BMC Research Notes

Table 4 The MSE, bias and relative bias of different methods of optimal cut-point selection when data generated under biexponential 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	1.3970	− 0.3006	− 0.1232	0.2183	− 0.0007	− 0.0004	0.3020	0.0184	0.0100	0.0946	− 0.1495	− 0.0813	2192.5	− 46.599	− 0.9320
	100	1.1067	− 0.1676	− 0.0687	0.1558	0.0183	0.0101	0.2040	0.0380	0.0206	0.0584	− 0.1334	− 0.0725	2157.9	− 46.167	− 0.9233
	200	0.8694	− 0.0393	− 0.0161	0.0830	0.0136	0.0075	0.1245	0.0257	0.0140	0.0433	− 0.1313	− 0.0714	2099.1	− 45.432	− 0.9086
Moderate	50	1.2422	− 0.1779	− 0.0544	0.3517	0.0263	0.0103	0.5716	0.0498	0.0182	0.3349	− 0.3786	− 0.1382	2262.8	− 47.362	− 0.9472
	100	0.8318	− 0.1231	− 0.0376	0.2096	0.0282	0.0110	0.3660	0.0574	0.0210	0.2350	− 0.3191	− 0.1165	2239.3	− 47.057	− 0.9411
	200	0.5211	− 0.0969	− 0.0296	0.1324	0.0279	0.0109	0.2294	0.0483	0.0176	0.1519	− 0.2507	− 0.0915	2239.5	− 47.020	− 0.9404
High	50	1.8496	− 0.2331	− 0.0469	0.8368	0.0728	0.0181	1.4758	− 0.0018	− 0.0004	1.1215	− 0.6995	− 0.1521	2401.6	− 48.911	− 0.9782
	100	1.0507	− 0.2031	− 0.0409	0.4273	0.0232	0.0058	0.9021	− 0.0029	− 0.0006	0.6957	− 0.5225	− 0.1136	2398.1	− 48.851	− 0.9770
	200	0.7329	− 0.1623	− 0.0327	0.2325	0.0212	0.0053	0.5498	− 0.0294	− 0.0064	0.3676	− 0.3916	− 0.0851	2403.6	− 48.902	− 0.9780

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	1.2307	− 0.2583	− 0.1059	0.1872	0.0363	0.0201	0.2866	0.0630	0.0343	0.0677	− 0.1283	− 0.0697	2302.7	− 47.799	− 0.9560
	50	150	1.3978	− 0.0562	− 0.0230	0.2039	0.0809	0.0138	0.3071	0.1205	0.0655	0.0633	− 0.1041	− 0.0566	2335.3	− 48.154	− 0.9631
	50	200	1.3240	− 0.0907	− 0.0372	0.1852	0.0580	0.0320	0.2724	0.0846	0.0460	0.0591	− 0.1108	− 0.0602	2354.0	− 48.360	− 0.9672
Moderate	50	100	1.1099	− 0.0389	− 0.0119	0.3138	0.0742	0.0290	0.5186	0.1006	0.0367	0.2738	− 0.3377	− 0.1232	2369.0	− 48.529	− 0.9706
	50	150	1.0450	0.0012	0.0004	0.3105	0.1373	0.0536	0.5531	0.1647	0.0601	0.2281	− 0.2742	− 0.1001	2384.9	− 48.686	− 0.9737
	50	200	1.1334	0.0518	0.0159	0.2600	0.0963	0.0376	0.4370	0.1119	0.0408	0.2043	− 0.2667	− 0.0973	2415.2	− 49.032	− 0.9806
High	50	100	1.4932	− 0.0966	− 0.0194	0.7014	0.1167	0.0290	1.3132	0.0918	0.0199	0.8665	− 0.5620	− 0.1222	2449.8	− 49.438	− 0.9888
	50	150	1.4370	− 0.0088	− 0.0018	0.6562	0.2136	0.0531	1.2091	0.1662	0.0360	0.7004	− 0.4604	− 0.1001	2451.6	− 49.450	− 0.9890
	50	200	1.4623	0.0945	0.0190	0.6928	0.2503	0.0623	1.2345	0.2275	0.0492	0.6146	− 0.4032	− 0.0876	2468.2	− 49.639	− 0.9928

\({X}_{D}\sim E\left({\lambda }_{D}\right)\), \({X}_{ND}\sim E\left(0.5\right)\), and \({\lambda }_{D}\) was taken as 0.33, 0.17, and 0.055, respectively
MSE: Mean square error, R.B.: Relative bias

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ISSN: 1756-0500

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