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Table 1 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 ‘even’ under three types of LTF proportions (‘low’, ‘moderate’, and ‘high’)

From: Additive-multiplicative hazards regression models for interval-censored semi-competing risks data with missing intermediate events

   Low (LTF(%)=22.6) Moderate (LTF(%)=34.2) High (LTF(%)=47.3)
Parameter True value r.Bias (%) SD (×105) SEM (×105) CP (%) r.Bias (%) SD (×105) SEM (×105) CP (%) r.Bias (%) SD (×105) SEM (×105) CP (%)
   Imputed-by-the-right-endpoint method
α 01 0.01 81.7 15026 15104 96.8 73.3 15105 14975 95.2 20.6 14450 15186 96.2
α 02 0.01 176.2 22297 22961 95.4 324.5 24408 24066 94.8 28.8 27643 27426 95.4
α 03 0.01 133.2 27006 26429 95.4 86.1 16223 17086 96.2 75.3 13291 13250 95.2
α 12 0.01 -145.7 28481 25849 95.2 -113.4 29996 26279 93.6 74.1 27309 25620 96.2
α 32 0.01 109.7 65489 55615 93.2 77.1 36087 33747 96.8 50.8 26680 25219 94.8
β 01 0.004 -10.1 81 87 93.8 -9.4 80 88 91.6 -8.6 87 88 92.6
β 02 0.004 1.1 92 92 94.6 -1.4 97 96 94.4 -0.4 103 101 94.0
β 03 0.004 -7.2 87 86 91.2 -6.4 105 105 93.4 -9.3 136 133 91.6
β 12 0.004 3.5 115 115 97.0 5.7 112 116 95.6 3.4 116 115 95.8
β 32 0.004 -0.3 217 199 96.8 7.6 174 173 96.4 5.3 148 152 97.2
σ 2 0.01 904.5 8164 8782 93.8 815.5 7848 8084 92.4 771.6 7626 7076 90.4
   Proposed method
α 01 0.01 32.2 15236 15136 96.2 64.8 15344 15084 95.0 20.7 14496 15279 96.2
α 02 0.01 70.2 22692 22951 95.0 286.1 24010 24133 95.2 100.4 28030 27569 95.2
α 03 0.01 289.4 27525 26349 95.0 121.3 16740 17161 95.0 86.3 13465 13391 95.0
α 12 0.01 -24.6 26718 25661 95.8 -83.4 29355 26230 94.0 -37.0 27102 25736 96.2
α 32 0.01 123.2 67188 56122 93.6 93.4 36291 33577 95.6 54.0 26591 25204 94.2
β 01 0.004 -5.5 89 90 95.0 -5.0 85 91 93.8 -5.3 88 91 94.4
β 02 0.004 5.9 95 97 96.2 4.0 99 100 94.2 4.8 107 106 94.8
β 03 0.004 -1.7 92 91 93.2 -1.7 107 110 95.6 -3.3 141 139 93.4
β 12 0.004 -1.9 109 110 96.4 0.9 108 112 95.2 0.1 110 111 96.0
β 32 0.004 1.0 214 199 96.6 8.4 179 175 96.2 4.4 150 153 97.0
σ 2 0.01 1016.2 9069 9074 92.2 897.8 7743 8198 91.0 874.1 7616 7423 87.2