BMC Research Notes

Table 3 The MSE, bias and relative bias of different methods of optimal cut-point selection when data generated under bigamma distributions with equal/unequal sample size from diseased (D) and non-diseased (ND) 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	0.5859	− 0.1071	− 0.0441	0.1371	− 0.0004	− 0.0002	0.2103	0.0196	0.0091	0.0770	− 0.1705	− 0.0772	1471.9	− 38.257	− 0.9507
	100	0.4081	− 0.0743	− 0.0306	0.0777	0.0176	0.0083	0.1084	0.0187	0.0087	0.0537	− 0.1516	− 0.0686	1449.5	− 37.921	− 0.9424
	200	0.2725	− 0.0479	− 0.0197	0.0469	0.0171	0.0080	0.0670	0.0169	0.0078	0.0410	− 0.1423	− 0.0644	1420.2	− 37.482	− 0.9315
Moderate	50	0.5225	− 0.1103	− 0.0398	0.1534	0.0018	0.0007	0.2263	0.0172	0.0068	0.1590	− 0.2720	− 0.1034	1506.7	− 38.726	− 0.9624
	100	0.3140	− 0.0545	− 0.0197	0.0872	0.0155	0.0063	0.1513	0.0432	0.0171	0.1180	− 0.2455	− 0.0934	1497.4	− 38.581	− 0.9588
	200	0.2175	− 0.0235	− 0.0085	0.0498	0.0092	0.0037	0.0851	0.0307	0.0121	0.0831	− 0.2027	− 0.0771	1487.7	− 38.423	− 0.9549
High	50	0.5156	− 0.1224	− 0.0316	0.2672	0.0140	0.0040	0.4176	− 0.0054	− 0.0054	0.4365	− 0.4156	− 0.1074	1577.0	− 39.684	− 0.9862
	100	0.3264	− 0.0723	− 0.0187	0.1556	0.0295	0.0085	0.2726	0.0278	0.0074	0.2632	− 0.3006	− 0.0777	1575.8	− 39.657	− 0.9855
	200	0.1990	− 0.0693	− 0.0179	0.0825	0.0208	0.0060	0.1500	− 0.0012	0.0003	0.1527	− 0.2242	− 0.0579	1574.1	− 39.626	− 0.9848

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	0.5428	− 0.0252	− 0.0104	0.1047	0.0392	0.0185	0.1623	0.0457	0.0211	0.0618	− 0.1407	− 0.0637	1519.8	− 38.889	− 0.9664
	50	150	0.5093	− 0.0299	− 0.0123	0.1030	0.0722	0.0340	0.1627	0.0741	0.0343	0.0528	− 0.1292	− 0.0585	1535.6	− 39.097	− 0.9716
	50	200	0.5077	0.0444	0.0183	0.1117	0.0617	0.0291	0.1749	0.0882	0.0408	0.0513	− 0.1295	− 0.0586	1555.6	− 39.373	− 0.9785
Moderate	50	100	0.4163	− 0.0318	− 0.0115	0.1334	0.0589	0.0239	0.2073	0.0656	0.0259	0.1285	− 0.2287	− 0.0870	1548.5	− 39.281	− 0.9762
	50	150	0.3968	0.0510	0.0184	0.1190	0.0745	0.0303	0.1983	0.0965	0.0382	0.1051	− 0.2000	− 0.0761	1560.1	− 39.432	− 0.9799
	50	200	0.4239	0.0658	0.0238	0.1117	0.0662	0.0269	0.1856	0.0733	0.0290	0.1051	− 0.2023	− 0.0769	1575.6	− 39.646	− 0.9852
High	50	100	0.4459	− 0.0482	− 0.0124	0.2211	0.0749	0.0215	0.3740	0.0492	0.0132	0.3226	− 0.3175	− 0.0820	1590.4	− 39.859	− 0.9905
	50	150	0.4828	− 0.0031	− 0.0008	0.2002	0.1011	0.0291	0.3835	0.0805	0.0216	0.2805	− 0.2716	− 0.0702	1597.8	− 39.958	− 0.9930
	50	200	0.3951	0.0234	0.0060	0.2119	0.1217	0.0350	0.3345	0.0861	0.0231	0.2615	− 0.2527	− 0.0653	1602.7	− 40.023	− 0.9946

\({1. X}_{D}\sim G\left(2,{\beta }_{D}\right)\), \({X}_{ND}\sim G\left(\text{2,1}\right)\), and \({\beta }_{D}\) was taken as 1.5, 2, and 4.5, respectively
MSE: Mean square error, R.B.: Relative bias

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ISSN: 1756-0500

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