Innovative thinking of clinical investigation for rare disease drug development

Table 3 Sample size comparison of composite hypothesis testing and single hypothesis testing

Effectiveness		Safety		\(N_{\text {com}}^a\)	\(N_{\text {eff}}^b\)
Treatment (\(\pi _{11}\))	Control (\(\pi _{21}\))	Treatment (\(\pi _{12}\))	Control (\(\pi _{22}\))	\(N_{\text {com}}^a\)	\(N_{\text {eff}}^b\)
\(\delta _{1N}=0.1, \delta _{2N}=0.001.\)
0.6	0.5	0.05	0.08	992	385
		0.06		2317
		0.07		9000
0.7	0.5	0.05	0.08	992	362
		0.06		2317
		0.07		9000
0.8	0.5	0.05	0.08	992	322
		0.06		2317
		0.07		9000
\(\delta _{1N}=0.1, \delta _{2N}=0.005.\)
0.6	0.5	0.05	0.08	778	385
		0.06		1635
		0.07		4840
0.7	0.5	0.05	0.08	778	362
		0.06		1635
		0.07		4840
0.8	0.5	0.05	0.08	778	322
		0.06		1635
		0.07		4840
\(\delta _{1N}=0.3, \delta _{2N}=0.001.\)
0.6	0.5	0.05	0.08	992	43
		0.06		2317
		0.07		9000
0.7	0.5	0.05	0.08	992	41
		0.06		2317
		0.07		9000
0.8	0.5	0.05	0.08	992	36
		0.06		2317
		0.07		9000

\(^{a}\) \(N_\text {com}\) = sample size for composite hypothesis testing for effectiveness and safety
\(^{b}\) \(N_\text {eff}\) = sample size for single hypothesis testing for effectiveness
Correlation between effectiveness and safety are assumed to be the same for treatment and control group, which is \(\rho _1=\rho _2=0.3\). \(\alpha =0.025\) and \(1-\beta =0.80\)

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