## Dropouts continued [Two-Stage / GS Designs]

Hi ElMaestro,

had a closer look into the loss of power due to dropouts.

» 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 […], if 2 subjects go lost in sequence RT during stage 2?
»
» […] stage 2's are often (not always, just often in practice) much larger than stage 1's…

Larger is OK but too large isn’t. With the exception of Xu’s methods (my current favorite) you don’t reach the target power with small n1. ‘Potvin B’:

                   power n1  N (median) stage 1 final 12      44      0.0671 0.784 14      44      0.104  0.799 16      44      0.155  0.810 24      36      0.413  0.830 30      30      0.566  0.834

In your example final power is 78.4%, 93.1% of studies proceed to the second stage, and the median total sample size is 44. Let’s add dropouts and see what happens to power.

 N  power 44  0.779 43  0.768 42  0.757 41  0.745 40  0.733

If n1 is small you are punished twice: You don’t reach the target power and the total sample sizes will be larger.
My current practice is to use n1 which is ~75–80% of the fixed sample design with a ‘best-guess’ CV. With n1 30 we exceed the target power with 83.4%, only 41.8% studies proceed to the second stage (i.e., you have a 56.6% chance to show BE already in the first), and the median total sample size is 30 (!). OK, the mean is 39… The distribution looks like that:

Even with a futility (Nmax 64) final power is with 77.6% close to the target but power in the first stage is still 56.6%. With a futility on the total sample size you can not only ease the sponsor but – hopefully – the BSWP. The Type I Error drops from 0.0440 to 0.0427.

I don’t like small first stages.

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Helmut Schütz

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