BMC Medical Research Methodology

Table 4 Estimated RMSE of estimators for the cut-off θ by varying distributional assumptions on the continuous risk indicator X for unbalanced sample sizes (60/20), (150/50) and (300,100) and Youden Index J = 0.6

From: oA novel nonparametric approach for estimating cut-offs in continuous risk indicators with application to diabetes epidemiology

		J = 0.6
		60/20		150/50		300/100
		Bias	RMSE	Bias	RMSE	Bias	RMSE
Normal, equal variances		θ = 6.921
	N	0.007	0.066	0.003	0.043	0.001	0.030
	TN	-0.035	0.078	-0.036	0.057	-0.037	0.048
	EMP	0.281	0.329	0.301	0.325	0.313	0.329
	KM	0.006	0.107	0.010	0.077	0.007	0.055
	DS	0.007	0.154	0.012	0.125	0.011	0.097
Normal^ (-1/3)		θ = 3.201
	N	0.442	0.498	0.484	0.509	0.514	0.530
	TN	-0.244	0.282	-0.257	0.271	-0.263	0.270
	EMP	0.539	0.688	0.567	0.650	0.624	0.678
	KM	0.193	0.307	0.147	0.212	0.116	0.166
	DS	0.001	0.344	0.005	0.257	0.009	0.216
Mix1		θ = 11.103
	N	0.399	0.440	0.416	0.432	0.415	0.423
	TN	-0.109	0.216	-0.085	0.144	-0.088	0.123
	EMP	-0.093	0.430	-0.049	0.322	-0.036	0.257
	KM	0.301	0.419	0.243	0.308	0.192	0.244
	DS	-0.036	0.406	-0.026	0.307	-0.018	0.250
Mix2		θ = 10.900
	N	0.379	0.430	0.395	0.412	0.400	0.409
	TN	-0.067	0.169	-0.074	0.117	-0.067	0.094
	EMP	-0.047	0.337	-0.031	0.253	-0.016	0.194
	KM	0.083	0.248	0.040	0.153	0.036	0.111
	DS	-0.010	0.312	-0.016	0.239	-0.003	0.184
Mix3		θ = 13.184
	N	0.378	0.459	0.396	0.429	0.393	0.409
	TN	-0.013	0.262	-0.012	0.168	-0.014	0.116
	EMP	-0.089	0.622	-0.048	0.472	-0.042	0.392
	KM	0.211	0.594	0.179	0.408	0.135	0.300
	DS	-0.027	0.574	-0.019	0.444	-0.013	0.373
Mix4		θ = 12.874
	N	0.715	0.766	0.717	0.737	0.717	0.727
	TN	0.296	0.405	0.294	0.341	0.294	0.318
	EMP	0.002	0.631	0.017	0.481	0.011	0.391
	KM	0.306	0.665	0.200	0.448	0.146	0.321
	DS	0.066	0.606	0.061	0.469	0.047	0.380

DS = Dempfle and Stute estimator; EMP = empirical conditional distribution function method; J = Youden Index;
KM = Kernel method; N = Normal method; TN = transformed normal method

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ISSN: 1471-2288

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