ElMaestro ★★★ Denmark, 20110116 20:13 (4640 d 19:28 ago) Posting: # 6423 Views: 31,250 

Ahoy bears and dlabes Wouldn't it be nice to include an option for (but not replace with) sample size calculation with adaptation to CIwidening ad modum the new BE guideline in Europe? It would be easy enough to internally adapt the theta's where the input CV is in the 30%50% range and the design is refreplicated. Best regards, EM. — Pass or fail! ElMaestro 
d_labes ★★★ Berlin, Germany, 20110117 14:19 (4640 d 01:22 ago) @ ElMaestro Posting: # 6427 Views: 28,656 

Ahoy my dear Capt'n, ❝ Wouldn't it be nice to include an option for (but not replace with) sample size calculation with adaptation to CIwidening ad modum the new BE guideline in Europe? THX for your suggestion. Theoretically the power of scaled ABE evaluation (if it could be done exact ) and therefore the sample size is independent of the variability. Therefore it should be enough to tabulate sample sizes for different powers to achieve. For this reason the FDA has discussed 24 or 32 subjects for scaled ABE. See this post. But don't know where these numbers exactly came from. Of course the 50% CV cutoff of the EMA complicates the situation. Moreover the widened limits are only an approximation to the problem. The constraint "point estimate within 0.8  1.25" is not part of the classical power considerations. ❝ It would be easy enough to internally adapt the theta's where the input CV is in the 30%50% range and the design is refreplicated. require(PowerTOST) Easy enough for the programmer of the famous EFG , although externally adapted? Lets see what the results are: # Targetpower=0.8, theta0=0.95, alpha=0.05, design=2x3x3 partial replicate Regulatory body: EMA k=0.760
CV theta1 theta2 Sample size Achieved power Regulatory body: FDA k=0.893
CV theta1 theta2 Sample size Achieved power — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110117 15:38 (4640 d 00:03 ago) @ d_labes Posting: # 6429 Views: 28,764 

Dear D. Labes! ❝ […] therefore the sample size is independent of the variability. […] For this reason the FDA has discussed 24 or32 subjects for scaled ABE. […] But don't know where these numbers exactly came from. 32 was FDA’s suggestion back in 2006 (see here). 24 is FDA’s current requirement (personal communication with Barbara Davit, Ljubljana, May 2010). ❝
❝ ❝ Lets see what the results are: ❝ ❝ Regulatory body: EMA k=0.760 ❝ ❝ ❝ Yes, we discussed that already in #5249pp. As the grumpy old man I am I was already lamenting in one of my lectures (slides 3233). Though I have only used exact widened limits of 0.75 and 0.75^{1} in the past (not UL of 1.3333) I woudn’t bet on the acceptability of the exact value (which I will use anyway). As you mentioned in your commented code, one will get the ‘correct’ limits by calculating the regulatory constant based on a CV of 30%. theta1 < exp(log(1.25)/CV2se(0.3)*CV2se(CVr)) P.S.: Do you think that engineers would use 3.14 instead of π, because it’s written in a guideline? Bridges would collpase, trains derail, etc. — 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 
d_labes ★★★ Berlin, Germany, 20110117 17:37 (4639 d 22:04 ago) @ Helmut Posting: # 6433 Views: 28,446 

Dear Helmut, I correct my code as following:
... I do this because I wont take liability of collpasing bridges, derailing trains of Deutsche Bahn, etc. BTW: R > options(digits=30) I have learned in my early days during learning draftsman in agrar melioration engineering that 22/7=3.142857 is an good estimate. Very near to your 3.14! Maybe there were not so much circles involved, but more triangles and rectangles . — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110117 19:06 (4639 d 20:35 ago) @ d_labes Posting: # 6434 Views: 30,390 

Dear D. Labes, THX for supporting an ol’ fart. ❝ BTW: R ❝ ❝ ❝ ❝ ❝ ❝ ❝ Right. Interesting, that signif doesn’t throw an error for values > 22.options(signif=32) However pi Doesn’t really surprise me; that’s the numeric resolution of my 32 bit XP; I guess you have one of these fancy 64 bit operating systems? There’s a package for R being able to handle floating point operations in arbitrary precision – essentially by converting all numbers to character strings. ❝ I have learned in my early days during learning draftsman in agrar melioration engineering that 22/7=3.142857 is an good estimate. Very near to your 3.14! Maybe there were not so much circles involved, but more triangles and rectangles . Yes, I’ve learned that one also. Another one is Archimedes’: 3+10/71 < π < 3+10/70 (the upper limit is your’s; the mean is just 0.008% off). Not so bad for 250 BCE! Maniacs might click here or there. Fascinating that calc.exe comes up with:Pi 3.1415926535897932384626433832795 Maybe it’s stored somewhere? Let’s try a true calculation: [o] Rad 1 [x] Inv tan 0.78539816339744830961566084581988 * 4 = 3.1415926535897932384626433832795 Amazing. According to the online help calculations are performed in 32 digit precision.  Pi = 1.393267707463821448075635979701e37 Gotcha! If you have Java onboard, a true overkill for nerds (calling a Java implementation of Python ‘Jython’, library sympy for symbolic mathematics from R): require(rSymPy) Wow! Remember that one? factorial(170) But: sympy("factorial(170)") (stopped testing at 100 000! – lots of digits) — 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 
d_labes ★★★ Berlin, Germany, 20110118 09:32 (4639 d 06:09 ago) @ Helmut Posting: # 6437 Views: 28,681 

Dear Helmut, Kudos to you! You can always top it . BTW: Try number of horns on a unicorn * the answer to life the universe and everything * once in a blue moon — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110118 12:44 (4639 d 02:57 ago) @ d_labes Posting: # 6441 Views: 28,581 

Dear D Labes, ❝ number of horns on a unicorn * the answer to life the universe and everything * once in a blue moon I didn't know the last one! Going For many years _{}maps contained another gem: When you asked for the route between any European city and let’s say, Times Square, New York, NY you were provided with detailed instructions going to the next harbour, a nice orthodrome suggesting to swim across the Atlantic making landfall in Battery Park, and to continue north via Broadway… Unfortunately _{} has removed this feature; a similar image here. Some others. — 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 
ElMaestro ★★★ Denmark, 20110119 18:50 (4637 d 20:51 ago) @ d_labes Posting: # 6451 Views: 28,464 

Ahoy dlabes, always a pleasure reading posts from you; I understand so little... ❝ Theoretically the power of scaled ABE evaluation (if it could be done exact ) and therefore the sample size is independent of the variability. This thing about 'If it could be done exact ' just made me wonder. Of course power calculations with computers is not an exact business but I will in the following not be discussing the 17th decimal. If I get you right you are looking for the answer to this question: If we have a power of P at T/R=soandso and CV being thisorthat, then what should the accetance range be if the CV is not thisorthat but blahblah? In principle, the EMA guideline provides the answer to that Question as it allows a construct of a curve of acceptance range versus CV. But trying to decipher your encrypted babblings, you're saying this is an approximation given that power should be the constant. Allow me to return to the famous german desert and ingestion of clothing, but this time garnished with some heavy metal (I use the simple example of a 2,2,2design although this is not the relevant one for scaling but it can be adapted pretty easily):
EatMyShorts < function (x, V, T, W) Pwr222(30,0.05, 0.8, 1.25, 0.95, 0.3) is 0.6850399. Let's check: OK, what acceptance range matches a 2,2,2design with T/R being 0.95, N=30 and power being 0.6850399? I_Eat_Cadmium (0.6850399, 0.95, 0.3, 0.05, 30) gives the answer. And if the CV is not 0.3 but 0.4 then which acc range can apply? I_Eat_Cadmium (0.6850399, 0.95, 0.4, 0.05, 30) Better approximation possible by this approach, no? EM. 
d_labes ★★★ Berlin, Germany, 20110120 16:00 (4636 d 23:41 ago) @ ElMaestro Posting: # 6456 Views: 28,618 

Ahoy dear "Der Meister", sorry but I must confess that I'm totally confused and that I can't follow your points and reasoning . ❝ If I get you right you are looking for the answer to this question: ❝ If we have a power of P at T/R=soandso and CV being thisorthat, then what should the accetance range be if the CV is not thisorthat but blahblah? I never asked that question (they never came into my mind!) and I can't imagine what the results of I_Eat_Cadmium() are. Eventually hard poisoning with some side effects on the CNS ? What I meant with my sentence is that using the original scaled ABE criterion (µTµR)^{2}/s^{2}WR < (theta/sw0)^{2} would let to power calculations that are independent from the variabilities, at least at true µTµR=0. This is well known for using the "effect size" in superiority studies. But this can only be proven for BE within the classical 2x2 design because in case of others the distribution of the test statistics are not known exactly. See f.i. L. Tothfalusi, L. Endrenyi and A. Garcia Arieta "Evaluation of Bioequivalence for Highly Variable Drugs with Scaled Average Bioequivalence" Clin Pharmacokinet 2009; 48 (11): 725743 The use of the widened acceptance limits according to the EMA guidance is only an approximation to the original problem (as well as the linearized criterion with approximate upper 95% CI in the FDA Progesterone guidance). Power calculations for the EMA widened acceptance limits can be done naively by inserting the widened limits depending on the assumed CV into the classical power formulas. I had thought that Your feature request is going in that direction. Lets see what happens with this approach: require(PowerTOST) Results:
GMR=1 You see (if not you need glasses ):
Thus my encrypted babblings are nothing more then the statement: "I'm not convinced that we are actually calculating somefink that can be called power of scABE if we do it that way". Long post but not any meaning . "Power Calculation  A guess masquerading as mathematics." — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110120 16:25 (4636 d 23:16 ago) @ d_labes Posting: # 6457 Views: 28,589 

Dear D. Labes! ❝ Lets see what happens with this approach: ❝ 08.3
❝ Moreover the classical power formulas have nowhere the scABE constraint ❝ "point est. must be within 0.81.25" as presupposition. We can't incoporate a political constraint in an explicit statistical formula. The only way IMHO would be to go with Monte Carlo simulations. Power: That which is wielded by the priesthood of clinical trials, the statisticians, P.S.: Added one missing ' } ' to your code above.— 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 
d_labes ★★★ Berlin, Germany, 20110120 17:15 (4636 d 22:26 ago) @ Helmut Posting: # 6460 Views: 28,407 

Dear Helmut! ❝ 08.3 ❝ We can't incorporate a political constraint in an explicit statistical formula. The only way IMHO would be to go with Monte Carlo simulations. IMHO right. All the power calculations seen in the literature about scABE were done via simulations. But this is not so easy to implement for all the designs covered in PowerTOST. If anybody out there has an idea or code, feel free to contact me to incorporate it in the package. Edit: I'll try to shanghai Martin and Jack... [Helmut] — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110121 05:13 (4636 d 10:28 ago) @ d_labes Posting: # 6464 Views: 28,425 

Dear D. Labes! no comment — 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 
d_labes ★★★ Berlin, Germany, 20110121 09:36 (4636 d 06:05 ago) (edited by d_labes on 20110121 10:48) @ Helmut Posting: # 6467 Views: 28,212 

Dear Helmut! ❝ … no comment Helmut: Forget my post or delete it. I have totally misinterpreted the graphics . Learned: First think, then post. BTW: Looking at the time of your post: did You suffer from senile Bettflucht (insomnia, Google translator "Bed run") ? — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110121 13:53 (4636 d 01:48 ago) @ d_labes Posting: # 6469 Views: 28,430 

Dear D. Labes! ❝ BTW: Looking at the time of your post: did You suffer from senile Bettflucht (insomnia, Google translator "Bed run") ? Not quite. I rarely go to bed earlier than 03:00 am – so this was just an outlier. — 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 
d_labes ★★★ Berlin, Germany, 20110121 13:12 (4636 d 02:29 ago) @ Helmut Posting: # 6468 Views: 28,691 

Dear Helmut! Look at this! I have combined the the graphics from the paper L. Tothfalusi, L. Endrenyi Limits for the scaled average bioequivalence of highly variable drugs and drug products Pharm. Res. 20, p382389 (2003) Figure 3 "Percentage of simulated twoperiod crossover studies in which BE was accepted ..." Wow! — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110121 14:01 (4636 d 01:40 ago) @ d_labes Posting: # 6471 Views: 28,250 

Dear D. Labes! ❝ Look at this! ❝ Wow! — 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 
d_labes ★★★ Berlin, Germany, 20110121 15:43 (4635 d 23:58 ago) @ Helmut Posting: # 6474 Views: 28,375 

Dear Helmut, beyond belief for me simple minded but seems definitely TRUE. Have a look at Figs. 3 and 4 of Haidar et. al. Evaluation of a Scaling Approach for the Bioequivalence of Highly Variable Drugs The AAPS Journal, Vol. 10, No. 3, p450454, 2008 online resource to see the same behaviour, also for the combined criteria scaled ABE + constraint on point estimate. See also Endrenyi, Tothfalusi Presentation at BASS 2010 Scaled Average bioequivalence: An Approach to Resolve a Difficult Program page 2123. See also Page 28 of that presentation to notice increasing power after CV=30% if point estimator is 1.1, same as we have had here for point estimator = 0.95. It would be interesting to know how good the real values of the simulated power are in accordance with our naive power calculations, not only the qualitative behaviour. Seems I had read all this stuff, but never had this figured out well. What we here see is the mean vs. variance tradeoff in the scaled ABE evaluation. Greater differences in the means µ_{T}µ_{R} are allowed with increasing variability to have the same value for the scaled ABE criterion. Eventually this is one of the sources for introducing the GMR constraint? — Regards, Detlew 
ElMaestro ★★★ Denmark, 20110121 13:59 (4636 d 01:42 ago) @ Helmut Posting: # 6470 Views: 28,203 

Ahoy HS, ❝ ❝ Moreover the classical power formulas have nowhere the scABE constraint "point est. must be within 0.81.25" as presupposition. ❝ ❝ We can't incoporate a political constraint in an explicit statistical formula. The only way IMHO would be to go with Monte Carlo simulations. I can't imagine this is really a big deal, because the chance that a PE is outside 0.8  1.25 while the CI still evaluates to BE must be next to nothing. — Pass or fail! ElMaestro 
Helmut ★★★ Vienna, Austria, 20110121 15:05 (4636 d 00:36 ago) @ ElMaestro Posting: # 6473 Views: 28,250 

Ahoy ElMeastro! ❝ ❝ We can't incoporate a political constraint in an explicit statistical formula. The only way IMHO would be to go with Monte Carlo simulations. ❝ ❝ I can't imagine this is really a big deal, because the chance that a PE is outside 0.8  1.25 while the CI still evaluates to BE must be next to nothing. To quote from L. Tóthfalusi et al. (2009), p.739: It is interesting to note the effect of the GMR constraint on the overall performance, notably on the producer risk of bioequivalence determinations. This effect depends on the comparative positions of the three criteria: the GMR constraint, the regulatory limit for SABE, and the estimated scaling variance. Depending on the relative magnitudes of these parameters, either SABE or the GMR restriction can become the dominant regulatory criterion. For instance, with a constraint of 0.80–1.25 on the GMR, when both the switching and scaling variations are 30%, then the combined criteria of SABE and the GMR restriction have, at moderately high withinsubject variability (CV = 35%), almost the same proportion of regulatory approvals as SABE alone. In contrast, at substantially higher withinsubject variability (CV = 60%), the proportion of approvals with the combined criteria is very similar to that with just the GMR constraint alone. Have a look at Fig.2B of Endrényi L and L Tóthfalusi The GMR constraint was 1.25, filled diamonds are the EMA's method (filled circles conventional ABE, open squares unconstrained SABE, open triangles PE 0.8125 without CI = Canada C_{max}). Simulation: 10,000 studies, 3period replicate, true GMR 1.01.6. Due to the variability inherent to HVDs almost 40% pass at 1.25 and still ≈20% at 1.35. — 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 
ElMaestro ★★★ Denmark, 20110121 15:52 (4635 d 23:49 ago) @ Helmut Posting: # 6475 Views: 28,399 

Thanks HS. My intuition which is most often counteracting reasonable decisions tells me something needs to be dug into here. E&T's paper says they do simulations and evaluate the simulated data with a simplified method by Hyslop. The reference (Hyslop et al. 2000) which I don't have is about IBE rather than ABE. Do you have it? Can you shed light onto this? Who's got some working Rcode for 223ABE evaluation (linear mixed model that specifies the covariance matrix with withinsigmas for the ref when the test is not replicated; I don't know how to do this)? — Pass or fail! ElMaestro 
d_labes ★★★ Berlin, Germany, 20110121 16:28 (4635 d 23:13 ago) @ ElMaestro Posting: # 6476 Views: 28,316 

Dear ElMaestro, ❝ E&T's paper says they do simulations and evaluate the simulated data with a simplified method by Hyslop. The reference (Hyslop et al. 2000) which I don't have is about IBE rather than ABE. Do you have it? Can you shed light onto this? See here and especially here for some discussions about how to calculate the scaled ABE criterion (linearized) including it's upper 95% CI according to Hyslop's method, sometimes the name Howe is also used. The SAS code given in the FDA Progesterone guidance can be rewritten for R with not so much difficulties I think. But a full working version I don't have. — Regards, Detlew 
ElMaestro ★★★ Denmark, 20110121 16:45 (4635 d 22:56 ago) @ d_labes Posting: # 6477 Views: 28,205 

Thanks dlabes, I am not sure I follow the code. As I indicated earlier, I'd be a little apprehensive at least for the case of imbalance between sequences; HOWEver () I assume simulations imply balanced seqs. Did Hyslop or whoever validate it against the (a) 'correct' linear mixed model under balance? Correction: Sorry, I meant something else than I initially wrote. It is missing values that is the concern issue because of the difference between a normal linear model and the reml approach by a mixed model. — Pass or fail! ElMaestro 
d_labes ★★★ Berlin, Germany, 20110121 17:19 (4635 d 22:22 ago) @ ElMaestro Posting: # 6478 Views: 28,554 

Hi ElMaestro ❝ Correction: Sorry, I meant something else than I initially wrote. It is missing values that is the concern issue because of the difference between a normal linear model and the reml approach by a mixed model. Good question! Next question please . To be honest: Don't know exactly. In the Progesterone guidance it is written "... Further assume that there are no missing observations ...". But only under the Heading "Example SAS Codes: fully replicated 4way design". My observation is that this guidance is in some instances rather vague or gives no sufficient explanation why what is done that way. Just to name "the unknown x = estimate^{2}  stderr^{2}" or "use GLM for partial replicate and MIXED for full replicate". — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20110121 19:41 (4635 d 20:00 ago) @ ElMaestro Posting: # 6479 Views: 28,314 

Ahoy ElMaestro! ❝ My intuition which is most often counteracting reasonable decisions tells me something needs to be dug into here. I try not to think with my gut. If I’m serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me into trouble. To be honest I'm struggling in preventing my little brain from overheating. My rumbling gut is uncomfortable with the 'fact' (?) that with any given sample size I have a higher chance of success for higher CVs. ❝ The reference (Hyslop et al. 2000) which I don't have is about IBE rather than ABE. Do you have it?
T Hyslop and B Iglewicz — 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 
ElMaestro ★★★ Denmark, 20110120 16:34 (4636 d 23:07 ago) @ d_labes Posting: # 6458 Views: 29,177 

Dear dlabes, Thanks for your continued support to my lack of understanding I cannot rule out the possibility that my metal poisoning is a factor in my posts. ❝ What I meant with my sentence is that using the original scaled ABE criterion ❝ ❝ would let to power calculations that are independent from the variabilities, at least at true µTµR=0. At T/R equal to 1 power and variability is independent. At T/R not equal to 1 it becomes unclear. As the intention with scaling is to keep power constant with varying CV one should/can not always assume T/R being one, I mean. My code would be attempt at calculating the limits that preserve constant power with varied CV where T/R is anything the user specifies. With this function, curves for acceptance range as function of CV can be constructed for any combo of T/R and N while the power is kept constant. — Pass or fail! ElMaestro 
d_labes ★★★ Berlin, Germany, 20110120 17:06 (4636 d 22:35 ago) @ ElMaestro Posting: # 6459 Views: 28,352 

Dear ElMaestro, ❝ With this function, curves for acceptance range as function of CV can be constructed for any combo of T/R and N while the power is kept constant. Oh I see! But for what end? I understand the EMA widened acceptance ranges as applicable regardless of point estimate obtained. — Regards, Detlew 
ElMaestro ★★★ Denmark, 20110120 17:52 (4636 d 21:49 ago) @ d_labes Posting: # 6461 Views: 28,323 

Dear dlabes, ❝ Oh I see! But for what end? ❝ I understand the EMA widened acceptance ranges as applicable regardless of point estimate obtained. A good point to make. On the other hand some people find pleasure in discussing if 0.760 is meaningful or if it should be 17 decimals. In this case I think it is a matter of doing what the guidelines says or doing what the guideline intends. I would expects this to be something you can discuss. The code above does not assume anything other than what the ordinary (and widely accepted power routines) do. I envisage Helmut examining the acceptance range for T/R deviating from 1 and comparing it to the EMA curve and presenting such stuff at a conference. Heck if he doesn't do it, I will. Here is a divideandconquer approach to the problem (simpler but not really faster ): I_Eat_Cadmium2 < function(P, TR, CV, alpha, N) — Pass or fail! ElMaestro 
ElMaestro ★★★ Denmark, 20110120 18:53 (4636 d 20:48 ago) @ d_labes Posting: # 6462 Views: 28,638 

OK, here what I meant with my last posts and the gibberish code. We have for instance 24 patients in a 2,2,3BE trial, expected T/R being 1.0 and expected CV is 30%. This gives us a power of 0.87. Scaling preserves power. Thus should the variability be 50% and with preserved power we have 0.6983 as our lower acceptance range and 1.4320 as the upper. Wunderbar. This is the blue line, or shall we call it the EMA line. I propose to check how the behavior is once the expected R/T diviates from 1.0 and being 0.95 (red), 0.90 (yellow) and 0.85 (green); these curves preserve the power within themselves but of course not between them. It was intended as a graphical illustration of the limitation of the EMA approximation when T/R differs from 1.0. Note: We are now no longer so intimately connected with the original thread topic. — Pass or fail! ElMaestro 