st: Detectable alternative calculation question

["Polis, Chelsea B." <cpolis@jhsph.edu>]

Dear Statalisters,

I am trying to understand how to perform a sample size calculation for a randomized crossover study.  Participants will be randomized to product A or B at baseline (Visit 1), will receive the alternate product in three months (Visit 2), and then freely choose their preferred product (A or B) at six months (Visit 3).

We expect about 500 people to complete Visit 3.  The sample size calculation was based upon product preference at Visit 3.  Assuming 250 randomized to each group, an alpha of 0.05, 80% power, and an equal probability of choosing either product, we originally calculated that we could detect significant differences of proportions in preference below 38% and above 62%.

I'm getting hung up on whether we need to calculate this differently though, since the proportion of participants choosing A affects the proportion of participants choosing B (i.e., those two proportions will always total 100%, so I think they are not independent).  Suggestions for how to think about this issue would be greatly appreciated!

Many thanks,
Chelsea

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