Table 1.
Results of the Monte Carlo simulations
| N | Mutual information | Youden | Likelihood ratio | |||||
|---|---|---|---|---|---|---|---|---|
| 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.