Log in
Register|
Ben ★ 2012-10-23 13:32 (4571 d 01:49 ago) Posting: # 9446 Views: 10,217 |
|
|
Dear all, While for EMA the 90% CI must fall within exp(± k*σWR), where k=0.760, the FDA has a different favored approach. One has to calculate the upper 95% limit of (μT-μR)2 - 0.797σWR2 and check whether it falls below 0 or not (btw, nice slides Helmut). Now, my question is whether this approach using the 95% upper limit can also be rephrased (equivalently) in an "easier" way, that is, in terms of 90% CI must fall within exp(± k*σWR) (using just a different k). On these slides from the FDA it seems that it is the same as scaling the acceptance range using k=0.893. Is it really equivalent? Thanks, Ben Edit: Category changed. [Helmut] |
|
Helmut ★★★   Vienna, Austria, 2012-10-23 17:35 (4570 d 21:46 ago) @ Ben Posting: # 9447 Views: 8,865 |
|
|
Dear Ben! ❝ nice slides THX! ❝ Now, my question is whether this approach using the 95% upper limit can also be rephrased (equivalently) in an "easier" way, that is, in terms of 90% CI must fall within exp(± k*σWR) (using just a different k). On these slides from the FDA it seems that it is the same as scaling the acceptance range using k=0.893. Is it really equivalent? First see this thread and the references within. Also a recent paper: Karalis V, Symillides M, P Macheras P. Bioequivalence of Highly Variable Drugs: A Comparison of the Newly Proposed Regulatory Approaches by FDA and EMA. Pharm Res. 2012;29(4): 1066–77. doi:10.1007/s11095-011-0651-y FDA’s switching condition θs is ~0.893 – based on a standardized variation σ0 of 0.25: ln(1.25)/0.25 ~ 0.89257… In principle you are right that the scaled limits could be derived according to U,L = e±0.893·σWR, but applied only if CVWR>30% – which leads to the nice discontinuity at CV 30%: CV% L UNow for the tricky part. Which model would you use to obtain CVWR (or σWR)? FDA wants to see SAS Proc GLM for the partial replicate (scaled) and SAS Proc Mixed for the full replicate and both designs in (unscaled) ABE. From EMA’s (in)famous ‘data set I’ we obtain with FDA’s RSABE code CVWR 46.96% (sWR 0.4464) and with the ABE code CVWR 47.33% (sWR 0.4496). I guess we should use the former. From the intra-subject contrasts of T vs. R ‘ ilat’ we can not only derive the PE, but also its CI: CVWR sWR L U PE 90% CICounter-question: Why would you attempt that? PS: Du hast Mehl in deiner Schachtel. — Dif-tor heh smusma 🖖🏼 Довге життя Україна! ![[image]](https://static.bebac.at/pics/Blue_and_yellow_ribbon_UA.png) Helmut Schütz ![[image]](https://static.bebac.at/img/CC by.png) The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes |
|
Ben ★ 2012-10-23 18:03 (4570 d 21:18 ago) @ Helmut Posting: # 9448 Views: 8,741 |
|
|
Dear Helmut, Thank you for the quick response. Regarding the model, well, I would use the one the FDA/EMA wants to see (as you wrote)  . But that's not the point.❝ Counter-question: Why would you attempt that? I want to present the two approaches to non-statisticians: Statement when SABE is achieved and how the scaled acceptance region looks like. Therefore I would like to use the 90% CI (to which they are used to) and the well known acceptance region 0.8 - 1.25 and the scaled version of it, respectively. I believe the 95% upper limit approach could cause confusion... Thanks, Ben |
|
Helmut ★★★ Vienna, Austria, 2012-10-23 18:23 (4570 d 20:58 ago) @ Ben Posting: # 9449 Views: 8,679 |
|
|
Dear Ben! ❝ I want to present the two approaches to non-statisticians: […] I believe the 95% upper limit approach could cause confusion... Definitely. I’m familiar with confusion I regularly cause in my presentations. If you make clear that this is just an illustrative example – and not what the FDA actually requires – no problem.— 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 |
|
d_labes ★★★ Berlin, Germany, 2012-10-23 18:23 (4570 d 20:58 ago) @ Helmut Posting: # 9450 Views: 8,718 |
|
|
Dear Helmut! ❝ FDA wants to see SAS Proc GLM for the partial replicate (scaled) and SAS Proc Mixed for the full replicate and both designs in (unscaled) ABE. I must confess that I never understood why the FDA statisticians (they are, really  ) recommend the use of SAS Proc GLM or MIXED within their analysis of intra-subject contrasts for the two different designs within the scABE framework.Since the contrasts (T-R or R1-R2) are analyzed via an model with sequence group as the solely effect (fixed) both SAS procedures will give exactly the same results AFAIK. At least as long as no special structure of the variance-covariance matrix of the error term is specified. On the other hand the Proc Mixed code for unscaled ABE in case of the partial replicate crossover doesn't work in all cases as we had discussed here often. — Regards, Detlew |
|
Helmut ★★★ Vienna, Austria, 2012-10-23 18:34 (4570 d 20:47 ago) @ d_labes Posting: # 9451 Views: 8,736 |
|
|
Dear Detlew! ❝ I must confess that I never understood why the FDA statisticians (they are, really Agree. Not the slightest (!) idea.  ❝ Since the contrasts (T-R or R1-R2) are analyzed via an model with sequence group as the solely effect (fixed) both SAS procedures will give exactly the same results AFAIK. Yes. ❝ On the other hand the Proc Mixed code for unscaled ABE in case of the partial replicate crossover doesn't work in all cases as we had discussed here often. Oh dear. — 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 |
|
Ben ★ 2012-10-27 19:04 (4566 d 20:17 ago) @ Helmut Posting: # 9470 Views: 8,571 |
|
|
Dear Helmut, Thanks again for the fresh Mehl. I have another question regarding your slides (Moscow). On slide 74 you write "Don’t jeopardize! Smaller sample sizes in the first stage than in a fixed design don’t pay off. Total sample sizes are ~10–20% higher." What exactly do you mean by that? If the sample size from the first stage is chosen to be equal to the fixed design, then why performing a sequential design at all? Then the only chance of concluding BE (if not after stage 1) after all is to have a greater sample size than a fixed design; but this means that one always has a sample size greater or equal to fixed design - no possibility for having less any more... Best, Ben |
|
Helmut ★★★ Vienna, Austria, 2012-10-27 19:57 (4566 d 19:24 ago) @ Ben Posting: # 9471 Views: 8,606 |
|
|
Dear Ben! ❝ I have another question regarding your slides (Moscow). On slide 72 you write "Don’t jeopardize! Smaller sample sizes in the first stage than in a fixed design don’t pay off. Total sample sizes are ~10–20% higher." A direct comparison of a particular fixed design (assuming a CV) and sequential design (sample size re-estimation) is somewhat delusionary. The sample size penalty in Method C (taboo in the EU…) is negligible if the study is powered like a fixed sample design (no α-adjustment in stage 1). For Method B you have a penalty even if passing in stage 1. Only if I have reliable CV data (previous studies of known quality) I go with a fixed design myself. ❝ If the sample size from the first stage is chosen to be equal to the fixed design, then why performing a sequential design at all? Then the only chance of concluding BE (if not after stage 1) after all is to have a greater sample size than a fixed design; but this means that one always has a sample size greater or equal to fixed design - no possibility for having less any more… If we want to compare the performance in terms of total sample sizes we would have to look at a number of fixed design studies (including failed ones due to higher than expected CVs) and sequential designs. I guess that the disadvantage of adaptive designs would disappear. Personally I see two-stage designs as a second chance to show BE if the assumptions about the CV turn out to be wrong. Tell your boss that he/she paid for failed/repeated studies in the past as well – or overpowering them “just to be sure”. Example (Method B, Potvin Table II): You think that the CV is 20%, but it may be as low as 10%. You perform the study with 12 subjects (reasonable if the CV is 10%). If the CV turns out to be 10% the chance to proceed to stage 2 is only 0.6%. But: If the CV is 20% (your primary assumption!) chances to proceed to the second stage are 56.4%. You loose a lot of time. On the other hand if you perform the study in 24 subjects chances for a second stage are only 8.6%. If the CV is 10% you pass in the first stage anyway. If the CV is higher (e.g., 30%) chance to proceed to stage 2 is 58.3%. In the fixed design you simply fail and run another study – this is what I call a sample size penalty! Up to you. — 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 |
|
Ben ★ 2012-10-28 14:57 (4565 d 23:24 ago) @ Helmut Posting: # 9476 Views: 8,547 |
|
|
Dear Helmut, I see, thanks. But allow me one more question. From your given example, let's say we plan with the primary/reasonable assumption CV=20% and start with n1=24. The fixed design would require a sample size of 20 ( sampleN.TOST(CV=0.2, alpha=0.05, targetpower=0.8)), correct? What do you mean by "total sample sizes 10-20% higher"? In case the CV turns out to be different and we have to go to stage two or compared to the case where we stop after stage 1? In the former, doesn't it depend on the different CV? E.g. CV=30% as you said, then we would require sampleN.TOST(alpha=0.0294, CV=0.3)-24 = 24 additional subjects and hence it's 100% higher (or using the mean total n from Table II: 39.9/24 = 1.6625). In the latter case we would have 20% (24/20 = 1.2) but is it reasonable to talk about "total" here?Best, Ben |
|
Helmut ★★★ Vienna, Austria, 2012-10-28 16:59 (4565 d 21:22 ago) @ Ben Posting: # 9477 Views: 8,634 |
|
|
Dear Ben! ❝ From your given example, let's say we plan with the primary/reasonable assumption CV=20% and start with n1=24. The fixed design would require a sample size of 20 ( Yes; power 83.5%. ❝ What do you mean by "total sample sizes 10-20% higher"? The full quote from the end of Potvin’s discussion section: There is some cost to using a two-stage design when the a priori variance assumption is correct. If the initial sample size, n1, is too small for the actual CV, the average total sample size for the two-stage design will be about 20% higher than that for the single stage design with a correct choice of CV for determining the sample size. Since the grid (sample size multiples of 12 and CVs multiples of 10%) was too coarse for my taste I repeated the simulations with a narrower grid (exact power instead of the shifted t). Potvin’s target (besides maintaining the patient’s risk) was to keep power >80% within the entire framework – which they almost met. See slide 61: With the exception of combinations of small n1 and high CV in the upper left corner power was >80%. For n1 24 and 20% power is 88.1%.❝ In case the CV turns out to be different and we have to go to stage two … Power will be higher than the 83.5% in fixed design, because in 8.6% of cases we proceed to the second stage and are able to show BE then. So we pay a penalty but gain power (88.1%). ❝ … or compared to the case where we stop after stage 1? In the former, doesn't it depend on the different CV? I’m not sure whether I understand you here. If the CV turns out to be ≤20%, we have to distinguish between Method B and C – I will concentrate on B here. If CV is 20% the study has to be evaluated for BE at 0.0294 (remember we planned like a fixed design with 0.05). Whether it passes/fails here is difficult to predict: We have some headroom because the fixed sample design with 0.0294 in 24 gives 83.6% power. Also the PE may be closer to 1. If we pass and the PE is 0.95 the penalty is 20% (24/20). If the CV is lower, the penalty is higher (but this is also the case in a fixed design – we pass and have wasted money). ❝ E.g. CV=30% as you said, then we would require sampleN.TOST(alpha=0.0294, CV=0.3)-24 = 24 additional subjects and hence it's 100% higher … Yes, that’s how it works. But it doesn’t make sense to say “it's 100% higher”. If in the fixed design (assumed 20%) the CV is 30% and you run the study in 24, power will be only 55.8% ( power.TOST(CV=0.3, n=24)).❝ … (or using the mean total n from Table II: 39.9/24 = 1.6625). In the latter case we would have 20% (24/20 = 1.2) but is it reasonable to talk about "total" here? Here again we are in the trap of comparing one particular study to the average of 106 simulated ones. Also you are comparing the wrong row of the table. You should stay at n1 24 and CV 20%. The simulations were run with T/R 0.95 and the given CVs with lognormal error. So with a target of 20%, for sure there were a few studies with only 5% and some with 50%. Average ntotal was 24.6 (5th, 50th, 95th percentiles: 24, 24, 28). On the average for this scenario the penalty is 24.6/24 = +2.5%. Only in 5% of cases the penalty was +16.7%. For an overview of penalties see slide 63. On the average (!) it’s not that bad. See also this goody: ![[image]](img/uploaded/image125.png) Funny, isn’t it? — 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 |
|
Ben ★ 2012-11-01 11:17 (4562 d 03:04 ago) @ Helmut Posting: # 9492 Views: 8,452 |
|
|
Thanks Helmut, everything is clear now  |
Ing. Helmut Schütz