Optimum binary cut-off threshold of a diagnostic test: comparison of different methods using Monte Carlo technique

Reibnegger, Gilbert; Schrabmair, Walter

doi:10.1186/s12911-014-0099-1

BMC Medical Informatics and Decision Making

Table 1 Results of the Monte Carlo simulations

From: Optimum binary cut-off threshold of a diagnostic test: comparison of different methods using Monte Carlo technique

	N		Mutual information		Youden		Likelihood ratio
	N		Mean	SD	Mean	Sd	Mean	SD
Scenario 1 (lognormal)	50	Cut-off	8.1 - 10.4	1.7 - 2.6	9.0 - 9.7	1.2 - 1.8	9.9 - 10.1	0.5 - 1.1
		Se	0.78 - 0.86	0.17 - 0.30	0.82 - 0.91	0.10 - 0.14	0.74 - 0.76	0.08 - 0.16
		Sp	0.69 - 0.76	0.18 - 0.23	0.73 - 0.82	0.12 - 0.17	0.78 - 0.78	0.06 - 0.14
	100	Cut-off	8.1 - 10.0	1.4 - 2.2	9.2 - 9.5	1.0 - 1.4	10.0 - 10.10	0.4 - 0.7
		Se	0.84 - 0.89	0.11 - 0.19	0.81 - 0.87	0.09 - 0.13	0.74 -0.75	0.05 - 0.11
		Sp	0.65 - 0.74	0.15 - 0.22	0.72 - 0.78	0.09 - 0.15	0.78 - 0.78	0.04 - 0.10
	200	Cut-off	7.8 - 9.7	1.1 - 1.9	9.2 - 9.4	0.8 - 1.1	10.0 - 10.1	0.3 - 0.5
		Se	0.83 - 0.91	0.08 - 0.16	0.82 - 0.85	0.07 - 0.10	0.74 - 0.74	0.04 - 0.08
		Sp	0.61 - 0.72	0.12 - 0.18	0.71 - 0.75	0.08 - 0.12	0.78 - 0.78	0.03 - 0.07
Scenario 2 (chi-square)	50	Cut-off	7.4 - 9.3	3.3 - 4.1	7.5 - 8.1	1.9 - 2.7	8.2 - 8.4	0.6 - 1.1
		Se	0.67 - 0.70	0.26 - 0.35	0.69 - 0.80	0.17 - 90.21	0.59 - 0.61	0.08 - 0.17
		Sp	0.62 - 0.73	0.24 - 0.30	0.65 - 0.77	0.17 - 0.22	0.69 - 0.70	0.07 - 0.15
	100	Cut-off	7.4 - 9.0	3.1 - 4.1	7.5 - 8.0	1.5 - 2.2	8.3 - 8.4	0.4 - 0.8
		Se	0.66 - 0.71	0.23 - 0.30	0.68 - 0.76	0.14 - 0.18	0.59 - 0.61	0.06 - 0.12
		Sp	0.61 - 0.69	0.23 - 0.29	0.64 - 0.72	0.14 - 0.19	0.69 - 0.70	0.05 - 0.10
	200	Cut-off	7.0 - 8.8	2.4 - 3.9	7.5 - 7.9	1.2 - 1.8	8.3 - 8.4	0.3 - 0.5
		Se	0.67 - 0.72	0.20 - 0.27	0.67 - 0.72	0.12 - 0.16	0.59 - 0.60	0.04 - 0.09
		Sp	0.59 - 0.65	0.21 - 0.26	0.63 - 0.67	0.12 - 0.17	0.69 - 0.70	0.03 - 0.07
Scenario 3 (inverse gamma)	50	Cut-off	5.1 - 7.1	1.7 - 2.6	5.1 - 5.8	0.9 - 1.6	5.4 - 5.8	0.5 - 0.9
		Se	0.64 - 0.76	0.17 - 0.34	0.75 - 0.83	0.11 - 0.17	0.69 - 0.72	0.08 - 0.17
		Sp	0.80 - 0.87	0.15 - 0.20	0.81 - 0.90	0.11 - 0.15	0.84 - 0.85	0.05 - 0.12
	100	Cut-off	5.1 - 7.2	1.4 - 2.3	5.1 - 5.6	0.8 - 1.3	5.4 - 5.7	0.3 - 0.6
		Se	0.63 - 0.76	0.15 - 0.27	0.75 - 0.79	0.09 - 0.14	0.69 - 0.71	0.06 - 0.12
		Sp	0.81 - 0.87	0.12 - 0.19	0.81 - 0.85	0.09 - 0.13	0.84 - 0.85	0.04 - 0.08
	200	Cut-off	5.1 - 7.2	1.1 - 2.2	5.1 - 5.3	0.6 - 1.0	5.5 - 5.6	0.2 - 0.5
		Se	0.62 - 0.76	0.12 - 0.21	0.75 - 0.78	0.08 - 0.11	0.69 - 0.71	0.04 - 0.09
		Sp	0.80 - 0.89	0.09 - 0.17	0.80 - 0.83	0.08 - 0.11	0.84 - 0.85	0.02 - 0.06
Scenario 4 (mixed)	50	Cut-off	9.9 - 14.2	1.6 - 2.5	10.4 - 14.1	1.6 - 2.9	12.1 - 14.6	1.1 - 1.8
		Se	0.41 - 0.47	0.32 - 0.45	0.99 - 1.00	0.01 - 0.03	0.98 - 1.00	0.02 - 0.03
		Sp	0.65 - 0.82	0.22 - 0.24	0.97 - 0.99	0.03 - 0.04	0.97 - 0.98	0.03 - 0.06
	100	Cut-off	11.0 - 14.6	1.3 - 2.0	11.7 - 14.2	1.2 - 2.3	12.6 - 13.9	0.7 - 1.6
		Se	0.48 - 0.69	0.43 - 0.47	0.98 - 1.00	0.02 - 0.02	0.98 - 0.99	0.02 - 0.03
		Sp	0.79 - 0.94	0.13 - 0.23	0.97 - 0.98	0.02 - 0.04	0.97 - 0.97	0.02 - 0.05
	200	Cut-off	11.4 - 14.6	1.0 - 1.4	12.5 - 13.9	0.9 - 1.7	13.1 - 13.6	0.5 - 1.2
		Se	0.65 - 0.91	0.26 - 0.46	0.98 - 0.99	0.01 - 0.02	0.98 - 0.98	0.01 - 0.02
		Sp	0.90 - 0.97	0.04 - 0.16	0.96 - 0.98	0.02 - 0.03	0.96 - 0.97	0.01 - 0.03

For the 4 distributional scenarios and for total numbers of 50, 100 and 200 fictitious "individuals", the ranges of mean values and SD values, found by varying P(D) from 0.1 to 0.9 in steps of 0.1, of optimal cut-off limits and sensitivities and specificities are reported. Mean values and SD values are based on 1000 repetitions each.

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