Suppose we plan a comparative study of two eye drops (A, B) to reduce intraocular pressure (IOP) among patients with glaucoma. A contralateral design is used, in which drop A is assigned to a random eye and drop B is assigned to the fellow eye. The patients take the eye drops for 1 month, after which their IOP is measured again. The outcome is a decrease in IOP of 5+ mm Hg in an eye. We expect the following: (i) that both eyes will be failures (i.e., not show a decrease of 5+ mm Hg) in 50% of patients; (ii) that both eyes will be successes (i.e., will show a decrease of 5+ mm Hg) in 30% of patients; (iii) that in 15% of patients the drop A eye will result in a decrease in IOP of 5+ mm Hg but the drop B eye will not; and (iv) that in 5% of patients the drop B eye will show a decrease in IOP of 5+ mm Hg but the drop A eye will not.
(a) What method of analysis can be used to compare the efficacy of drop A vs. drop B?
(b) How many patients do we need to randomize to achieve 80% power if we have a two-sided test with α = .05, assuming that all patients take their drops?
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