BMC Research Notes

Table 2 The MSE, bias and relative bias of different methods of optimal cut-point selection when data generated under binormal distributions with heteroscedastic variance and equal/unequal sample size from diseased (D) and non-diseased (ND) distributions according to degree of overlap/accuracy

From: Comparison of methods of optimal cut-point selection for biomarkers in diagnostic medicine: a simulation study with application of clinical data in health informatics

Equal sample size¹
Degree of overlap	Sample size	Youden index			Euclidian index			Product method			Index of Union			Diagnostic odds ratio
Degree of overlap	D = ND	MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B
Low	50	0.1922	0.0662	− 0.4731	0.0419	0.0141	0.1006	0.0572	0.0105	0.0959	0.0169	0.0503	0.3352	9.6550	− 2.9039	− 2.5473
	100	0.1270	0.0025	− 0.0178	0.0242	0.0030	0.0215	0.0345	0.0085	0.0773	0.0108	0.0521	0.3471	11.816	− 3.3278	− 2.9191
	200	0.0775	0.0075	− 0.0533	0.0148	0.0028	0.0198	0.0217	0.0017	0.0152	0.0079	0.0482	0.3213	13.601	− 3.5951	− 3.1536
Moderate	50	0.1043	− 0.0287	− 0.1197	0.0319	− 0.0025	− 0.0065	0.0482	0.0009	0.0027	0.0300	0.1065	0.3551	17.799	− 4.1671	− 1.9028
	100	0.0658	− 0.0230	− 0.0958	0.0212	0.0002	0.0004	0.0334	− 0.0068	− 0.0194	0.0231	0.0989	0.3296	20.387	− 4.4862	− 2.0485
	200	0.0427	− 0.0097	− 0.0402	0.0125	− 0.0061	− 0.0160	0.0187	− 0.0074	− 0.0211	0.0164	0.0877	0.2922	22.621	− 4.7287	− 2.1592
High	50	0.0577	− 0.0313	− 0.0337	0.0296	− 0.0152	− 0.0153	0.0436	0.0009	0.0010	0.0345	0.0224	0.0241	52.676	− 7.2479	− 1.3912
	100	0.0350	− 0.0232	− 0.0250	0.0162	− 0.0062	− 0.0063	0.0266	0.0044	0.0047	0.0239	0.0170	0.0183	56.903	− 7.5361	− 1.4465
	200	0.0232	− 0.0129	− 0.0139	0.0101	− 0.0000	− 0.0000	0.0187	0.0082	0.0086	0.0189	0.0069	0.0074	60.626	− 7.7801	− 1.4933

Unequal sample size¹
	D \(\ne\) ND		MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B	MSE	Bias	R.B
Low	50	100	0.1617	0.0504	− 0.3603	0.0328	0.0234	0.1672	0.0452	0.0276	0.2511	0.0157	0.0618	0.4120	11.805	− 3.3304	− 2.9214
	50	150	0.1527	0.0779	− 0.5567	0.0318	0.0344	0.2459	0.0415	0.0387	0.3515	0.0160	0.0732	0.4878	12.970	− 3.5326	− 3.0988
	50	200	0.1385	0.0769	− 0.5493	0.0315	0.0418	0.2983	0.0437	0.0402	0.3653	0.0148	0.0710	0.4733	13.707	− 3.6564	− 3.2074
Moderate	50	100	0.0843	− 0.0025	− 0.0104	0.0298	0.0160	0.0420	0.0430	0.0091	0.0259	0.0321	0.1208	0.4028	20.419	− 4.4900	− 2.0502
	50	150	0.0814	0.0249	0.1037	0.0268	0.0269	0.0708	0.0390	0.0227	0.0647	0.0331	0.1305	0.4351	21.834	− 4.6543	− 2.1253
	50	200	0.0794	0.0556	0.2318	0.0249	0.0308	0.0809	0.0388	0.0367	0.1049	0.0332	0.1344	0.4479	22.692	− 4.7500	− 2.1690
High	50	100	0.0482	− 0.0107	− 0.0115	0.0227	0.0111	0.0112	0.0398	0.0048	0.0051	0.0317	0.0424	0.0456	56.925	− 7.5369	− 1.4466
	50	150	0.0469	0.0253	0.0272	0.0240	0.0280	0.0282	0.0402	0.0324	0.0341	0.0363	0.0652	0.0701	59.199	− 7.6875	− 1.4755
	50	200	0.0450	0.0265	0.0285	0.0216	0.0345	0.0349	0.0365	0.0379	0.0399	0.0347	0.0709	0.0763	60.553	− 7.7751	− 1.4923

\(1. {X}_{D}\sim N\left({\mu }_{D},0.81\right)\), \({X}_{ND}\sim N\left(\text{0,1}\right)\), and \({\mu }_{D}\) was taken as 0.4, 0.8, and 1.85, respectively
MSE: Mean square error, R.B.: Relative bias

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ISSN: 1756-0500

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