Table 2 Empirical results for the averages of the relative bias (r.Bias) and standard errors (SEM), standard deviation (SD), and coverage probability (CP) for the regression parameters and variance parameter of the log-normal frailty based on the ‘imputed-by-the-right-endpoint’ and ‘proposed’ methods when the type of regression coefficients is ‘dec’ under three types of LTF proportions (‘low’, ‘moderate’, and ‘high’)
| Â | Â | Low (LTF(%)=19.4) | Moderate (LTF(%)=31.4) | High (LTF(%)=43.5) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | True value | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) | r.Bias (%) | SD (×105) | SEM (×105) | CP (%) |
| Â | Â | Imputed-by-the-right-endpoint method | |||||||||||
α 01 | 0.01 | 36.6 | 15548 | 14973 | 93.8 | -110.5 | 15890 | 15137 | 94.2 | -97.0 | 15327 | 15425 | 94.6 |
α 02 | 0.02 | -8.8 | 23990 | 22697 | 96.0 | 2.5 | 23708 | 25122 | 97.0 | 44.4 | 29732 | 28452 | 95.2 |
α 03 | 0.01 | 400.1 | 27926 | 26768 | 95.8 | 9.1 | 18791 | 17136 | 93.8 | -80.3 | 14385 | 13500 | 93.6 |
α 12 | 0.01 | 100.0 | 27898 | 26371 | 94.6 | 199.2 | 28271 | 25833 | 92.8 | 172.0 | 29132 | 26387 | 93.8 |
α 32 | 0.01 | 274.6 | 66261 | 56538 | 93.6 | 121.0 | 35562 | 33829 | 94.4 | 125.5 | 29879 | 26193 | 94.2 |
β 01 | 0.004 | -6.6 | 99 | 97 | 90.0 | -8.7 | 89 | 96 | 93.4 | -6.3 | 95 | 97 | 95.2 |
β 02 | 0.008 | -0.9 | 137 | 139 | 94.0 | -2.8 | 129 | 140 | 95.8 | -0.3 | 143 | 149 | 96.0 |
β 03 | 0.004 | -2.8 | 96 | 98 | 93.0 | -5.7 | 121 | 116 | 91.0 | -9.5 | 142 | 144 | 94.4 |
β 12 | 0.004 | 6.4 | 120 | 125 | 97.2 | 6.2 | 120 | 127 | 98.4 | 5.8 | 124 | 125 | 96.8 |
β 32 | 0.004 | 0.6 | 234 | 218 | 96.8 | 7.6 | 204 | 188 | 96.4 | 9.5 | 177 | 169 | 95.0 |
σ 2 | 0.01 | 631.4 | 7287 | 8545 | 97.6 | 705.2 | 6851 | 7982 | 96.2 | 714.8 | 7217 | 7540 | 90.4 |
| Â | Â | Proposed method | |||||||||||
α 01 | 0.01 | 21.6 | 15586 | 15134 | 94.0 | -56.8 | 16268 | 15285 | 94.0 | -92.4 | 15530 | 15487 | 94.2 |
α 02 | 0.02 | -0.6 | 24316 | 22833 | 95.8 | -18.9 | 24116 | 25162 | 96.6 | 104.0 | 30008 | 28458 | 95.0 |
α 03 | 0.01 | 337.6 | 27943 | 26924 | 95.4 | -9.4 | 18629 | 17265 | 94.0 | -83.6 | 14279 | 13600 | 94.2 |
α 12 | 0.01 | 43.2 | 27653 | 26452 | 94.6 | 175.4 | 27650 | 25973 | 93.8 | 102.5 | 28481 | 26251 | 93.2 |
α 32 | 0.01 | 296.4 | 67196 | 57028 | 93.4 | 140.3 | 36513 | 34261 | 94.8 | 170.0 | 30037 | 26145 | 93.8 |
β 01 | 0.004 | -2.5 | 106 | 101 | 91.8 | -4.5 | 95 | 99 | 94.6 | -2.3 | 100 | 100 | 95.8 |
β 02 | 0.008 | 3.8 | 146 | 146 | 95.6 | 2.0 | 133 | 148 | 98.6 | 3.6 | 148 | 155 | 97.0 |
β 03 | 0.004 | 1.3 | 102 | 102 | 93.4 | -0.3 | 124 | 121 | 94.0 | -3.0 | 149 | 150 | 95.4 |
β 12 | 0.004 | 0.3 | 112 | 119 | 96.0 | 0.8 | 116 | 122 | 98.0 | 1.1 | 117 | 121 | 96.4 |
β 32 | 0.004 | 2.5 | 232 | 222 | 97.2 | 8.5 | 204 | 189 | 96.4 | 9.7 | 178 | 170 | 95.6 |
σ 2 | 0.01 | 838.4 | 8153 | 9217 | 94.2 | 852.3 | 7505 | 8446 | 93.8 | 791.2 | 7447 | 7745 | 89.2 |