Table 4.
The mean of the difference between the estimated MR and the value of the information criterion in each model and its 5 and 95 percentiles, and the estimated MR for the selected model (the proportion of covariates: q=0.5; the number of simulations: R=20,000).
| c (%) | θ | n | Mean difference (5 percentile, 95 percentile) |
|
|||||
|---|---|---|---|---|---|---|---|---|---|
| Model 6 (true model) | Model 11 (full model) | ||||||||
| AICF | AIC∗ | AICF | AIC∗ | AICF | AIC∗ | ||||
| 90 | 1 | 100 | −0.4 (−43.9, 45.9) | −2.7 (−44.2, 42.1) | −1.1 (−44.4, 45.5) | −4.8 (−44.7, 39.2) | 94.38 | 95.05 | |
| 90 | 1 | 200 | 0.1 (−71.4, 74.6) | −4.4 (−74.8, 68.9) | −0.1 (−71.6, 74.9) | −7.7 (−77.1, 65.5) | 212.87 | 214.55 | |
| 90 | 1 | 1000 | 1.6 (−206.1, 218.1) | −8.0 (−215.2, 208.0) | 1.6 (−206.9, 218.2) | −14.4 (−222.1, 201.4) | 1373.64 | 1375.61 | |
| 90 | 2 | 100 | −0.4 (−43.8, 45.8) | −2.7 (−44.1, 42.0) | −1.0 (−44.2, 45.6) | −4.7 (−44.6, 39.3) | 94.40 | 95.04 | |
| 90 | 2 | 200 | −0.6 (−72.0, 74.4) | −5.2 (−75.4, 68.8) | −0.9 (−72.4, 74.6) | −8.5 (−77.8, 65.2) | 212.82 | 214.48 | |
| 90 | 2 | 1000 | 1.3 (−205.9, 217.1) | −8.3 (−215.1, 207.0) | 1.3 (−206.6, 217.4) | −14.8 (−221.8, 200.6) | 1375.21 | 1377.21 | |
| 90 | 4 | 100 | −0.7 (−44.2, 45.7) | −3.0 (−44.5, 41.9) | −1.4 (−44.6, 45.4) | −5.1 (−45.0, 39.1) | 94.73 | 95.36 | |
| 90 | 4 | 200 | 0.0 (−71.6, 74.2) | −4.6 (−74.9, 68.6) | −0.3 (−71.5, 74.3) | −7.9 (−77.1, 65.0) | 212.88 | 214.50 | |
| 90 | 4 | 1000 | −1.8 (−216.9, 214.8) | −11.4 (−226.1, 204.7) | −1.9 (−215.8, 213.4) | −17.9 (−231.0, 196.7) | 1376.07 | 1378.04 | |
| 90 | 16 | 100 | −0.7 (−43.4, 45.9) | −3.0 (−43.8, 42.1) | −1.4 (−44.0, 45.2) | −5.1 (−44.4, 38.9) | 94.49 | 95.15 | |
| 90 | 16 | 200 | −0.6 (−71.3, 74.0) | −5.2 (−74.7, 68.3) | −0.9 (−71.5, 74.0) | −8.5 (−77.1, 64.6) | 212.88 | 214.54 | |
| 90 | 16 | 1000 | 0.1 (−207.5, 217.3) | −9.5 (−216.6, 207.3) | 0.1 (−207.6, 217.4) | −15.9 (−222.8, 200.6) | 1374.48 | 1376.42 | |
| 50 | 1 | 100 | 0.1 (−64.8, 62.8) | −7.4 (−71.8, 54.9) | −0.4 (−65.8, 62.3) | −12.8 (−77.4, 49.1) | 432.37 | 434.56 | |
| 50 | 1 | 200 | −1.1 (−110.0, 104.1) | −10.7 (−119.2, 94.2) | −1.3 (−109.7, 104.7) | −17.2 (−125.1, 88.2) | 1000.80 | 1002.75 | |
| 50 | 1 | 1000 | 3.0 (−322.5, 325.7) | −11.5 (−336.8, 311.1) | 2.9 (−322.5, 325.9) | −21.2 (−346.3, 301.5) | 6602.19 | 6603.65 | |
| 50 | 2 | 100 | −0.4 (−64.5, 63.2) | −7.8 (−71.4, 55.2) | −0.9 (−65.6, 62.8) | −13.3 (−77.1, 49.7) | 432.28 | 434.21 | |
| 50 | 2 | 200 | 0.9 (−108.1, 107.4) | −8.7 (−117.3, 97.4) | 0.6 (−108.1, 106.9) | −15.3 (−123.5, 90.4) | 999.82 | 1001.35 | |
| 50 | 2 | 1000 | −2.9 (−322.7, 319.4) | −17.4 (−337.0, 304.8) | −3.0 (−322.5, 318.6) | −27.1 (−346.4, 294.3) | 6601.73 | 6601.85 | |
| 50 | 4 | 100 | −0.9 (−66.0, 61.9) | −8.4 (−73.0, 54.0) | −1.6 (−66.9, 61.3) | −14.0 (−78.4, 48.2) | 432.62 | 434.21 | |
| 50 | 4 | 200 | 0.1 (−107.2, 104.3) | −9.5 (−116.4, 94.4) | −0.3 (−107.3, 103.9) | −16.3 (−122.6, 87.4) | 999.69 | 1000.66 | |
| 50 | 4 | 1000 | −3.0 (−323.1, 312.3) | −17.4 (−337.4, 297.7) | −3.2 (−323.1, 311.9) | −27.3 (−347.0, 287.6) | 6595.55 | 6595.42 | |
| 50 | 16 | 100 | 0.1 (−64.3, 63.4) | −7.3 (−71.2, 55.5) | −0.7 (−65.6, 62.4) | −13.1 (−77.0, 49.3) | 431.82 | 433.14 | |
| 50 | 16 | 200 | −1.1 (−107.8, 104.4) | −10.6 (−117.0, 94.5) | −1.6 (−108.1, 104.4) | −17.6 (−123.4, 87.9) | 999.22 | 999.75 | |
| 50 | 16 | 1000 | 0.8 (−320.5, 319.0) | −13.7 (−334.8, 304.4) | 0.5 (−321.0, 318.5) | −23.6 (−344.8, 294.1) | 6589.13 | 6589.34 | |
| 0 | 1 | 100 | −0.4 (−9.9, 5.9) | −9.8 (−19.2,−3.5) | −1.1 (−11.2, 6.0) | −16.7 (−26.7,−9.7) | 728.44 | 728.71 | |
| 0 | 1 | 200 | −0.1 (−12.1, 8.8) | −11.7 (−23.7,−2.8) | −0.5 (−13.2, 9.0) | −19.8 (−32.4,−10.3) | 1722.43 | 1722.27 | |
| 0 | 1 | 1000 | 0.2 (−23.8, 21.1) | −16.2 (−40.3, 4.6) | 0.1 (−24.3, 21.3) | −27.4 (−51.8,−6.3) | 11779.42 | 11780.44 | |
| 0 | 2 | 100 | −0.5 (−17.2, 14.1) | −9.6 (−26.2, 4.7) | −1.2 (−18.4, 13.8) | −16.6 (−33.6,−1.7) | 705.35 | 706.37 | |
| 0 | 2 | 200 | −0.2 (−23.6, 20.8) | −11.6 (−34.8, 9.3) | −0.5 (−23.9, 20.5) | −19.5 (−42.9, 1.4) | 1675.67 | 1676.76 | |
| 0 | 2 | 1000 | 0.4 (−48.9, 48.0) | −15.9 (−65.2, 31.7) | 0.3 (−49.3, 48.2) | −27.0 (−76.6, 20.8) | 11548.20 | 11549.24 | |
| 0 | 4 | 100 | −0.5 (−24.1, 21.7) | −9.2 (−32.6, 12.8) | −1.1 (−24.9, 21.4) | −16.0 (−39.5, 6.2) | 657.00 | 658.21 | |
| 0 | 4 | 200 | −0.5 (−33.3, 30.8) | −11.4 (−44.1, 19.8) | −0.9 (−34.0, 30.7) | −19.5 (−52.4, 12.0) | 1578.08 | 1579.22 | |
| 0 | 4 | 1000 | −0.4 (−72.1, 69.9) | −16.2 (−87.8, 54.0) | −0.4 (−72.1, 69.9) | −27.3 (−98.8, 43.0) | 11053.44 | 11054.48 | |
| 0 | 16 | 100 | −0.3 (−26.8, 26.5) | −7.9 (−34.0, 18.4) | −0.8 (−27.7, 26.2) | −14.6 (−41.0, 12.0) | 575.12 | 576.30 | |
| 0 | 16 | 200 | −0.1 (−37.4, 37.8) | −10.0 (−47.0, 27.6) | −0.4 (−37.8, 37.6) | −17.9 (−55.1, 19.8) | 1411.05 | 1412.15 | |
| 0 | 16 | 1000 | 0.4 (−81.5, 84.4) | −14.4 (−96.3, 69.4) | 0.4 (−82.0, 84.4) | −25.5 (−107.8, 58.5) | 10203.57 | 10204.62 | |
MR, mean risk; Mean difference (5 percentile, 95 percentile), mean of the difference between the estimated mean risk, , and the value of the information criterion in each model and its 5 and 95 percentiles; , estimated MR for the selected model based on new data; c, proportion of random censoring; θ, regression parameters; n, total sample size. The values that are superior to other are highlighted.