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ElMaestro ★★★ Denmark, 2011-10-18 06:23 (4996 d 02:27 ago) Posting: # 7508 Views: 6,551 |
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Dear all, recently Dr_Dan asked about feasibility of a parallel two-stage BE study. I can't think of any reason not to do it but there's at present zero documentation. Of course, I couldn't help thinking a little bit about how such documentation can be produced. Let's for a second forget the discussion about unequal variances - better do that in another thread. The evaluation with a simple (one-stage) parallel study is a normal linear model with a single factor (treatment) of two levels (Test or Ref). For stage two we need to calculate sample size, and here I am not so sure what to do. For evaluation at stage 2, I imagine -and I'd really love to hear your opinion- that the factors are treatment (two levels) + stage (two levels) + stage x treatment. Stage is in this regard the joker. In a two-stage 2,2,2-BE study stage is a between-subject factor, so this factor itself does not affect the residual. In a parallel two-stage evaluation, stage is also a between-subject factor, and hence it does affect the residual. Should one therefore take that fact into consideration when calculating sample size for stage 2? If yes, any idea how? I would be inclined to say we argue that a well-planned and executed study should not have any significant stage effect, and hence we can ignore the latter issue and just calculate sample size as if it were a just the one-factor situation. But on the other hand, if the anova after stage 2 comes out with a significant p-value for stage as a factor, would this then be bad? I think not, I'd prefer to just look at it as a nuisance and conclude that if the 90% CI is good and stage has a significant p-value then we were perhaps little lucky because our assumption used to calculate sample size was violated but there's nothing wrong with the conclusion towards BE per se. Is this thinking all wrong or completely irrelevant like most of my utterings? Does anyone have any views to share? Many thanks. — Pass or fail! ElMaestro |
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d_labes ★★★ Berlin, Germany, 2011-10-18 13:03 (4995 d 19:47 ago) @ ElMaestro Posting: # 7511 Views: 5,437 |
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Dear EM, ❝ The evaluation with a simple (one-stage) parallel study is a normal linear model with a single factor (treatment) of two levels (Test or Ref). For stage two we need to calculate sample size, and here I am not so sure what to do. For evaluation at stage 2, I imagine -and I'd really love to hear your opinion- that the factors are treatment (two levels) + stage (two levels) + stage x treatment. I'm not sure if you really need the stage x treatment interaction in stage 2 model. If you apply the same prerequisite like Potvin et.al. "... Does not require poolability criteria (or at least should know whether results from both stages are poolable before sample analysis, i.e. base poolability on study conduct such as subject demographics, temporal considerations, use of same protocol, use of same site, etc., rather than a statistical test of poolability)." then IMHO the model with treatment + stage is sufficient. ❝ ... In a parallel two-stage evaluation, stage is also a between-subject factor, and hence it does affect the residual. Should one therefore take that fact into consideration when calculating sample size for stage 2? If yes, any idea how? Since you don't know how the stage effect affects your residual variance in stage 2 the only thing you can do is to use the residual variance from stage 1 in your sample size adaptation. Regardless of a significant or insignificant stage effect in stage 2 evaluation your assumption is that the residual variance from stage 1 or stage 2 measure the same variability and will be used in calculating the (1-2*alphastage)-confidence intervals as a test of BE in both stages. The only way you can consider the stage effect is the use of the degrees of freedom for stage 2 ANOVA in your sample size calculation after stage 1 data are obtained. This is also done by Potvin et.al. for the 2x2 crossover. But I don't think this will make a great difference. ❝ ... But on the other hand, if the anova after stage 2 comes out with a significant p-value for stage as a factor, would this then be bad? Like you I would consider stage as nuisance effect and thus would not worry about it's significance. Hope this helps. — Regards, Detlew |
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ElMaestro ★★★ Denmark, 2011-10-18 17:02 (4995 d 15:48 ago) @ d_labes Posting: # 7514 Views: 5,348 |
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Dear d_labes, thanks for your input. ❝ I'm not sure if you really need the stage x treatment interaction in stage 2 model. If you apply the same prerequisite like Potvin et.al. "... Does not require poolability criteria (or at least should know whether results from both stages are poolable before sample analysis, i.e. base poolability on study conduct such as subject demographics, temporal considerations, use of same protocol, use of same site, etc., rather than a statistical test of poolability)." then IMHO the model with treatment + stage is sufficient. OK, my general impression is that it is desirable to factor in as much as possible in the model, so that all factors and combinations are accounted for in order to get a residual that only reflects random noise. As a side effect this reduces the residual as much as possible which is in a sponsor's interest. The latter, however, is not an argument but just a fact, I think. At a general level I am not sure I realise when one would not specify "everything", despite the quote from Potvin's paper. Are you able to elaborate? Many thanks, EM. |
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d_labes ★★★ Berlin, Germany, 2011-10-18 18:32 (4995 d 14:18 ago) @ ElMaestro Posting: # 7518 Views: 5,421 |
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Dear ElMaestro, ❝ At a general level I am not sure I realise when one would not specify "everything", despite the quote from Potvin's paper. Are you able to elaborate? Sorry. To quote myself: "I'm not sure ...". It was just a feeling resulting from what I have seen in meta-analyses where likewise often only a study effect is specified. I think that one may run in trouble if the stage x treatment interaction comes out as statistical significant. If this is not just by chance IMHO this would mean that a pooling of the data from both stages is not appropriate because the treatments behave different between them. But this is a case of a pre-test with all the bells and whistles of such a method ... Moreover interactions are known in common to be hardly detectable as statistical significant. Then a parsimonious model would not specify them. But as I said, it's just a feeling. — Regards, Detlew |
Ing. Helmut Schütz