. Author manuscript; available in PMC: 2014 Jun 10.

Published in final edited form as: Biometrika. 2013 Jun 10;100(3):695–708. doi: 10.1093/biomet/ast018

Table 1.

Comparison of two methods with a single disease outcome: β₁ = log 2 = 0·693

Event proportion	Size of subcohort	τ_θ	The proposed method				Borgan et al.’s method				SRE
Event proportion	Size of subcohort	τ_θ	β̃₁	SE	SD	CR	β̂₁	SE	SD	CR	SRE
8%	100	0·83	0·706	0·32	0·32	94	0·705	0·33	0·33	94	1·04
		0·11	0·718	0·31	0·32	94	0·719	0·33	0·33	94	1·07
		0·05	0·708	0·32	0·32	94	0·705	0·33	0·33	94	1·06
	200	0·83	0·715	0·28	0·28	95	0·716	0·28	0·28	95	1·02
		0·11	0·704	0·28	0·28	95	0·705	0·28	0·29	95	1·03
		0·05	0·697	0·28	0·27	95	0·698	0·28	0·28	95	1·05
20%	100	0·83	0·703	0·25	0·25	94	0·704	0·26	0·27	95	1·13
		0·11	0·694	0·23	0·23	94	0·694	0·26	0·27	95	1·31
		0·05	0·700	0·23	0·23	94	0·701	0·26	0·26	95	1·29
	200	0·83	0·693	0·20	0·20	95	0·692	0·21	0·21	95	1·10
		0·11	0·696	0·19	0·19	95	0·699	0·21	0·21	95	1·17
		0·05	0·694	0·19	0·19	95	0·695	0·21	0·21	95	1·26

SE, average standard errors; SD, sample standard deviation; CR, coverage rate (%) of the nominal 95% confidence intervals; $SRE = {SD}_{c}^{2} / {SD}_{p}^{2}$ , sample relative efficiency, where SD_c and SD_p are the sample standard deviation for the Borgan et al. (2000)’s method and the proposed method, respectively.