with mixed model approach = 13.4 % Intersubject CV calculated from ANOVA table with denominator 3 = 13.4 % (right) Intersubject CV calculated from ANOVA table with denominator 2 = 16.5 % (wrong) So here when using (wrong) All at once approach, the number in the denominator should be the same as the total number of treatments (the number of all treatments we are evaluating) b) Two at a Time approach (incomplete block design); B vs. C Intersubject CV given directly with mixed model approach = 6.6 % Intersubject CV calculated from ANOVA table with denominator 3 = 5.4 % (wrong) Intersubject CV calculated from ANOVA table with denominator 2 = 6.6 % (right) But here when using Two at a Time approach (where we are evaluating just 2 treatments), it seems that we have to use number 2 in the denominator. So it seems that the denominator is affected by whether the model is complete or incomplete. c) Two at a Time approach (incomplete block design); A vs. C Here we should of course as above also probably use number 2 in the denominator but here interestingly something else happens: Intersubject CV given directly with mixed model approach = ERROR Intersubject CV calculated from ANOVA table with denominator 3 = ERROR Intersubject CV calculated from ANOVA table with denominator 2 = ERROR Even when using Subject as fixed effect (which is the solution for such cases according to Certara) MSE (0.22973) is larger than MSS (0.20599), therefore intersubject variance is negative (0.0119; the same number is given directly with mixed model). Therefore the calculation of intersubject CV is impossible (error). Why is this so and what should be done in this case? This probably happens because intrasubject CV is so much higher than intersubject CV? I know these data that I used is made up but nevertheless it could happen with realworld data as well? 
zizou ★ Plzeň, Czech Republic, 20230426 00:43 (564 d 03:30 ago) (edited on 20230426 19:05) @ BEQool Posting: # 23540 Views: 3,588 

Dear BEQool, well done! ❝ So it seems that the denominator is affected by whether the model is complete or incomplete. Btw. total (pooled) CV in 2x2x2 can also be obtained by fitting the model with factors Formulations, Periods, Sequences (i.e. without Subjects(Sequences)). Then use MSE in equation: CV=sqrt(e^(MSE)1) (multiplicative model with residual variance sigma^2 which is estimated by MSE from ANOVA) For parallel design, it's trivial and only the total (pooled) CV can be obtained. For higherorder designs with more than two formulations I never tried it but it could be another option for recalculation. ❝ ... it could happen with realworld data as well? 
BEQool ★ 20230504 10:17 (555 d 17:56 ago) @ zizou Posting: # 23542 Views: 3,276 

❝ Btw. total (pooled) CV in 2x2x2 can also be obtained by fitting the model with factors Formulations, Periods, Sequences (i.e. without Subjects(Sequences)). Then use MSE in equation: ❝ CV=sqrt(e^(MSE)1) (multiplicative model with residual variance sigma^2 which is estimated by MSE from ANOVA) ❝ For parallel design, it's trivial and only the total (pooled) CV can be obtained. Interesting, thanks! ❝ For higherorder designs with more than two formulations I never tried it but it could be another option for recalculation. Just for curiosity, with above mentioned data I tried some calculations for 3x6x3 design with and without factor Subject(Sequence) for both approaches (All at once and Two at a time) but I couldnt get matched CVtotal numbers so like you said there is probably another option for recalculation. ❝ ❝ ... it could happen with realworld data as well? ❝ Sometimes (not often) it happens. It was discussed e.g. in this thread. Thanks! 
Dipesh Jayswal ● 20070724 10:52 (6318 d 17:21 ago) @ Nav Coelho Posting: # 928 Views: 24,446 

Dear Nav Coelho, The following article may help u out for determination of sample size assuming different variances of test and reference formulation which is recommanded by FDA. "Hansheng Wang and SheinChung Chow, A practical approach for comparing means of two groups without equal variance assumption, Statistics in Medicine 2002; 21:3137–3151" Dipesh Jayswal Edit: Online resource. [Helmut] 