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Kalyani Kothapalli, Erin Hoerl Leone, Dale Usner; Simulations to estimate power in correlated binary data. Invest. Ophthalmol. Vis. Sci. 2020;61(7):5121.
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To identify the optimal treatment design for a Phase 3 ophthalmology study, we compared the power of three designs based on response rates for two dose levels (low and high): Design 1) contralateral design where each subject was randomized to a different dose in each eye, Design 2) bilateral design where half of the subjects were randomized to high dose in both eyes and half of the subjects to low dose in both eyes, and Design 3) half of the subjects were randomized to contralateral design and half to bilateral design. We compared across response rates of 17-50% for high dose and 8-25% for low dose and correlations of 0.0, 0.2, and 0.3, with a sample size of 48 total subjects.
Power was calculated using closed-form equations for McNemar’s test in Design 1, using simulations analyzed with Pearson chi-square test and Generalized Estimating Equations (GEE) for Design 2, and using simulations analyzed with GEE for Design 3. Correlated binary data were generated from 5,000 simulations. For example, in Design 2, in each simulation, 24 pairs of eyes each with 17% response rate and a correlation of 0.3 between eyes were generated for the high dose, and similarly, 24 pairs of eyes each with 8% response rate and a correlation of 0.3 between eyes were generated for the low dose. For the chi-square test, a responder was defined as a subject with a response in either eye. For the GEE model, a responder was defined as an eye using binomial errors with a logit link to account for correlation between eyes. Power was calculated as a proportion of significance tests (p-value < 0.05) out of 5,000 simulations.
Power increased as the correlation increased in Designs 1 and 3, while power decreased as the correlation increased in Design 2. In Design 2, power was generally higher with chi-square tests for lower response rates in the low dose and with GEE for higher response rates in both the high dose and low dose. Power was highest for Design 1 (McNemar’s), followed by Design 3 (GEE), and then Design 2 (GEE).
Power calculations were helpful in identifying Design 1 as the preferred study design for the Phase 3 study and in selecting the appropriate statistical method for the primary endpoint analysis in Design 2 should it be selected instead.
This is a 2020 ARVO Annual Meeting abstract.
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