Table 4.

Efficiency (ratio of observed variances in simulation studies) of the semiparametric “empirical” estimator and nonparametric estimator relative to the semiparametric maximum likelihood estimator of the predictiveness curve in nested case-control studies for the linear logistic model. SPE denotes the semiparametric “empirical” estimator, NPMLE denotes the nonparametric maximum likelihood estimator. Here n = ∞ denotes the asymptotic variance.

		v = 0.1	v = 0.3	v = 0.5	v = 0.7	v = 0.9
R(v)		0.045	0.094	0.15	0.24	0.43
n = 100	SPE	1.02	0.97	0.97	0.90	0.91
	NPMLE	0.45	0.41	0.27	0.18	0.29
n = 500	SPE	0.98	0.98	0.96	0.90	0.89
	NPMLE	0.25	0.25	0.16	0.10	0.18
n = 2000	SPE	0.99	0.98	0.96	0.90	0.91
	NPMLE	0.17	0.16	0.10	0.06	0.11
n = ∞	SPE	0.99	0.97	0.97	0.90	0.91
		p = 0.045	p = 0.094	p = 0.15	p = 0.24	p = 0.43
R–1(p)		0.1	0.3	0.5	0.7	0.9
n = 100	SPE	0.99	0.99	0.96	0.91	0.91
	NPMLE	0.47	0.47	0.32	0.21	0.38
n = 500	SPE	0.99	0.98	0.95	0.90	0.90
	NPMLE	0.28	0.27	0.17	0.10	0.20
n = 2000	SPE	0.99	0.98	0.96	0.91	0.91
	NPMLE	0.18	0.16	0.10	0.06	0.12
n = ∞	SPE	0.99	0.97	0.97	0.90	0.91