Derivation and assessment of risk prediction models using case-cohort data

Sanderson, Jean; Thompson, Simon G; White, Ian R; Aspelund, Thor; Pennells, Lisa

doi:10.1186/1471-2288-13-113

BMC Medical Research Methodology

Table 2 Results of simulation study with alternative incidence rates

From: Derivation and assessment of risk prediction models using case-cohort data

a) Discrimination measures
Incidence* 10 years (25 years)	Sampling fraction	% Cases (25 years)	Harrell’s C							Royston and saubrei’s D
			Full cohort	Case-cohort						Full cohort	Case-cohort
				UW (bias %)	W	SE	ESE**	RE^‡	ERE^‡‡		UW (bias %)	W	SE	ESE**	RE^‡	ERE^‡‡
0.073 (0.277)	0.03	91	0.674	0.552 (18.1)	0.675	0.018	0.018	0.135	0.126	1.060	0.336 (68.3)	1.099	0.162	0.172	0.064	0.055
	0.1	76		0.591 (12.4)	0.675	0.011	0.011	0.354	0.349		0.568 (46.5)	1.070	0.094	0.092	0.192	0.197
	0.3	52		0.637 (5.5)	0.674	0.008	0.008	0.678	0.672		0.832 (21.4)	1.063	0.060	0.057	0.474	0.479
	0.5	39		0.655 (2.7)	0.674	0.007	0.007	0.831	0.817		0.942 (11.0)	1.060	0.050	0.047	0.671	0.682
	0.9	26		0.672 (0.3)	0.675	0.007	0.006	0.978	0.981		1.046 (1.4)	1.061	0.043	0.040	0.933	0.935
0.027 (0.112)	0.03	76	0.679	0.576 (15.3)	0.681	0.021	0.020	0.283	0.288	1.073	0.491 (54.4)	1.087	0.173	0.167	0.147	0.157
	0.1	49		0.627 (7.6)	0.679	0.014	0.014	0.582	0.580		0.771 (28.1)	1.072	0.109	0.102	0.368	0.4179
	0.3	24		0.662 (2.5)	0.679	0.012	0.011	0.843	0.862		0.970 (9.4)	1.073	0.080	0.075	0.682	0.7407
	0.5	16		0.671 (1.1)	0.679	0.011	0.011	0.926	0.928		1.023 (4.3)	1.069	0.073	0.07	0.823	0.8868
	0.9	10		0.679 (0.1)	0.680	0.011	0.011	0.991	0.997		1.070 (0.5)	1.076	0.068	0.066	0.956	0.9835
b) NRI
*Incidence 10 years (25 years)**	Sampling fraction	% Cases (25 years)	Category-based NRI						Continuous NRI
			Full cohort	Case-cohort					Full cohort	Case-cohort
				NRI	SE	ESE**	RE ^‡	ERE ^‡‡		NRI	SE	ESE**	RE ^‡	ERE ^‡‡
0.073 (0.277)	0.03	97	0.028	0.029	0.025	0.033	0.414	0.265	0.170	0.166	0.086	0.095	0.296	0.214
	0.1	86		0.028	0.019	0.023	0.713	0.506		0.170	0.060	0.069	0.602	0.490
	0.3	76		0.027	0.017	0.018	0.906	0.798		0.169	0.050	0.051	0.854	0.753
	0.5	52		0.028	0.017	0.018	0.960	0.814		0.171	0.048	0.050	0.932	0.898
	0.9	26		0.028	0.016	0.018	0.997	0.963		0.170	0.047	0.046	0.992	0.981
0.027 (0.112)	0.03	91	0.011	0.015	0.014	0.022	0.571	0.308	0.156	0.154	0.106	0.114	0.561	0.456
	0.1	66		0.012	0.012	0.015	0.813	0.603		0.160	0.087	0.096	0.822	0.730
	0.3	49		0.010	0.011	0.012	0.954	0.965		0.156	0.081	0.080	0.947	0.903
	0.5	24		0.011	0.011	0.013	0.990	0.933		0.160	0.080	0.083	0.976	0.959
	0.9	10		0.011	0.011	0.012	1.008	0.944		0.155	0.079	0.076	0.997	0.978

Results are shown for the full cohort, the case-cohort subsample with Prentice weights using the standard unweighted measures of discrimination (UW) as well as the weighted versions (W). For the weighted estimates we also show the analytical and empirical SE and relative efficiency.
* Incidence from Kaplan-Meier.
** Empirical standard error.
^‡ Relative efficiency calculated as the ratio of analytical variances (full cohort/case-cohort).
^‡‡ Empirical relative efficiency calculated as the ratio of empirical variances (full cohort/case-cohort).

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ISSN: 1471-2288

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