Goodness-of-fit two-phase sampling designs for time-to-event outcomes: a simulation study based on New York University Women’s Health Study for breast cancer

Table 2 Performance measures of the simulated biomarker coefficient \(\left(\widehat{\alpha }\right)\): Relative efficiency of the asymptotic variance of \(\widehat{\alpha }\) under SMLE relative to each method

Stratification	Event rate	\(\alpha\)	Ratio	IPW:Two-phase	SMLE:Two-phase	Standard:CC	SMLE:CC
Unstratified	5%	0.2	1:1	0.744	1.000	0.533	0.720
		0.2	1:2	0.864	1.000	0.607	0.756
		0.5	1:1	0.758	1.000	0.600	0.767
		0.5	1:2	0.856	1.000	0.634	0.770
	10%	0.2	1:1	0.840	1.000	0.555	0.687
		0.2	1:2	0.920	1.000	0.685	0.765
		0.5	1:1	0.850	1.000	0.597	0.725
		0.5	1:2	0.930	1.000	0.669	0.748
Stratified by median AGE	5%	0.2	1:1	0.745	1.006	0.531	0.720
		0.2	1:2	0.869	1.003	0.602	0.754
		0.5	1:1	0.747	0.994	0.596	0.767
		0.5	1:2	0.855	1.001	0.626	0.766
	10%	0.2	1:1	0.849	1.005	0.554	0.688
		0.2	1:2	0.919	0.998	0.683	0.766
		0.5	1:1	0.848	0.994	0.594	0.722
		0.5	1:2	0.926	1.001	0.665	0.746

Abbreviations: Ratio Case and control ratio, IPW IPW based Cox PH model, Two-phase GOF two-phase sampling design, SMLE semiparametric maximum-likelihood method, Standard Prentice method as unstratified approach and Borgan I method as stratified approach, CC standard case-cohort design. Note that we describe each method under each design as method:design using the abbreviations. In the calculation of relative efficiency, the asymptotic variance of SMLE was numerator, while denominator was the asymptotic variance of each method

ISSN: 1471-2288