BMC Medical Research Methodology

Table 3 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 = 0.4

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

		J = 0.4
		60/20		150/50		300/100
		Bias	RMSE	Bias	RMSE	Bias	RMSE
Normal, equal variances		θ = 6.762
	N	0.000	0.096	0.001	0.057	0.003	0.041
	TN	-0.016	0.090	-0.016	0.053	-0.015	0.039
	EMP	0.463	0.513	0.489	0.520	0.499	0.519
	KM	0.019	0.153	0.012	0.106	0.008	0.080
	DS	0.010	0.188	0.007	0.145	0.009	0.125
Normal^ (-1/3)		θ = 3.068
	N	0.370	0.434	0.424	0.453	0.436	0.451
	TN	-0.154	0.242	-0.151	0.199	-0.145	0.171
	EMP	0.697	0.850	0.757	0.852	0.785	0.841
	KM	0.133	0.310	0.083	0.190	0.072	0.151
	DS	-0.007	0.367	-0.004	0.287	0.001	0.238
Mix1		θ = 11.659
	N	-0.260	0.317	-0.254	0.280	-0.250	0.263
	TN	-0.706	0.755	-0.694	0.716	-0.689	0.701
	EMP	-0.357	0.680	-0.226	0.496	-0.132	0.363
	KM	-0.088	0.365	-0.092	0.269	-0.088	0.213
	DS	-0.292	0.593	-0.176	0.450	-0.107	0.346
Mix2		θ = 10.665
	N	0.532	0.575	0.545	0.562	0.551	0.559
	TN	-0.050	0.196	-0.055	0.133	-0.055	0.101
	EMP	-0.058	0.419	-0.026	0.332	-0.007	0.254
	KM	0.150	0.393	0.102	0.265	0.069	0.186
	DS	-0.023	0.388	-0.002	0.318	0.007	0.246
Mix3		θ = 14.244
	N	-1.831	1.854	-1.840	1.850	-1.850	1.854
	TN	-1.209	1.246	-1.213	1.228	-1.211	1.219
	EMP	-0.947	1.539	-1.013	1.614	-0.867	1.502
	KM	-1.700	2.059	-1.754	2.098	-1.672	2.043
	DS	-1.059	1.589	-1.084	1.641	-0.919	1.531
Mix4		θ = 14.430
	N	-1.823	1.849	-1.836	1.846	-1.838	1.843
	TN	-1.133	1.175	-1.129	1.145	-1.141	1.149
	EMP	-0.698	1.418	-0.478	1.174	-0.352	0.992
	KM	-1.408	1.876	-1.144	1.636	-0.924	1.450
	DS	-0.799	1.447	-0.549	1.197	-0.391	1.018

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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