Table 2.

Average apparent and cross-validated (CV) estimates for the Brier score using T, Z information ( ${\text{BS}}_{t_0,\tau }^{(2)}$) and Z information only ( ${\text{BS}}_{t_0,\tau }^{(1)}$), and the increase in proportion of explained variation(IPEV) with corresponding empirical SEs (ESE), average of the SE estimates from the perturbation-resampling method (ASE) for the apparent estimates and empirical coverage levels (Cvg) from setting (i), the low event rate setting and (ii), the moderate event rate setting. All entries are multiplied by 100.

(i) low event rate setting
	n=2000
	Apparent			CV (3-fold)
	Average	ESE	ASE	Average	ESE	Cvg
${\text{BS}}_{t_0,\tau }^{(2)}$	7.6	0.4	0.5	7.9	0.4	95.6
${\text{BS}}_{t_0,\tau }^{(1)}$	8.5	0.4	0.5	8.6	0.5	95.2
IPEV2/1	10.7	2.4	2.8	7.7	2.8	90.3
	n=5000
	Apparent			CV (3-fold)
	Average	ESE	ASE	Average	ESE	Cvg
${\text{BS}}_{t_0,\tau }^{(2)}$	7.7	0.3	0.3	7.8	0.3	95.5
${\text{BS}}_{t_0,\tau }^{(1)}$	8.5	0.3	0.3	8.6	0.3	93.7
IPEV2/1	10.4	1.5	1.7	8.6	1.6	95.3
	(ii) moderate event rate setting
	n=2000
	Apparent			CV (3-fold)
	Average	ESE	ASE	Average	ESE	Cvg
${\text{BS}}_{t_0,\tau }^{(2)}$	9.6	0.4	0.5	10.2	0.5	89.8
${\text{BS}}_{t_0,\tau }^{(1)}$	14.6	0.5	0.5	14.7	0.5	94.9
IPEV2/1	33.9	2.7	2.9	30.6	2.8	92.2
	n=5000
	Apparent			CV (3-fold)
	Average	ESE	ASE	Average	ESE	Cvg
${\text{BS}}_{t_0,\tau }^{(2)}$	9.8	0.3	0.3	10.0	0.3	93.0
${\text{BS}}_{t_0,\tau }^{(1)}$	14.6	0.3	0.3	14.6	0.3	94.9
IPEV2/1	32.9	1.7	1.8	31.7	1.8	94.6