Table 1.

Total sample size (equally sized groups; r =0.5) required for evaluating the joint effects of both relative risks with an overall power of 1 − β =0.80 and 0.90 for a one-sided test at the significance level of α =0.025

Assumption		Overall power	Sample Size	Correlation
				0.0	0.3	0.5	0.8	0.99
A1	1. CDD 50% reduction with CDD frequencies of 4% in placebo	0.80	Normal approximation	2,222	2,212	2,204	2,198	2,198
			(Empirical power)	(0.796)	(0.796)	(0.794)	(0.793)	(0.793)
			Simulation-based	2,260	2,240	2,238	2,234	2,234
			(Empirical power)	(0.802)	(0.800)	(0.801)	(0.802)	(0.802)
	2. AAD 50% reduction with ADD frequencies of 10% in placebo	0.90	Normal approximation	2,978	2,976	2,974	2,972	2,972
			(Empirical power)	(0.902)	(0.898)	(0.900)	(0.900)	(0.900)
			Simulation-based	2,968	2,972	2,974	2,972	2,972
			(Empirical power)	(0.900)	(0.900)	(0.900)	(0.900)	(0.900)
A2	1. CDD: 50% reduction with CDD frequencies of 4% in placebo	0.80	Normal approximation	3,130	3,052	3,014	3,014	3,014
			(Empirical power)	(0.799)	(0.799)	(0.798)	(0.798)	(0.798)
			Simulation-based	3,134	3,060	3,022	3,022	3,022
			(Empirical power)	(0.802)	(0.802)	(0.800)	(0.800)	(0.800)
	2. AAD: 25% reduction with ADD frequencies of 15% in placebo	0.90	Normal approximation	3,940	3,886	3,858	3,858	3,858
			(Empirical power)	(0.902)	(0.900)	(0.900)	(0.900)	(0.900)
			Simulation-based	3,928	3,886	3,856	3,856	3,856
			(Empirical power)	(0.900)	(0.900)	(0.900)	(0.900)	(0.900)

The empirical powers under the given sample size using 100,000 Monte-Carlo trials. Monte-Carlo simulation-based sample size was calculated using 100,000 Monte-Carlo trials.