Helmut ★★★ Vienna, Austria, 20111030 17:36 Posting: # 7559 Views: 6,466 

Dear all! Here comes the bonusquestion for hardcoresimulants: How to deal with α in a doseproportionality study when a twostage design is to be planned? In the past I have used a Bonferronicorrection (see this post), which is
Opinions, ideas? — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
ElMaestro ★★★ Belgium?, 20111030 18:26 @ Helmut Posting: # 7560 Views: 5,727 

Dear HS, » Opinions, ideas? There are quite a few SPC's out there which state dose proportionality or dose linearity and where the originator as far as I know hasn't really done that fancy stuff but just administered a series of doses and checked AUC or Cmax or Cl. That's good enough isn't it. At least for EU, I guess part of the story is to live with the BEguideline's requirement "Assessment of linearity will consider whether differences in doseadjusted AUC meet a criterion of ± 25%." which can be dealt with very simply. Perhaps your angle is different and that where the complexity comes in? I am eager to hear. Btw, in spite of the links to previous definitions and discussions I still think we need some useful definitions, preferably in guidelines. Cmax etc vs dose being a straight line, I am perfectly willing to call that linearity; Wikipedia does an excellent job at confusing readers. — I could be wrong, but... Best regards, ElMaestro "Pass or fail" (D. Potvin et al., 2008) 
Helmut ★★★ Vienna, Austria, 20111102 22:30 @ ElMaestro Posting: # 7590 Views: 5,677 

Dear ElMaestro! » At least for EU, I guess part of the story is to live with the BEguideline's requirement "Assessment of linearity will consider whether differences in doseadjusted AUC meet a criterion of ± 25%." which can be dealt with very simply. » Perhaps your angle is different and that where the complexity comes in? I am eager to hear. Yes. I’m aiming at a confirmatory study – not the stuff mentioned in the GL (“If you come up with some serious writing about the drug’s PK from the Library of Alexandria – whether it might be on parchment or papyrus – we accept that and you have to perform the study on the highest dose only.”) » […] Cmax etc vs dose being a straight line, I am perfectly willing to call that linearity; I’m not happy with assessing doseproportionality based on C_{max}. It’s a f_{**}g composite metric. I prefer AUC by far. » Wikipedia does an excellent job at confusing readers. Yeah, that’s funny reading matter. Should read the talkpage as well. — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20111101 11:11 @ Helmut Posting: # 7574 Views: 5,747 

Dear Helmut! » ... Since in doseproportionality (aside from setting up a power model) we often compare doseadjusted responses to one doselevel (and do not perform all pairwise tests) a variant of Dunnett’s test might be suitable. Unfortunately Dunnett is only applicable for nominal scales, not for continuous ones (doses). (emphasis by me) Where does this opinion come from . AFAIK is Dunnett's test a posthoc test within the ANOVA framework to compare many means to one control. ANOVA always deals with measurements on continuous (metric) scales. Or do I miss somefink here? Moreover Hauschke, Steinijans and Pigeot [1] explicitly recommend Dunnett's test for evaluation of studies with more than one Test formulations versus one reference. See Chapter 7. For dose linearity studies (comparing more then 2 dose adjusted PK characteristics) they derive from the intersectionunion principle "... Hence for a joint decision rule where all requirements must be fulfilled, no adjustment of the comparison wise type I error is needed ...". See page 170 of the reference. The argumentation given is plausible for me also as an amateur in statistics I'm not able to prove it. BTW: Where does the 2stage design come into play for doseproportionality studies? [1] Hauschke, Steinijans and Pigeot Bioequivalence Studies in Drug Development Wiley, Chichester 2007 — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20111102 22:18 @ d_labes Posting: # 7589 Views: 5,759 

Dear Detlew! » » […] Unfortunately Dunnett is only applicable for nominal scales, not for continuous ones (doses). » (emphasis by me) » Where does this opinion come from . AFAIK is Dunnett's test a posthoc test within the ANOVA framework to compare many means to one control. ANOVA always deals with measurements on continuous (metric) scales. Or do I miss somefink here? No, no – sorry. Should have done my homework before. I had in mind that Dunnett is applicable if a continuous variable if tested based on an ordered (nominal) covariate. You are right. » Moreover Hauschke, Steinijans and Pigeot […]. See page 170 of the reference. The argumentation given is plausible for me also as an amateur in statistics I'm not able to prove it. Yes, sounds good for another amateur. Now for the big but (p170–171): […] no adjustment of the comparisonwise type I error is needed to keep the familywise type I error under control. However, this intersectionunion testing procedure inflates the type II error, that is the probability of erroneously failing to reject at least one of the nullhypotheses. This inflation has to be taken into account by an adequate sample size determination. This procedure inflates the relevant type II error […], which in the worst case scenario is the sum of the type II error errors connected with the individual hypotheses. Oh wow!» BTW: Where does the 2stage design come into play for doseproportionality studies? For some background see the end of this post. I have the frivolous idea to plan for a similar study. If I want to go with the worstcase scenario (3 simultaneous comparisons, each at β 0.20/3) in my specific case (T/R 0.95, CV 20%) I would end up with a sample size of 28 instead of 20 in a single comparison with 80% power. +40% penalty. BTW: Can you please check the new requirements for Rpackages? Since the update to R 2.14.0 the helpfiles of PowerTOST are not accessible any more. Has something to do with a missing vignette / base URL? — Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
d_labes ★★★ Berlin, Germany, 20111103 13:18 @ Helmut Posting: # 7593 Views: 5,638 

Dear Helmut! » BTW: Can you please check the new requirements for Rpackages? Since the update to R 2.14.0 the helpfiles of PowerTOST are not accessible any more. Has something to do with a missing vignette / base URL? Sorry for the inconvenience. It had to do with a violation of name conventions which was not fully documented. After a hint from Prof. Ripleys about that I had created a new version 0.87 last week which should meanwhile be accessible via CRAN. — Regards, Detlew 
Helmut ★★★ Vienna, Austria, 20111103 14:28 @ d_labes Posting: # 7594 Views: 5,622 

Dear Detlew! » Sorry for the inconvenience. It had to do with a violation of name conventions which was not fully documented. After a hint from Prof. Ripleys about that I had created a new version 0.87 last week which should meanwhile be accessible via CRAN. Sorry for the confusion  forget it. Seems that after installing 2.14.0 and update.packages(checkBuilt=TRUE, ask=FALSE) the local HTTPDserver had hiccups. After a reboot the help system of 0.87 is working like a charm. Same on my notebook, where I have 0.87 on 2.13.2 installed.— Diftor heh smusma 🖖 Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. 🚮 Science Quotes 
martin ★★ Austria, 20111103 22:28 (edited by martin on 20111104 14:16) @ Helmut Posting: # 7600 Views: 5,759 

Dear HS! A good „introduction“ to the intersectionunion test (IUT) for hypothesis of equivalence is given in chapter 7.1 in Wellek (2010). I set up a simulation study to evaluate the power and the type I error when testing 3 hypothesis of equivalence simultaneously based on the IUT using a common CV and lognormal distributed random variables. I used identical magical margins (i.e. 0.8 to 1.25) for all three comparisons. I evaluated the power (2 scenarios) and the type I error (2 scenarios) for a parallel group design. You may find the code useful.
library(gmodels) best regards Martin PS.: There are different definitions of power available when comparing more than 2 groups. I simulated the power for claiming equivalence for all three comparisons (i.e. overall equivalence) suitable for the IUT. PPS.: I implemented the confidence interval inclusion approach but IMHO a SOST (six onesided tests ) approach should also be applicable. 
martin ★★ Austria, 20111105 23:43 (edited by martin on 20111106 11:04) @ martin Posting: # 7615 Views: 5,634 

Dear HS ! Please find enclosed a modified (rather slow) code for evaluation of power and type I error for Dunnett and IUT for 2to1 comparisons (i.e. B vs. A and C vs. A) providing:
Martin library(multcomp) 