Table 2.

Comparison of two methods with multiple disease outcomes: [β₁, β₂] = [0·1, 0·7]

Event proportion	Size of subcohort	τθ	The proposed method				Kang & Cai’s method				SRE
			${\stackrel{\sim }{\beta }}_1^M$	SE	SD	CR	${\widehat{\beta }}_1^M$	SE	SD	CR	β̂1
[8%, 14%]	100	0·83	0·099	0·31	0·30	95	0·101	0·32	0·31	95	1·07
		0·11	0·101	0·30	0·30	95	0·098	0·32	0·32	95	1·13
		0·05	0·109	0·30	0·31	94	0·111	0·32	0·33	94	1·11
	200	0·83	0·106	0·26	0·27	95	0·105	0·27	0·27	95	1·04
		0·11	0·096	0·26	0·26	94	0·096	0·27	0·27	94	1·05
		0·05	0·098	0·26	0·27	94	0·098	0·27	0·27	94	1·05
[20%, 35%]	100	0·83	0·098	0·23	0·24	94	0·094	0·26	0·27	94	1·24
		0·11	0·099	0·22	0·22	94	0·097	0·26	0·26	95	1·42
		0·05	0·095	0·22	0·22	94	0·101	0·26	0·27	95	1·44
	200	0·83	0·103	0·19	0·19	94	0·104	0·20	0·21	95	1·19
		0·11	0·098	0·18	0·18	95	0·097	0·20	0·20	95	1·29
		0·05	0·098	0·18	0·18	95	0·100	0·20	0·20	96	1·31

SE, average standard errors; SD, sample standard deviation; CR, coverage rate (%) of the nominal 95% confidence intervals; $\text{SRE}={\text{SD}}_e^2/{\text{SD}}_p^2$, sample relative efficiency, where SD_e and SD_p are the sample standard deviation for the Kang & Cai (2009)’s method and the proposed method, respectively.