# Bioequivalence and Bioavailability Forum

Back to the forum  2018-06-20 07:53 CEST (UTC+2h)

## Potvin designs w. imbalance - what would you expect? [Two-Stage / GS Designs]

Hi all,

I decided to look into the effects of imbalance on Potvin designs.
This is plain hell, since the Potvin equations only work for balanced situations. So I either have to derive equations that work for imbalance or I have to do everything on basis of matrix algebra in which case I need to switch to R in stead of C.
I went for the latter and had to find ways to speed up the fits. Done now, took some hundred hours.

The practical (though possibly not ideal) way of looking into imbalance is to force imbalance into stage 2. I.e. we look at stage 1 as normal, then we calculate stage 2 normally and expect balance but we happen to loose e.g. 1 or 2 or whatever subjects from, say, sequence RT.
That is how I am implementing it now.

I am looking at my results now and trying to figure out if there is a story in this. So let me ask you experts: Let us say we look at e.g. CV=.3 and N1=12 (6 per sequence at stage 1). What would you expect in terms of power and type I error (i.e. any difference from table I in Potvin's work), if 2 subjects go lost in sequence RT during stage 2?

Note: 2 RT subjects cannot go lost in stage two if there is only 1 per sequence at this stage, in which case I have programmed the loss as 1.

And yes, I know, the underlying imbalance model is not ideal - much better to assume random dropouts across sequences and stages, but that is speed-wise almost impossible to implement. It would simply take forever to compute it with my skills. Let me add, since stage 2's are often (not always, just often in practice) much larger than stage 1's (when N go small and CV go high) there is not much of a crime committed byu focusing on imbalance arising at the second stage.

Have a good day and thanks for any input.

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Best regards,
ElMaestro

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