Table 1 Evaluation criteria for models for which MLEs were found with 2-parameter symmetrical protection curves fitted to illustrative datasets
From: Some extensions in continuous models for immunological correlates of protection
−2×log-likelihood (rank) |  |  |  |  |  |  |
|---|---|---|---|---|---|---|
Goodness-of-fit (rank) | Â | Â | Â | Â | Â | Â |
Coef. of Var. \( \widehat{\lambda} \) (rank) | Protection curve/function | |||||
Dataset (cases of disease:subjects) | Error function | Logistic function | Square root sigmoid | Double exponential | Arctangent function | Absolute sigmoid function |
German pertussis FHA IgG (44:1988) | 375.441 (6) 0.1799 (1) 0.4365 (6) | 375.247 (5) 0.1645 (3) 0.3247 (5) | 374.949 (4) 0.1427 (4) 0.2234 (4) | 374.393 (3) 0.1775 (2) 0.2072 (3) | 374.384 (2) 0.1302 (6) 0.1708 (2) | 373.629 (1) 0.1329 (5) 0.1552 (1) |
German pertussis PT IgG (44:1987) | 379.477 (6) 0.1891 (6) 2.1025 (6) | 378.741 (5) 0.1906 (5) 0.5796 (5) | 376.344 (3) 0.2837 (3) 0.2250 (3) | 377.239 (4) 0.2622 (4) 0.2296 (4) | 373.950 (2) 0.5100 (2) 0.1748 (2) | 373.595 (1) 0.5233 (1) 0.1530 (1) |
German pertussis PRN IgG (44:1992) | 381.059 (2) 0.8700 (1) 0.4318 (6) | 381.081 (4) 0.8619 (2) 0.3044 (5) | 381.124 (6) 0.8263 (4) 0.1855 (4) | 381.028 (1) 0.8560 (3) 0.1819 (3) | 381.080 (3) 0.8141 (5) 0.1719 (2) | 381.087 (5) 0.7829 (6) 0.1514 (1) |
German pertussis FIM IgG (44:1986) | 376.847 (6) 0.8273 (1) 0.5638 (6) | 376.683 (5) 0.8039 (3) 0.4063 (5) | 376.553 (3) 0.7381 (4) 0.2784 (4) | 376.080 (1) 0.8222 (2) 0.2771 (3) | 376.640 (4) 0.7028 (5) 0.2288 (2) | 376.518 (2) 0.6791 (6) 0.1936 (1) |
German pertussis FHA IgA (44:1932) | 418.378 (4) 0.7157 (4) 0.1317 (1) | - | 417.617 (3) 0.7216 (3) 0.1490 (4) | - | 417.604 (2) 0.7217 (1) 0.1490 (3) | 417.603 (1) 0.7217 (2) 0.1490 (2) |
German pertussis PT IgA (44:1933) | 418.782 (5) 0.5103 (1) 0.2860 (4) | 418.784 (6) 0.5099 (2) 0.3207 (5) | 418.101 (3) 0.4777 (6) 0.1490 (3) | 418.751 (4) 0.5042 (3) 0.3621 (6) | 418.076 (2) 0.4781 (5) 0.1490 (2) | 418.075 (1) 0.4781 (4) 0.1490 (1) |
German pertussis PRN IgA (44:1968) | - | - | 406.932 (3) 0.2489 (3) 0.1490 (3) | - | 406.479 (2) 0.2528 (2) 0.1489 (2) | 406.432 (1) 0.2532 (1) 0.1488 (1) |
German pertussis FIM IgA (44:1994) | 410.398 (6) 0.0107 (5) 0.8372 (6) | 410.361 (5) 0.0113 (3) 0.7657 (5) | 410.349 (4) 0.0118 (2) 0.5205 (4) | 409.896 (3) 0.0109 (4) 0.2282 (3) | 408.899 (2) 0.0063 (6) 0.1776 (2) | 407.798 (1) 0.0196 (1) 0.1721 (1) |
Piedra RSV/A (34:175) | - | - | 159.291 (3) 0.6080 (4) 0.9513 (4) | 159.477 (4) 0.6156 (3) 0.4410 (3) | 158.612 (2) 0.6694 (2) 0.2956 (2) | 157.895 (1) 0.7361 (1) 0.2119 (1) |
Piedra RSV/B (34:175) | - | - | 154.415 (2) 0.6934 (3) 0.7328 (3) | - | 154.395 (1) 0.7439 (2) 0.3734 (2) | 154.553 (3) 0.7591 (1) 0.2643 (1) |
White/varicella (79:3459) | 643.035 (4) 0.9848 (5) 0.2887 (6) | 642.145 (3) 0.9987 (3) 0.2297 (5) | 641.683 (1) 1.0000 (1) 0.1802 (3) | 641.765 (2) 1.0000 (2) 0.2000 (4) | 643.060 (5) 0.9934 (4) 0.1403 (2) | 643.507 (6) 0.9841 (6) 0.1314 (1) |
Swedish pertussis FHA IgG (92:209) | - | - | 284.404 (1) 0.0100 (1) 0.0777 (1) | - | - | - |
Swedish pertussis PT IgG (92:209) | 270.365 (6) 0.9223 (6) 0.1577 (4) | 270.205 (5) 0.9274 (5) 0.1587 (5) | 269.832 (4) 0.9379 (4) 0.1483 (3) | 269.757 (3) 0.9407 (3) 0.1938 (6) | 269.374 (2) 0.9529 (2) 0.1341 (2) | 268.871 (1) 0.9754 (1) 0.1216 (1) |
Swedish pertussis PRN IgG (92:209) | 247.593 (5) 0.7605 (6) 0.0807 (4) | 247.621 (6) 0.7700 (5) 0.0813 (5) | 247.571 (4) 0.8123 (1) 0.0813 (6) | 247.304 (3) 0.7736 (4) 0.0791 (3) | 246.989 (2) 0.7884 (2) 0.0772 (2) | 246.071 (1) 0.7863 (3) 0.0763 (1) |
Swedish pertussis FIM IgG (92:209) | 251.075 (6) 0.2775 (6) 0.3644 (6) | 250.822 (5) 0.2921 (5) 0.2708 (5) | 250.161 (4) 0.3250 (4) 0.1697 (4) | 249.765 (3) 0.3530 (3) 0.1470 (3) | 248.902 (2) 0.3691 (2) 0.1103 (2) | 247.731 (1) 0.4765 (1) 0.0941 (1) |
Black Nicolay HAI (22:777) | 181.035 (6) 0.5029 (6) 0.2875 (6) | 180.649 (5) 0.5241 (4) 0.2661 (5) | 179.402 (3) 0.5209 (5) 0.2267 (3) | 179.675 (4) 0.5886 (2) 0.2329 (4) | 177.247 (2) 0.5479 (3) 0.2122 (2) | 176.743 (1) 0.6813 (1) 0.2120 (1) |