Suppose we want to estimate the number of participants needed in the main study so that there is a 90% chance of finding a significant difference between active and placebo eyes using a two-sided test with a significance level of .05. We expect the active eyes to have a mean redness score 0.5 unit less than that of the placebo eyes. How many participants are needed in the main study? 

Ophthalmology

A study is being planned to assess whether a topical antiallergic eye drop is effective in preventing the signs and symptoms of allergic conjunctivitis. In a pilot study, at an initial visit, participants are given an allergen challenge; that is, they are subjected to a substance that provokes allergy signs (e.g., cat dander) and their redness score is noted 10 minutes after the allergen challenge (visit 1 score). At a follow-up visit, the same procedure is followed, except that participants are given an active eye drop in one eye and the placebo in the fellow eye 3 hours before the challenge; a visit 2 score is obtained 10 minutes after the challenge. The data collected are shown in Table 8.26.

Table 8.26: Effect of an eye drop in reducing ocular redness among participants subjected to an allergen challenge

 

^aThe redness score ranges from 0 to 4 in increments of 0.5, where 0 is no redness at all and 4 is severe redness.

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Change score in active eye - change score in placebo eye Active Placebo eye eye Mean t sd Mean + sd Mean t sd Change in -0.61 + 0.70 -0.04 + 0.68 -0.57 + 0.86 average redness score (visit 2 – visit 1 score)